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1
Hajj, M. R., R. W. Miksad und E. J. Powers. „Fundamental–subharmonic interaction: effect of phase relation“. Journal of Fluid Mechanics 256 (November 1993): 403–26. http://dx.doi.org/10.1017/s0022112093002824.
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The effect of the phase relation (i.e. phase difference and coupling) between the fundamental and subharmonic modes on the transition to turbulence of a mixing layer is investigated. Experiments are conducted to study the development of the subharmonic and fundamental modes under different phase-controlled excitations. Higher-order spectral moments are used to measure phase differences, levels of phase coupling, and energy transfer rates between the two modes at different downstream locations. Local measurements of the wavenumber–frequency spectra are used to examine the phase-speed matching conditions required for efficient energy transfer. The results show that when the phase coupling between the fundamental and the subharmonic is high, maximum subharmonic growth is found to occur at a critical phase difference close to zero. The subharmonic growth is found to result from a resonant parametric interaction between the fundamental and the subharmonic in which phase-speed matching conditions are satisfied. In contrast, when the phase coupling level is low, the phase difference is irregular and varying, the efficiency of parametric interactions is low, phase-speed matching conditions are not met and subharmonic growth is suppressed.
2
Qiu, Zhan, Wenhao Xu, Jiaxin Yuan und Fuxin Wang. „Secondary resonances in aeroelastic response of oscillating airfoil under dynamic stall“. Journal of Vibration and Control 24, Nr. 23 (26.03.2018): 5665–80. http://dx.doi.org/10.1177/1077546318764191.
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To clarify the mechanism of the complex aeroelastic responses of flexible blades of helicopter rotors under dynamic stall, experiments on a 2D aeroelastic system are performed. In the spectra of the response from experiment results, special frequency components are found. Then, a numerical method based on the same aeroelastic model is introduced. Here, the flow field is solved using a zonal solver based on vorticity dynamics. When changing a system’s natural frequency, the same extra frequency components in the response spectra are found when particular ratios of natural and forcing frequencies are achieved. Secondary resonances are believed to then happen, which feature a larger response amplitude, multiple periodic motion and a subharmonic peak of driving frequency in the load spectra. With an analysis of the flow field, the 1/2 subharmonic in the airload spectra (i.e. the period doubling of the loads) is believed to be associated with the nonlinear variation of vortex structures. With a dynamic mode decomposition analysis, a counter-rotating vortex interaction instability is detected as the physical mechanism of period doubling. The coincidence of natural frequency with the odd times of the subharmonic leads to the secondary resonances.
3
Meiburg, E. „On the role of subharmonic perturbations in the far wake“. Journal of Fluid Mechanics 177 (April 1987): 83–107. http://dx.doi.org/10.1017/s0022112087000879.
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The possibility of an excitation of individual subharmonic perturbations in each of the shear layers forming the far wake is investigated numerically. Principal considerations allow for the existence of two equivalent subharmonic modes which by opposite routes can lead to a doubling of the wavelength in the wake. Since vortical disturbances in the far wake are amplified only convectively, the simultaneous existence of both modes in the flow field is possible, which could provide an explanation for the group structure observed experimentally in the far wake. These considerations also provide a logical explanation of the finding of a very regular vortex pairing process in forced wakes.Two-dimensional numerical simulations assuming incompressible flow and almost inviscid dynamics illustrate the opposite developments of regions dominated by the two different modes and also confirm the possibility of a resulting group structure. As an important result it is demonstrated that, if vortex pairing plays an important role in the growth of the far-wake structure, this does not have to be related to the excitation of the subharmonic peak in the frequency spectrum. Quite the contrary, it is to be expected that the subharmonic itself is of minor importance and that instead a small frequency and its multiples related to the group structure of the flow dominate the spectrum. In the light of these considerations measurements by Cimbala (1984) are discussed and frequency spectra recorded by him are analysed more closely. Various properties of these spectra seem to indicate that vortex pairing might be significant with respect to the evolution of the far-wake structure.
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Zhang, Liang, Mariano Méndez, Diego Altamirano, Jinlu Qu, Li Chen, Konstantinos Karpouzas, Tomaso M. Belloni et al. „A systematic analysis of the phase lags associated with the type-C quasi-periodic oscillation in GRS 1915+105“. Monthly Notices of the Royal Astronomical Society 494, Nr. 1 (24.03.2020): 1375–86. http://dx.doi.org/10.1093/mnras/staa797.
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ABSTRACT We present a systematic analysis of the phase lags associated with the type-C quasi-periodic oscillations (QPOs) in GRS 1915+105 using RXTE data. Our sample comprises 620 RXTE observations with type-C QPOs ranging from ∼0.4 to ∼6.3 Hz. Based on our analysis, we confirm that the QPO phase lags decrease with QPO frequency, and change sign from positive to negative at a QPO frequency of ∼2 Hz. In addition, we find that the slope of this relation is significantly different between QPOs below and above 2 Hz. The relation between the QPO lags and QPO rms can be well fitted with a broken line: as the QPO lags go from negative to positive, the QPO rms first increases, reaching its maximum at around zero lag, and then decreases. The phase-lag behaviour of the subharmonic of the QPO is similar to that of the QPO fundamental, where the subharmonic lags decrease with subharmonic frequency and change sign from positive to negative at a subharmonic frequency of ∼1 Hz; on the contrary, the second harmonic of the QPO shows a quite different phase-lag behaviour, where all the second harmonics show hard lags that remain more or less constant. For both the QPO and its (sub)harmonics, the slope of the lag–energy spectra shows a similar evolution with frequency as the average phase lags. This suggests that the lag–energy spectra drive the average phase lags. We discuss the possibility for the change in lag sign, and the physical origin of the QPO lags.
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Kahraman, A., und G. W. Blankenship. „Experiments on Nonlinear Dynamic Behavior of an Oscillator With Clearance and Periodically Time-Varying Parameters“. Journal of Applied Mechanics 64, Nr. 1 (01.03.1997): 217–26. http://dx.doi.org/10.1115/1.2787276.
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A number of experiments on a physical system with clearance having combined parametric and external forcing excitation are presented. The data demonstrate several nonlinear phenomena that exist in periodically excited oscillators subject to clearance at a contact interface. Jump discontinuities in forced response curves are shown to exist and subharmonic resonances which are formed by period-n (nT) motions with n ≥ 2 are demonstrated. Long-period subharmonic motions with periods as long as nine times the excitation period are reported. Finally, several cases of measured chaotic motions are also illustrated through time-traces, phase portraits, Fourier spectra, and Poincare plots which form strange attractors.
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Spalart, Philippe R., und Kyung-Soo Yang. „Numerical study of ribbon-induced transition in Blasius flow“. Journal of Fluid Mechanics 178 (Mai 1987): 345–65. http://dx.doi.org/10.1017/s0022112087001253.
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The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.
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Ali, Mohamed G. S., Nour Z. Elsayed und Ebtsam A. Eid. „A Simulation for Detecting Nonlinear Echoes from Microbubbles Packets“. Archives of Acoustics 40, Nr. 2 (01.06.2015): 151–57. http://dx.doi.org/10.1515/aoa-2015-0017.
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Abstract This work presents a simulation of the response of packets of microbubbles in an ultrasonic pulse-echo scan line. Rayleigh-Plesset equation has been used to predict the echo from numerically obtained radial dynamics of microbubbles. Varying the number of scattering microbubbles on the pulse wave form has been discussed. To improve microbubble-specific imaging at high frequencies, the subharmonic and second harmonic signals from individual microbubbles as well as microbubbles packets were simulated as a function of size and pressure. Two different modes of harmonic generation have been distinguished. The strength and bandwidth of the subharmonic component in the scattering spectrum of microbubbles is greater than that of the second harmonic. The pressure spectra provide quantitative and detailed information on the dynamic behaviour of ultrasound contrast agent microbubbles packet.
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BREUER, KENNETH S., JACOB COHEN und JOSEPH H. HARITONIDIS. „The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer“. Journal of Fluid Mechanics 340 (10.06.1997): 395–411. http://dx.doi.org/10.1017/s0022112097005417.
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The evolution of a wavepacket in a laminar boundary layer is studied experimentally, paying particular attention to the stage just prior to the formation of a turbulent spot. The initial stages of development are found to be in very good agreement with previous results and indicate a stage in which the disturbance grows according to linear theory followed by a weakly nonlinear stage in which the subharmonic grows, apparently through a parametric resonance mechanism. In a third stage, strong non-linear interactions are observed in which the disturbance develops a streaky structure and the corresponding wavenumber–frequency spectra exhibit an organized cascade mechanism in which spectral peaks appear with increasing spanwise wavenumber and with frequencies which alternate between zero and the subharmonic frequency. Higher harmonics are also observed, although with lower amplitude than the low-frequency peaks. The final (breakdown) stage is characterized by the appearance of high-frequency oscillations with random phase, located at low-speed ‘spike’ regions of the primary disturbance. Wavelet transforms are used to analyse the structure of both coherent and random small-scale structure of the disturbance. In particular, the breakdown oscillations are also observed to have a wavepacket character riding on the large-amplitude primary disturbance.
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Zhao, J. Y., I. W. Linnett und L. J. McLean. „Stability and Bifurcation of Unbalanced Response of a Squeeze Film Damped Flexible Rotor“. Journal of Tribology 116, Nr. 2 (01.04.1994): 361–68. http://dx.doi.org/10.1115/1.2927236.
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The stability and bifurcation of the unbalance response of a squeeze film damper-mounted flexible rotor are investigated based on the assumption of an incompressible lubricant together with the short bearing approximation and the “π” film cavitation model. The unbalanced rotor response is determined by the trigonometric collocation method and the stability of these solutions is then investigated using the Floquet transition matrix method. Numerical examples are given for both concentric and eccentric damper operations. Jump phenomenon, subharmonic, and quasi-periodic vibrations are predicted for a range of bearing and unbalance parameters. The predicted jump phenomenon, subharmonic and quasi-periodic vibrations are further examined by using a numerical integration scheme to predict damper trajectories, calculate Poincare´ maps and power spectra. It is concluded that the introduction of unpressurized squeeze film dampers may promote undesirable nonsynchronous vibrations.
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Hebboul, S. E., und J. C. Garland. „rf power dependence of subharmonic voltage spectra of two-dimensional Josephson-junction arrays“. Physical Review B 47, Nr. 9 (01.03.1993): 5190–95. http://dx.doi.org/10.1103/physrevb.47.5190.
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Chen, Zhao Jiang, Shu Yi Zhang und Zhi Liang Zhang. „FEM Modeling of Vibro-Impact Response of Metal Plates Excited by a High-Power Ultrasonic Transducer“. Applied Mechanics and Materials 197 (September 2012): 278–82. http://dx.doi.org/10.4028/www.scientific.net/amm.197.278.
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When thin metal plates are excited by a high-power ultrasonic transducer, superharmonic and high-order subharmonic vibration phenomena of the plates are observed in our experiments. However, the nonlinear mechanism in the system is still not fully understood. In this paper, a finite element model is established based on the experimental conditions and numerical simulations are performed to explore the generation mechanism of the nonlinear vibration. By comparing the waveforms and frequency spectra of the vibration velocity of the plate to these of the contact force between the ultrasonic horn tip and the plates, it can be found that waveform distortion of the contact force is the main reason for generating the superharmonic vibration, while the intermittent contact-impact between the horn tip and the plate is the reason for subharmonic vibration in the plate. The FEM simulation results can explain reasonably the observed experimental phenomena, which are useful to help to improve the effects of the nonlinear phenomena occurred in ultrasonic processing.
12
Senjanovic, I. „Harmonic Analysis of Nonlinear Oscillations of Cubic Dynamical Systems“. Journal of Ship Research 38, Nr. 03 (01.09.1994): 225–38. http://dx.doi.org/10.5957/jsr.1994.38.3.225.
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Cubic dynamical systems are of great interest in marine technology. The state of the art concerning ship rolling and vessel mooring is described. Time-domain simulation is an indirect and unreliable way to determine harmonic response characteristics of nonlinear systems; frequency-domain analysis is therefore preferable. Numerical methods for deterministic and random oscillations are approximate. In order to establish a general sophisticated method, the well-known harmonic balance method is extended to polyharmonic excitation and improved to operate completely in the frequency domain. Special recurrent and simultaneous algorithms are given for the case of monoharmonic and polyharmonic excitation and multi-and single-valued response respectively. Subharmonic oscillations are analyzed using the general method. Random oscillations are treated as a set of periodic responses caused by the same excitation spectrum and different phase angles. Illustrative examples are chosen from marine technology practice. Principal, superharmonic and subharmonic response spectra are analyzed. The importance of further research which would cover other nonlinear effects by harmonic analysis is pointed out.
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Tsai, Wu-Ting, Dick K. P. Yue und Kenneth M. K. Yip. „Resonantly excited regular and chaotic motions in a rectangular wave tank“. Journal of Fluid Mechanics 216 (Juli 1990): 343–80. http://dx.doi.org/10.1017/s0022112090000465.
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We consider the resonant excitation of surface waves inside a rectangular wave tank of arbitrary water depth with a flap-type wavemaker on one side. Depending on the length and width of the tank relative to the sinusoidal forcing frequency of the wave paddle, three classes of resonant mechanisms can be identified. The first two are the well-known synchronous, resonantly forced longitudinal standing waves, and the subharmonic, parametrically excited transverse (cross) waves. These have been studied by a number of investigators, notably in deep water. We rederive the governing equations and show good comparisons with the experimental data of Lin & Howard (1960). The third class is new and involves the simultaneous resonance of the synchronous longitudinal and subharmonic cross-waves and their internal interactions. In this case, temporal chaotic motions are found for a broad range of parameter values and initial conditions. These are studied by local bifurcation and stability analyses, direct numerical simulations, estimations of the Lyapunov exponents and power spectra, and examination of Poincaré surfaces. To obtain a global criterion for widespread chaos, the method of resonance overlap (Chirikov 1979) is adopted and found to be remarkably effective.
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Pisarchik, Alexander N., Rider Jaimes-Reátegui und J. Hugo García-López. „Synchronization of coupled bistable chaotic systems: experimental study“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, Nr. 1864 (06.08.2007): 459–73. http://dx.doi.org/10.1098/rsta.2007.2103.
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We carried out an experimental study of the synchronization of two unidirectionally coupled Rössler-like electronic circuits with two coexisting chaotic attractors. Different stages of synchronization are identified on the route from asynchronous motion to complete synchronization, as the coupling parameter is increased: intermittent asynchronous jumps between coexisting attractors; intermittent anticipating phase synchronization; and generalized synchronization in the form of subharmonic entrainment terminated by complete synchronization. All these regimes are analysed with time-series, power spectra and phase-space plots of the drive and response oscillators. The experimental study implicitly confirms the results of numerical simulations.
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Iwaniec, Joanna, Grzegorz Litak, Marek Iwaniec, Jerzy Margielewicz, Damian Gąska, Mykhaylo Melnyk und Wojciech Zabierowski. „Response Identification in a Vibration Energy-Harvesting System with Quasi-Zero Stiffness and Two Potential Wells“. Energies 14, Nr. 13 (30.06.2021): 3926. http://dx.doi.org/10.3390/en14133926.
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In this paper, the frequency broadband effect in vibration energy harvesting was studied numerically using a quasi-zero stiffness resonator with two potential wells and piezoelectric transducers. Corresponding solutions were investigated for system excitation harmonics at various frequencies. Solutions for the higher voltage output were collected in specific branches of the power output diagram. Both the resonant solution synchronized with excitation and the frequency responses of the subharmonic spectra were found. The selected cases were illustrated and classified using a phase portrait, a Poincaré section, and recurrence plot (RP) approaches. Select recurrence quantification analysis (RQA) measures were used to characterize the discussed solutions.
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CETINER, O., und D. ROCKWELL. „Streamwise oscillations of a cylinder in a steady current. Part 1. Locked-on states of vortex formation and loading“. Journal of Fluid Mechanics 427 (25.01.2001): 1–28. http://dx.doi.org/10.1017/s0022112000002214.
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Streamwise oscillations of a circular cylinder in a steady uniform flow are investigated experimentally using a technique of high-image-density particle image velocimetry, in conjunction with instantaneous force measurements. This approach allows insight into the relationship between the loading and the patterns of vorticity and streamline topology in the near wake.In analogy with the classical locked-on state arising from transverse oscillations of a cylinder in uniform flow, it is possible to attain either locked-on or quasi-locked-on states due to streamwise oscillations. In these cases, however, the repetitive signature of the transverse force is not sinusoidal; rather, it is strongly modulated and the corresponding spectra can exhibit several sharply defined peaks. The predominant peak can vary over a remarkably wide range, extending from the subharmonic to the third harmonic of the cylinder oscillation frequency; for certain locked-on states of the transverse force signature, the spectral peak at the cylinder oscillation frequency is actually suppressed. Corresponding instantaneous traces and spectra of the in-line force simply show dominance of the spectral peak at the cylinder oscillation frequency. Further interpretation of the loading is provided in terms of Lissajous patterns of the transverse and in-line force coefficients.All of these features are related to the instantaneous patterns of vortex formation in the near wake. During a typical cycle of the cylinder oscillation, these patterns can be divided into two broad categories: Kármán-like shedding; and a nearly ‘frozen’ array of shed vortices. The order of occurrence of these basic patterns during an oscillation cycle dictates the instantaneous signatures and time-averaged spectra of the transverse force.
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Ehrich, F. F. „Spontaneous Sidebanding in High Speed Rotordynamics“. Journal of Vibration and Acoustics 114, Nr. 4 (01.10.1992): 498–505. http://dx.doi.org/10.1115/1.2930291.
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Several observations have been made in the Fourier spectra of high speed rotor-dynamic response of uniformly spaced frequency spikes on either side of key synchronous or subharmonic or superharmonic response frequencies. In instances where this so-called “sidebanding” could not readily be explained as the nonlinear interaction or combination tones of two distinct stimuli at slightly different frequencies, we have referred to this class of phenomena as spontaneous sidebanding. It is invariably noted that the sideband spacing frequency appears to be a whole number fraction (1/J) of the operating speed which suggests that the wave form is periodic and completes a full cycle every J rotations of the rotor. Using a numerical model of a rotor which simulates local contact with a stator in close proximity as a bilinear spring, several studies have been carried out to explore the circumstances for this spontaneous sidebanding. Two general classes of this type of response have been found in systems that are effectively single-degree-of-freedom: (A) For highly nonlinear systems, the chaotic-like response in transition zones between successive orders of subharmonic and superharmonic operation is actually periodic, with a repetition index (J), and results in spontaneous sidebands clustered around the key subharmonic or superharmonic frequencies. No systematic relationship has been determined for the value of (J). (B) In transcritical operation of highly nonlinear and very lightly damped systems, a major sideband frequency spike is noted at a frequency which is approximately the system’s natural frequency. Recognition of this fact permits a simple estimate of the repetition index (J). All these observations from operation of the numerical model have been compared with experimental data derived from incidents of spontaneous sidebanding on aircraft gas turbine rotors. Excellent qualitative agreement has been found in most instances.
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Kosevich, Yuriy A. „Fluctuation subharmonic and multiharmonic phonon transmission and Kapitza conductance between crystals with very different vibrational spectra“. Physical Review B 52, Nr. 2 (01.07.1995): 1017–24. http://dx.doi.org/10.1103/physrevb.52.1017.
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Kosevich, Yuriy A. „Fluctuation subharmonic and multiharmonic phonon transmission and Kapitza conductance between solids with very different vibrational spectra“. Czechoslovak Journal of Physics 46, S5 (Mai 1996): 2721–22. http://dx.doi.org/10.1007/bf02570347.
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Campbell, Bryce K., Kelli Hendrickson und Yuming Liu. „Nonlinear coupling of interfacial instabilities with resonant wave interactions in horizontal two-fluid plane Couette–Poiseuille flows: numerical and physical observations“. Journal of Fluid Mechanics 809 (14.11.2016): 438–79. http://dx.doi.org/10.1017/jfm.2016.636.
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We investigate mechanisms governing the initial growth and nonlinear evolution of interfacial waves in horizontal two-fluid plane Couette–Poiseuille flows. Nonlinear coupling of the Kelvin–Helmholtz interfacial instability with resonant wave interactions has been shown to be capable of rapidly generating long waves through the transfer of energy from linearly unstable short waves to stable long-wave components within the context of potential flow theory. The objective of this work is to determine whether that coupled mechanism persists in laminar and turbulent viscous flows. Utilizing both theoretical and computational methods, we analyse the initial Orr–Sommerfeld instability to quantify the frequencies and growth/decay rates of each wave mode for two-fluid laminar and turbulent channel flows. The obtained dispersion relation allows for the identification of resonant and/or near-resonant triads among (unstable and damped) wave components in an interfacial wave spectrum. We perform direct numerical simulations (DNS) of the two-phase Navier–Stokes equations with a fully nonlinear interface to formally establish the validity of our theoretical predictions for viscous flows. DNS results show the existence of a nonlinear energy cascade from unstable short- to damped long-wavelength waves due to resonant subharmonic and/or triadic interactions in both laminar Couette and turbulent Poiseuille flows. Spectral analysis of the interfacial evolution confirms that the combined instability–resonance mechanism persists in the presence of viscosity despite being derived under the assumption of potential flow theory. Finally, we perform a detailed examination of experimentally measured wave power spectra from Jurman et al. (J. Fluid Mech., vol. 238, 1992, pp. 187–219) and carry out a numerical sensitivity study of the flow conditions to demonstrate and verify the existence of the coupled instability–resonance mechanism in physical systems. Our analysis accurately predicts the initial instability and the resulting nonlinear energy cascade through subharmonic and triadic interfacial wave resonances.
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Zhao, J. Y., und E. J. Hahn. „Subharmonic, Quasi-Periodic and Chaotic Motions of a Rigid Rotor Supported by an Eccentric Squeeze Film Damper“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 207, Nr. 6 (November 1993): 383–92. http://dx.doi.org/10.1243/pime_proc_1993_207_145_02.
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This paper analyses the complexity of the unbalance response possible with a simple rigid rotor supported by an eccentric squeeze film damper. The damper forces are obtained from the ‘π’ film short bearing approximation to the Reynolds equation and a fourth-order Runge-Kutta integration is used to evaluate the rotor response. Poincaré maps, rotor trajectories, bifurcation diagrams and power spectra are used to elucidate and to illustrate the diversity of the system behaviour. It is shown that for a large unbalance and static eccentricity ratio, the system can exhibit undesirable jump phenomenon and subharmonic, quasi-periodic and even chaotic motions, which limit the operating conditions at which dampers should be used.
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Zhang, Yu, Christopher R. Krausert, Michael P. Kelly und Jack J. Jiang. „Typing Vocal Fold Vibratory Patterns in Excised Larynx Experiments Via Digital Kymography“. Annals of Otology, Rhinology & Laryngology 118, Nr. 8 (August 2009): 598–605. http://dx.doi.org/10.1177/000348940911800812.
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Objectives Signal typing is central to the understanding of vocal fold vibratory patterns. Digital kymography (DKG) allows the direct observation of vocal fold vibratory patterns, and therefore, using DKG for vibratory signal typing may provide a useful complement to traditional signal typing techniques. Methods Video data collected from 20 larynges excised from mongrel dogs were observed with DKG in order to find examples of type 1 (nearly periodic), type 2 (subharmonic), and type 3 (aperiodic) vibratory patterns. The time series, frequency spectra, and correlation dimensions were calculated for each signal type. Results The type 1 pattern showed a periodic time series of glottal edges and a discrete frequency spectrum. The type 2 vibratory pattern displayed a time series of alternating high- and low-amplitude waves and a frequency spectrum that included a subharmonic (F0/2) frequency component. Regular and symmetric vibratory patterns were observed in the type 1 and type 2 patterns. The type 3 vibratory pattern was characterized by an aperiodic time series of glottal edges, a broadband frequency spectrum, and irregular and asymmetric vibratory patterns. The correlation dimension estimates increased from type 1 to type 2 to type 3. Conclusions Imaging with DKG demonstrated an ability to assign a signal type to various laryngeal vibrations. Signal typing techniques utilizing direct observation of the vocal folds could be useful in determining valid methods for the analysis of vocal fold vibrations.
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Shen, Guangyan, Zhonghui Xiao, Wen Zhang und Tiesheng Zheng. „Nonlinear Behavior Analysis of a Rotor Supported on Fluid-Film Bearings“. Journal of Vibration and Acoustics 128, Nr. 1 (14.07.2005): 35–40. http://dx.doi.org/10.1115/1.2149394.
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A fast and accurate model to calculate the fluid-film forces of a fluid-film bearing with the Reynolds boundary condition is presented in the paper by using the free boundary theory and the variational method. The model is applied to the nonlinear dynamical behavior analysis of a rigid rotor in the elliptical bearing support. Both balanced and unbalanced rotors are taken into consideration. Numerical simulations show that the balanced rotor undergoes a supercritical Hopf bifurcation as the rotor spin speed increases. The investigation of the unbalanced rotor indicates that the motion can be a synchronous motion, subharmonic motion, quasi-period motion, or chaotic motion at different rotor spin speeds. These nonlinear phenomena are investigated in detail. Poincaré maps, bifurcation diagram and frequency spectra are utilized as diagnostic tools.
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Wang, Cheng-Chi, Her-Terng Yau und Chi-Chang Wang. „Chaotic and Subharmonic Motion Analysis of Floating Ring Gas Bearing System by Hybrid Numerical Method“. Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/145716.
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This paper studies the nonlinear dynamic behaviors including chaotic, subharmonic, and quasi-periodic motions of a rigid rotor supported by floating ring gas bearing (FRGB) system. A hybrid numerical method combining the differential transformation method and the finite difference method used to calculate pressure distribution of FRGB system and rotor orbits. The results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional finite difference approach. Moreover, the hybrid method avoids the numerical instability problem suffered by the finite difference scheme at low values of the rotor mass and computational time-step. Moreover, power spectra, Poincaré maps, bifurcation diagrams and Lyapunov exponents are applied to examine the nonlinear dynamic response of the FRGB system over representative ranges of the rotor mass and bearing number, respectively. The results presented summarize the changes which take place in the dynamic behavior of the FRGB system as the rotor mass and bearing number are increased and therefore provide a useful guideline for the bearing system.
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Nuzzi, F., C. Magness und D. Rockwell. „Three-dimensional vortex formation from an oscillating, non-uniform cylinder“. Journal of Fluid Mechanics 238 (Mai 1992): 31–54. http://dx.doi.org/10.1017/s0022112092001629.
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A cylinder having mild variations in diameter along its span is subjected to controlled excitation at frequencies above and below the inherent shedding frequency from the corresponding two-dimensional cylinder. The response of the near wake is characterized in terms of timeline visualization and velocity traces, spectra, and phase plane representations. It is possible to generate several types of vortex formation, depending upon the excitation frequency. Globally locked-in, three-dimensional vortex formation can occur along the entire span of the flow. Regions of locally locked-in and period-doubled vortex formation can exist along different portions of the span provided the excitation frequency is properly tuned. Unlike the classical subharmonic instability in free shear flows, the occurrence of period-doubled vortex formation does not involve vortex coalescence; instead, the flow structure alternates between two different states.
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Popovic, Pavol, Ali H. Nayfeh, Kyoyul Oh und Samir A. Nayfeh. „An Experimental Investigation of Energy Transfer from a High- Frequency Mode to a Low-Frequency Mode in a Flexible Structure“. Journal of Vibration and Control 1, Nr. 1 (Januar 1995): 115–28. http://dx.doi.org/10.1177/107754639500100108.
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The objective of the present article is to experimentally observe and characterize the transfer of energy from low-amplitude, high-frequency modes to high-amplitude, low-frequency modes. The subject of the study is a three-beam frame. The excitation amplitude is restricted to below 2 g peak. The authors have focused on observing, characterizing, and documenting the excitation of the first mode by high-frequency forcing. The energy-transfer processes are identified by power spectra and characterized further by frequency and amplitude sweeps. The energy-transfer routes observed in the experiment are subharmonic resonance of order one-half, combination resonance of the additive type, and interaction between widely spaced modes. In the latter route, an excitation at a frequency that is more than 100 times the first-mode frequency has been observed to excite the first mode.
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Wang, C.-C., M.-J. Jang und C.-K. Chen. „Non-linear dynamic analysis of a flexible rotor supported by self-acting gas journal bearings“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, Nr. 12 (01.12.2004): 1527–38. http://dx.doi.org/10.1243/0954406042690407.
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This paper studies the bifurcation of a flexible rotor supported by gas film bearings. A time dependent mathematical model for gas journal bearings is presented. The finite difference method, with the successive overrelation method (SOR), is employed to solve the Reynolds equation. The system state trajectory, Poincare maps, power spectra and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor and journal centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and subharmonic response of the rotor and journal centre. This paper shows how the dynamic behaviour of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the non-linear dynamics of gas film rotor-bearing systems.
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Wang, Cheng-Chi, und Cha’o-Ku`ang Chen. „Bifurcation Analysis of Self-Acting Gas Journal Bearings“. Journal of Tribology 123, Nr. 4 (05.02.2001): 755–67. http://dx.doi.org/10.1115/1.1388302.
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This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.
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Chen, Chieh-Li, Her-Terng Yau und Yunhua Li. „Subharmonic and Chaotic Motions of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor With Active Control“. Journal of Vibration and Acoustics 124, Nr. 2 (26.03.2002): 198–208. http://dx.doi.org/10.1115/1.1448318.
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The hybrid squeeze-film damper bearing with active control is proposed in this paper. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincare´ maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the nondimensional speed ratio s=3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action.
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Chang-Jian, Cai-Wan, Shiuh Ming Chang und Hsieh-Chung Hsu. „Couple-Stress Fluid Improves Dynamic Response of Gear-Pair System Supported by Journal Bearings“. Journal of Applied Mathematics 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/527878.
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A systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, couple-stress fluid flow effect, nonlinear oil-film force, and nonlinear gear mesh force is performed in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless rotational speed ratio as a control parameter. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents and fractal dimension of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, subharmonic, quasiperiodic, and chaotic behaviors. The couple-stress fluid would be a useful lubricating fluid to suppress nonlinear dynamic responses and improve the steady of the systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.
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Broze, George, und Fazle Hussain. „Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors“. Journal of Fluid Mechanics 263 (25.03.1994): 93–132. http://dx.doi.org/10.1017/s0022112094004040.
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Conclusive experimental evidence is presented for the existence of a low-dimensional temporal dynamical system in an open flow, namely the near field of an axisymmetric, subsonic free jet. An initially laminar jet (4 cm air jet in the Reynolds number range 1.1 × 104 [Lt ] ReD × 9.1 × 104) with a top-hat profile was studied using single-frequency, longitudinal, bulk excitation. Two non-dimensional control parameters – forcing frequency StD (≡fexD/Ue, where fez is the excitation frequency, D is the jet exit diameter and Ue is the exit velocity) and forcing amplitude af (≡ u’f/Ue, where u’f is the jet exit r.m.s. longitudinal velocity fluctuation at the excitation frequency) – were varied over the ranges 10-4 < af < 0.3 and 0.3 < StD < 3.0 in order to construct a phase diagram. Periodic and chaotic states were found over large domains of the parameter space. The periodic attractors correspond to stable pairing (SP) and stable double pairing (SDP) of rolled-up vortices. One chaotic attractor, near SP in the parameter space, results from nearly periodic modulations of pairing (NPMP) of vortices. At large scales (i.e. approximately the size of the attractor) in phase space, NPMP exhibits approximately quasi-periodic behaviour, including modulation sidebands around ½fex in u-spectra, large closed loops in its Poincaré sections, correlation dimension v ∼ 2 and largest Lyapunov exponent λ1 ∼ 0. But investigations at smaller scales (i.e. distances greater than, but of the order of, trajectory separation) in phase space reveal chaos, as shown by v > 2 and λ1 > 0. The other chaotic attractor, near SDP, results from nearly periodic modulations of the first vortex pairing but chaotic modulations of the second pairing and has a broadband spectrum, a dimension 2.5 [Lt ] v [Lt ] 3 and the largest Lyapunov exponent 0.2 [Lt ] λ1 [Lt ] 0.7 bits per orbit (depending on measurement locations in physical and parameter spaces).A definition that distinguishes between physically and dynamically open flows is proposed and justified by our experimental results. The most important conclusion of this study is that a physically open flow, even one that is apparently dynamically open due to convective instability, can exhibit dynamically closed behaviour as a result of feedback. A conceptual model for transitional jets is proposed based on twodimensional instabilities, subharmonic resonance and feedback from downstream vortical structures to the nozzle lip. Feedback was quantified and shown to affect the exit fundamental–subharmonic phase difference ϕ – a crucial variable in subharmonic resonance and, hence, vortex pairing. The effect of feedback, the sensitivity of pairings to ϕ, the phase diagram, and the documented periodic and chaotic attractors demonstrate the validity of the proposed conceptual model.
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Boguslawski, A., K. Wawrzak und A. Tyliszczak. „A new insight into understanding the Crow and Champagne preferred mode: a numerical study“. Journal of Fluid Mechanics 869 (25.04.2019): 385–416. http://dx.doi.org/10.1017/jfm.2019.220.
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The paper presents a new insight into understanding a mechanism to trigger the Crow and Champagne preferred mode. It is shown on the basis of numerical simulations that the preferred mode is established as a result of nonlinear interactions of primary structures generated by the Kelvin–Helmholtz instability. These interactions form larger coherent vortices characterized with frequency equal to half of the frequency of the primary perturbation. The paper shows that the shear-layer thickness at the nozzle exit constitutes a key parameter that influences significantly the jet response to an external forcing. The simulations were performed for jets with different shear-layer thicknesses. For the thicker shear layer the classical Kelvin–Helmholtz instability is observed. In this case the jet response to an external varicose forcing seems to be very similar to the experimental results of Crow and Champagne. The results presented shed new light on the preferred mode and the frequency selection mechanism confirming the suggestion of Crow and Champagne that nonlinearity is responsible for the preferred frequency. Significantly different results were obtained for a jet characterized by a thin shear layer. In this case the jet could be introduced into a self-sustained regime. External forcing with a frequency equal to the frequency of the natural self-sustained mode or with its subharmonic has practically no effect on the jet dynamics. The jet response to the forcing with frequencies different from the natural one depends on the forcing amplitude. A weak forcing disturbs the self-sustained mode leading to an interaction of two different modes that is observed in spectra with many frequencies related to both the self-sustained mode and the oscillations triggered by forcing. A stronger forcing suppresses the self-sustained mode and only the frequency components related to the stimulation are observed in the spectra. A mechanism responsible for the jet response to an external forcing under the self-sustained regime has not been extensively studied so far and a full understanding of these phenomena needs further studies and careful analysis.
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DE ZHOU, MING, und I. WYGNANSKI. „The response of a mixing layer formed between parallel streams to a concomitant excitation at two frequencies“. Journal of Fluid Mechanics 441 (15.08.2001): 139–68. http://dx.doi.org/10.1017/s0022112001004827.
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Simultaneous excitation of a turbulent mixing layer by two frequencies, a fundamental and a subharmonic, was investigated experimentally. Plane perturbations were introduced to the flow at its origin by a small oscillating flap. The results describe two experiments that differ mainly in the amplitudes of the imposed perturbations and both are compared to the data acquired while the mixing layer was forced at a single frequency.Conventional statistical quantities such as: mean velocity profiles, widths of the flow, turbulent intensities, spectra, phase-locked velocity and vorticity fields, as well as streaklines were computed. The rate of spread of the flow under concomitant excitation at the two frequencies was much greater than under a single frequency, although it remained dominated by two-dimensional eddies. The Reynolds stresses and turbulence production are associated with the deformation and orientation of the large coherent vortices. When the major axis of the coherent vortices starts leaning forward on the high-speed side of the flow, the production of turbulent energy changes sign (i.e. becomes negative) and this results in the flow thinning in the direction of streaming. It also indicates that energy is extracted from the turbulence to the mean motion. Resonance phenomena play an important role in the evolution of the flow. A vorticity budget showed that the change in mean vorticity was mainly caused by the nonlinear interaction between coherent vorticities. Nevertheless, the locally dominant frequency scales the mean growth rate, the inclination and distortion of the mean velocity profiles as well as the phase-locked vorticity contours.
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Ghasemi, Abbas, Burak Ahmet Tuna und Xianguo Li. „Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct“. Journal of Fluid Mechanics 864 (01.02.2019): 141–80. http://dx.doi.org/10.1017/jfm.2018.988.
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Rectangular air jets of aspect ratio $2$ are studied at $Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$ using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ($f_{n}$) and subharmonic ($f_{n}/2$) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at $f_{n}/2$ shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.
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Monkewitz, Peter A. „Subharmonic resonance, pairing and shredding in the mixing layer“. Journal of Fluid Mechanics 188 (März 1988): 223–52. http://dx.doi.org/10.1017/s0022112088000710.
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An instability-wave analysis is presented to describe the spatial evolution of a fundamental mode and its subharmonic on an inviscid parallel mixing layer. It incorporates explicitly the weakly nonlinear interaction between the two modes. The computational finding that the development of the subharmonic, leading eventually to pairing or shredding, crucially depends on its phase relation with the fundamental is fully confirmed. Furthermore it is shown that a critical fundamental amplitude has to be reached before the (spatial) subharmonic becomes phase locked with the fundamental and exhibits a modified growth rate. Then the analysis is exploited to explain the occurrence of amplitude modulations in ‘natural’ mixing layers and to estimate the width of the subharmonic spectral peaks. Also, the case of oblique subharmonic waves is briefly touched upon. In the last part, ways are explored to model non-parallel effects, i.e. to handle the saturation of the rapidly growing subharmonic. Using this wave description, the role of mode interaction in the ‘vortex pairing’ and ‘shredding’ process is assessed.
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Jahanbakhshi, Reza, und Tamer A. Zaki. „Nonlinearly most dangerous disturbance for high-speed boundary-layer transition“. Journal of Fluid Mechanics 876 (31.07.2019): 87–121. http://dx.doi.org/10.1017/jfm.2019.527.
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Laminar-to-turbulent transition in a zero-pressure-gradient boundary layer at Mach 4.5 is studied using direct numerical simulations. For a given level of total disturbance energy, the inflow spectrum was designed to correspond to the nonlinearly most dangerous condition that leads to the earliest possible transition Reynolds number. The synthesis of the inlet disturbance is formulated as a constrained optimization, where the control vector is comprised of the amplitudes and relative phases of the inlet modes; the constraints are the prescribed total energy and that the flow evolution satisfies the full nonlinear compressible Navier–Stokes equations; the cost function is defined in terms of the mean skin-friction coefficient and, once maximized, ensures the earliest possible transition location. An ensemble-variational (EnVar) technique is developed to solve the optimization problem. Starting from an initial guess, here a broadband disturbance, EnVar updates the estimate of the control vector at the end of each iteration using the gradient of the cost function, which is evaluated from the outcomes of an ensemble of possible solutions. Two inflow conditions are computed, each corresponding to a different level of energy, and their spectra are contrasted: the lower-energy case includes two normal acoustic waves and one oblique vorticity perturbation, whereas the higher-energy condition consists of oblique acoustic and vorticity waves. The focus is placed on the former case because it cannot be categorized as any of the classical breakdown scenarios (fundamental, subharmonic or oblique), while the higher-energy condition undergoes a second-mode oblique transition. At the lower energy level, the instability wave that initiates the rapid breakdown to turbulence is not present at the inlet plane. Instead, it appears at a downstream location after a series of nonlinear interactions that spur the fastest onset of turbulence. The results from the nonlinearly most potent inflow condition are also compared to other inlet disturbances that are selected solely based on linear theory, and which all yield relatively delayed transition onset.
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Ghasemi, Abbas, Burak Ahmet Tuna und Xianguo Li. „Shear/rotation competition during the roll-up of acoustically excited shear layers“. Journal of Fluid Mechanics 844 (12.04.2018): 831–54. http://dx.doi.org/10.1017/jfm.2018.214.
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Naturally developing and acoustically excited shear layers at the Reynolds numbers $Re_{\unicode[STIX]{x1D703}_{0}}=U\unicode[STIX]{x1D703}_{0}/\unicode[STIX]{x1D708}=85{-}945$ are studied using the hot-wire (HW) anemometry and particle image velocimetry (PIV), with a focus on the shear/rotation competition during the initial Kelvin–Helmholtz (KH) roll-up. Velocity spectra and the spatial linear stability (LST) analysis characterize the fundamental ($f_{n}$) and its subharmonic ($f_{n}/2$) mode interacting due to the vortex pairing. For $276\leqslant Re_{\unicode[STIX]{x1D703}_{0}}\leqslant 780$, the root-mean-square (r.m.s.) of the streamwise turbulence intensity shows a double-peaking phenomenon, i.e. major and minor peaks of the $u_{rms}$ coexist towards the high-speed (HS) and the low-speed (LS) sides, respectively. The single/double-peaked $u_{rms}$ profiles are found to be correlated with the scattered/organized distribution of the shear/rotation, demonstrating a transitioning character with the downstream distance, $Re_{\unicode[STIX]{x1D703}_{0}}$ and the upstream turbulence levels. The rotating vortex cores and the corresponding peripheral shear regions, demonstrate the phase reversal of the velocity fluctuations with respect to the HS and the LS sides. Excitation at $f_{n}$ increases the vortex count by 21 %, advances the location of the first KH roll-up and hence also the minor peak formation location. Due to the enhanced pairing at the $f_{n}/2$ forcing, the vortex count reduces by 23 %. Before merging into the downstream rotation core, the upstream vortex is shifted towards the HS side and the major peak is accordingly augmented. Actuation advances the transition to the nonlinear state, as well as the saturation of the amplification factor. The volumetric topologies of the shear/rotation loops tracked in consecutive phases during the period of the acoustic excitation, separate from the edge and grow in time–space due to the viscous diffusion. The shearing and rotating loops are found to be associated with the thinning (elongation) and expansion (accumulation) of the vorticity, respectively.
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Kim, Ki-Ha, und Jung-Il Choi. „Lock-in regions of laminar flows over a streamwise oscillating circular cylinder“. Journal of Fluid Mechanics 858 (06.11.2018): 315–51. http://dx.doi.org/10.1017/jfm.2018.787.
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In this paper, flow over a streamwise oscillating circular cylinder is numerically simulated to examine the effects of the driving amplitude and frequency on the distribution of the lock-in regions in laminar flows. At $Re=100$, lock-in is categorized according to the spectral features of the lift coefficient as two different lock-in phenomena: harmonic and subharmonic lock-in. These lock-in phenomena are represented as maps on the driving amplitude–frequency plane, which have subharmonic lock-in regions and two harmonic lock-in regions. The frequency range of the subharmonic region is shifted to lower frequencies with increasing amplitude, and the lower boundary of this subharmonic region is successfully predicted. A symmetric harmonic region with a symmetric vortex pattern is observed in a certain velocity range for a moving cylinder. Aerodynamic features induced by different flow patterns in each region are presented on the driving amplitude–frequency plane. The lock-in region and aerodynamic features at $Re=200$ and $40$ are compared with the results for $Re=100$. A subharmonic region and two harmonic regions are observed at $Re=200$, and these show the same features as for $Re=100$ at a low driving amplitude. Lock-in at $Re=40$ also shows one subharmonic region and two harmonic regions. However, compared with the $Re=100$ case, the symmetric harmonic lock-in is dominant. The features of aerodynamic force at $Re=200$ and $40$ are represented on a force map, which shows similar characteristics in corresponding regions for the $Re=100$ case.
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Nygaard, Kris J., und Ari Glezer. „The effect of phase variations and cross-shear on vortical structures in a plane mixing layer“. Journal of Fluid Mechanics 276 (10.10.1994): 21–59. http://dx.doi.org/10.1017/s0022112094002454.
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The evolution of spanwise phase variations of nominally two-dimensional instability modes in a plane shear layer is studied in a closed-return water facility using time-harmonic excitation having spanwise-non-uniform phase or frequency distributions. The excitation waveform is synthesized by a linear array of 32 surface film heaters flush-mounted on the flow partition. A span wise-linear phase distribution leads to the excitation of oblique waves and to the rollup of oblique primary vortices. When the prescribed phase distribution is piecewise-constant and spanwise-periodic, the flow is excited with a linear combination of a two-dimensional wavetrain and pairs of equal and opposite oblique waves, the amplitudes of which depend on the magnitude of the phase variation ΔΦ. As a result of the excitation, the primary vortices undergo spanwise-non-uniform rollup and develop spanwise-periodic deformations that induce cross-shear and secondary vortices in the braid region. The amplitude of the deformations of the primary vortices and the shape and strength of the secondary vortices depend on the magnitude of ΔΦ. When ΔΦ is small, the secondary vortices are counter-rotating vortex pairs. As ΔΦ increases, cross-shear induced by oblique segments of the primary vortices in the braid region results in the formation of single secondary vortex strands. The flow is not receptive to spanwise phase variations with wavelengths shorter than the streamwise wavelength of the Kelvin–Helmholtz instability. When the phase variation is ΔΦ = ϕ, the flow is excited with pairs of oblique waves only and undergoes a double rollup, resulting in the formation of spanwise-deformed vortices at twice the excitation frequency. Measurements of the streamwise velocity component show that the excitation leads to a substantial increase in the cross-stream spreading of the shear layer and that distortions of transverse velocity profiles are accompanied by an increase in the high-frequency content of velocity power spectra. Detailed schlieren visualizations shed light on the nature of ‘vortex dislocations’ previously observed by other investigators. Complex spanwise-non-uniform pairing interactions between the spanwise vortices are forced farther downstream by spanwise-amplitude or phase variations of subharmonic excitation wavetrains.
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YEO, K. S., X. ZHAO, Z. Y. WANG und K. C. NG. „DNS of wavepacket evolution in a Blasius boundary layer“. Journal of Fluid Mechanics 652 (19.05.2010): 333–72. http://dx.doi.org/10.1017/s0022112009994095.
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This paper presents the direct numerical simulation (DNS) of wavepacket evolution and breakdown in a Blasius boundary layer. The study covers the physical, spectral and structural aspects of the whole transition process, whereas previous studies have tended to focus on issues of a more limited scope. The simulations are modelled after the experiments of Cohen, Breuer & Haritonidis (J. Fluid Mech., vol. 225, 1991, p. 575). The disturbance wavepackets are initiated here by a u-velocity and a v-velocity delta pulse. They evolve through a quasi-linear growth stage, a subharmonic stage and a strongly nonlinear stage before breaking down into the nascent turbulent spots. Pulse-initiated wavepackets provide a plausible model for naturally occurring laminar–turbulent transition because they contain disturbances in a broadband of frequencies and wavenumbers, whose sum of interactions determines the spatio-temporal progress of the wavepackets. The early development of the wavepackets accords well with established linear results. The ensuing subharmonic evolution of the wavepackets appears to be underpinned by a critical-layer-based mechanism in which the x-phase speeds of the fundamental two-dimensional and dominant three-dimensional waves with compatible Squire wavenumbers are approximately matched. Spectral data over the bulk of the subharmonic stage demonstrate good consistency with the action of a phase-locked theory recently proposed by Wu, Stewart & Cowley (J. Fluid Mech., vol. 590, 2007, p. 265), strongly suggesting that the latter may be the dominant mechanism in the broadband nonlinear evolution of wavepackets. The dominant two-dimensional and three-dimensional waves are observed to be spontaneously evolving towards triad resonance in the late subharmonic stage. The simulations reproduce many key features in the experiments of Cohen et al. (1991) and Medeiros & Gaster (J. Fluid Mech., vol. 399, 1999b, p. 301). A plausible explanation is also offered for the apparently ‘deterministic’ subharmonic behaviour of wavepackets observed by Medeiros & Gaster. The strongly nonlinear stage is signified by the appearance of low-frequency streamwise-aligned u-velocity structures at twice the spanwise wavenumber of the dominant three-dimensional waves, distortion of the local base flow by the strengthening primary Λ-vortex and rapid expansion of the spanwise wavenumber (β) spectrum. These are in broad agreement with the experimental observations of Breuer, Cohen & Haritonidis (J. Fluid Mech., vol. 340, 1997, p. 395). The breakdown into incipient turbulent spots occurs at locations consistent with the experiments of Cohen et al. (1991). A visualization shows that the evolving wavepackets comprise very thin overlapping vorticity sheets of alternating signs, in stacks of two or three. Strong streamwise stretching of the flow at the centre of the wavepacket in the late subharmonic and strongly nonlinear stages promotes the roll-up and intensification of the vorticity sheets into longitudinal vortices, whose mutual induction precedes the breakdown of the wavepacket. The critical layer of the dominant two-dimensional and oblique wave modes reveals the progressive coalescence of a strong pair of vortices (associated with the Λ-vortex) during the subharmonic stage. Their coalescence culminates in a strong upward burst of velocity that transports lower momentum fluid from below the critical layer into the upper boundary layer to form a high shear layer in the post-subharmonic stage.
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Hertrich, Ingo, und Hermann Ackermann. „Gender-Specific Vocal Dysfunctions in Parkinson's Disease: Electroglottographic and Acoustic Analyses“. Annals of Otology, Rhinology & Laryngology 104, Nr. 3 (März 1995): 197–202. http://dx.doi.org/10.1177/000348949510400304.
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Electroglottographic (EGG) and acoustic recordings were obtained during sustained vowel production in men and women suffering from Parkinson's disease (PD). The computed EGG spectrograms allowed us to differentiate various kinds of phonatory disturbances: intervals with subharmonic energy (“low-frequency segments”), “noise-like regions,” and abrupt shifts of fundamental frequency (F0). Female PD subjects presented with a significantly increased portion of subharmonic segments and with significantly more abrupt F0 shifts as compared to both controls and male PD subjects. Presumably, these alterations in spectral energy distribution reflect different oscillatory modes of the glottal source. Thus, PD seems to have a differential impact on phonation in men and women. Conceivably, these gender-specific vocal dysfunctions are determined by the well-known sexual dimorphism of laryngeal size.
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Zhang, Weifeng G., und Timothy F. Duda. „Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break“. Journal of Physical Oceanography 43, Nr. 12 (01.12.2013): 2641–60. http://dx.doi.org/10.1175/jpo-d-12-0239.1.
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Abstract To quantify dynamical aspects of internal-tide generation at the Mid-Atlantic Bight shelf break, this study employs an idealized ocean model initialized by climatological summertime stratification and forced by monochromatic barotropic tidal currents at the offshore boundary. The Froude number of the scenario is subunity, and the bathymetric slope offshore of the shelf break is supercritical. A barotropic-to-baroclinic energy conversion rate of 335 W m−1 is found, with 14% of the energy locally dissipated through turbulence and bottom friction and 18% radiated onto the shelf. Consistent with prior studies, nonlinear effects result in additional super- and subharmonic internal waves at the shelf break. The subharmonic waves are subinertial, evanescent, and mostly trapped within a narrow beam of internal waves at the forcing frequency. They likely result from nonresonant triad interaction associated with strong nonlinearity. Strong vertical shear associated with the subharmonic waves tends to enhance local energy dissipation and turbulent momentum exchange (TME). A simulation with reduced tidal forcing shows an expected diminished level of harmonic energy. A quasi-linear simulation verifies the role of momentum advection in controlling the relative phases of internal tides and the efficiency of barotropic-to-baroclinic energy conversion. The local TME is tightly coupled with the internal-wave dynamics: for the chosen configuration, neglecting TME causes the internal-wave energy to be overestimated by 12%, and increasing it to high levels damps the waves on the continental shelf. This work implies a necessity to carefully consider nonlinearity and turbulent processes in the calculation of internal tidal waves generated at the shelf break.
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VUKASINOVIC, BOJAN, MARC K. SMITH und ARI GLEZER. „Dynamics of a sessile drop in forced vibration“. Journal of Fluid Mechanics 587 (31.08.2007): 395–423. http://dx.doi.org/10.1017/s0022112007007379.
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The interfacial dynamics of a sessile water drop was investigated experimentally. The low-viscosity drop was forced by an underlying diaphragm driven vertically by a piezoelectric actuator. This high-frequency forcing produced very low diaphragm displacements, even at high acceleration amplitudes. As the driving amplitude was increased from zero, the drop exhibited several transitions to states of increasing spatio-temporal complexity. The first state of the forced drop consisted of harmonic axisymmetric standing waves that were present for even the smallest diaphragm motion. Wave modes up to 14 were observed an compared to theoretical results. As the forcing amplitude increased above a critical value, a parametrically driven instability occurred that resulted in the appearance of subharmonic azimuthal waves along the contact line. The critical accelerations and the resulting wavenumbers of the azimuthal waves were documented. For larger values of the forcing amplitude, the subharmonic azimuthal waves coupled with the harmonic axisymmetric waves to produce a striking new lattice-like wave pattern. With a further increase in the forcing amplitude, the lattice mode disappeared and the interface evolved into a highly disordered state, dominated by subharmonic wave motion. The characteristics of the lattice and pre-ejection modes were documented with phase-locked measurements and spectral analysis. Finally, as the forcing amplitude increased above another critical value, the interface broke up via droplet ejection from individual wave crests.
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Bae, Sungryong, und Pilkee Kim. „Load Resistance Optimization of a Broadband Bistable Piezoelectric Energy Harvester for Primary Harmonic and Subharmonic Behaviors“. Sustainability 13, Nr. 5 (06.03.2021): 2865. http://dx.doi.org/10.3390/su13052865.
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In this study, optimization of the external load resistance of a piezoelectric bistable energy harvester was performed for primary harmonic (period-1T) and subharmonic (period-3T) interwell motions. The analytical expression of the optimal load resistance was derived, based on the spectral analyses of the interwell motions, and evaluated. The analytical results are in excellent agreement with the numerical ones. A parametric study shows that the optimal load resistance depended on the forcing frequency, but not the intensity of the ambient vibration. Additionally, it was found that the optimal resistance for the period-3T interwell motion tended to be approximately three times larger than that for the period-1T interwell motion, which means that the optimal resistance was directly affected by the oscillation frequency (or oscillation period) of the motion rather than the forcing frequency. For broadband energy harvesting applications, the subharmonic interwell motion is also useful, in addition to the primary harmonic interwell motion. In designing such piezoelectric bistable energy harvesters, the frequency dependency of the optimal load resistance should be considered properly depending on ambient vibrations.
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Ehrich, F. „Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics“. Journal of Vibration and Acoustics 114, Nr. 1 (01.01.1992): 93–100. http://dx.doi.org/10.1115/1.2930240.
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When a rotor, excited by unbalance, is operating eccentrically within a clearance and in local contact with the stator it behaves as a bilinear oscillator with a natural periodic motion that resembles bouncing. When excited by unbalance at a subcritical rotative speed which is exactly or nearly 1/Nsuper times its natural frequency, the nonlinear system will respond by bouncing at or nearly at its natural frequency, or superharmonically at a frequency exactly Nsuper times the operating speed or forcing frequency. As in supercritical subharmonic response, there is a zone with characteristics of chaotic behavior in the transition zone between any order of superharmonic response and the next highest order of superharmonic response. There is also an intricate pattern of progressive bifurcations of the orbit on entry into this characteristically chaotic region and a reverse progression on exit from this region. The response is a mirror image or reciprocal set of the more thoughly studied supercritical subharmonic response of the same bilinear oscillator system which, when excited by unbalance at a supercritical rotative speed which is exactly or nearly a whole number Nsub times its natural frequency, the nonlinear system will respond by bouncing at exactly or nearly its natural frequency at a frequency exactly 1/Nsub times the operating speed or forcing frequency. Such supercritical subharmonic response is also characterized by the appearance of characteristically chaotic behavior in the transition zone between successive orders of subharmonic response and by patterns of progressive bifurcations of the orbit on entry into and exit from each region of characteristically chaotic response. Various aspects of subcritical superharmonic response are studied in a numerical model of the nonlinear system, and are compared to data taken on the core spool of an aircraft engine gas turbine. The engine data show many of the unique characteristics of response, wave form, and spectral content predicted by the numerical model of the bilinear oscillator when operating at subcritical rotative speed.
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REUTER, ROBERT, REINHOLD ORGLMEISTER und HANSPETER HERZEL. „SIMULATIONS OF VOCAL FOLDS WITH AN ANALOG CIRCUIT“. International Journal of Bifurcation and Chaos 09, Nr. 06 (Juni 1999): 1075–88. http://dx.doi.org/10.1142/s0218127499000742.
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The human voice source generates complex signals including subharmonics and toroidal oscillations. Essential features of voice production are covered by two-mass models where each vocal fold is represented by two oscillators. We present a related analog circuit which allows online analysis of the generated complex signals. Using narrow-band spectrograms various bifurcations due to left–right asymmetry are monitored. Time series, spectra, return maps, and response measurements provide further detailed information about phase-locking and toroidal oscillations. Finally, possible clinical applications are discussed.
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Weng, Wenle, Aleksandra Kaszubowska-Anandarajah, Junqiu Liu, Prince M. Anandarajah und Tobias J. Kippenberg. „Frequency division using a soliton-injected semiconductor gain-switched frequency comb“. Science Advances 6, Nr. 39 (September 2020): eaba2807. http://dx.doi.org/10.1126/sciadv.aba2807.
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With optical spectral marks equally spaced by a frequency in the microwave or the radio frequency domain, optical frequency combs have been used not only to synthesize optical frequencies from microwave references but also to generate ultralow-noise microwaves via optical frequency division. Here, we combine two compact frequency combs, namely, a soliton microcomb and a semiconductor gain-switched comb, to demonstrate low-noise microwave generation based on a novel frequency division technique. Using a semiconductor laser that is driven by a sinusoidal current and injection-locked to microresonator solitons, our scheme transfers the spectral purity of a dissipative soliton oscillator into the subharmonic frequencies of the microcomb repetition rate. In addition, the gain-switched comb provides dense optical spectral emissions that divide the line spacing of the soliton microcomb. With the potential to be fully integrated, the merger of the two chipscale devices may profoundly facilitate the wide application of frequency comb technology.
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Frendi, A., und L. Maestrello. „On the Combined Effect of Mean Flow and Acoustic Excitation on Structural Response and Radiation“. Journal of Vibration and Acoustics 119, Nr. 3 (01.07.1997): 448–56. http://dx.doi.org/10.1115/1.2889744.
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Numerical experiments in two dimensions are carried out in order to investigate the response of a typical aircraft structure to a mean flow and an acoustic excitation. Two physical problems are considered; one in which the acoustic excitation is applied on one side of the flexible structure and the mean flow is on the other side while in the second problem both the mean flow and acoustic excitation are on the same side. Subsonic and supersonic mean flows are considered together with a random and harmonic acoustic excitation. In the first physical problem and using a random acoustic excitation, the results show that at low excitation levels the response is unaffected by the mean flow Mach number. However, at high excitation levels the structural response is significantly reduced by increasing the Mach number. In particular, both the shift in the frequency response spectrum and the broadening of the peaks are reduced. In the second physical problem, the results show that the response spectrum is dominated by the lower modes (1 and 3) for the subsonic mean flow case and by the higher modes (5 and 7) in the supersonic case. When a harmonic excitation is used, it is found that in the subsonic case the power spectral density of the structural response shows a subharmonic (f/4) while in the supersonic case no subharmonic is obtained.
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de Paula, I. B., W. Würz, E. Krämer, V. I. Borodulin und Y. S. Kachanov. „Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves“. Journal of Fluid Mechanics 732 (12.09.2013): 571–615. http://dx.doi.org/10.1017/jfm.2013.420.
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AbstractWeakly nonlinear interactions involving amplitude-modulated Tollmien–Schlichting waves in an incompressible, two-dimensional aerofoil boundary layer are investigated experimentally. Selected resonant regimes are examined with emphasis on the regimes where more than one fundamental Tollmien–Schlichting (TS) wave is present in the flow. The experiments were performed on an NLF-type aerofoil section for glider applications. Disturbances with controlled frequency-spanwise-wavenumber spectra were excited in the boundary layer and studied by phase-locked hot-wire measurements. The results show that nonlinear mechanisms connected with the steepening of the primary TS wave modulation do not play any significant role in the transition scenarios studied. It is also shown that modulations of the two-dimensional fundamental waves tend to generate additional modes at modulation frequency. These low-frequency disturbances are found to be produced by a non-resonant quadratic combination of spectral components of the primary, modulated TS wave. The investigations show that the efficiency of the process is higher for three-dimensional low-frequency modes in comparison with two-dimensional modes. Thus, the emergence of three-dimensionality for the low-frequency waves does not require any resonant interactions. In a subsequent nonlinear stage, the self-generated detuned subharmonics are found to be strongly amplified due to resonant interactions with the primary TS waves. The sequence of weakly nonlinear mechanisms found and investigated here seems to be the most likely route to the laminar–turbulent transition, at least for two-dimensional boundary layers of aerofoils with a long extent of laminar flow and in a ‘natural’ disturbance environment.
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McGaughey, Donald R., Michael J. Korenberg, Kathryn M. Adeney, Susan D. Collins und G. J. M. Aitken. „Using the Fast Orthogonal Search with First Term Reselection to Find Subharmonic Terms in Spectral Analysis“. Annals of Biomedical Engineering 31, Nr. 6 (Juni 2003): 741–51. http://dx.doi.org/10.1114/1.1574024.
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