Artykuły w czasopismach: „Non-axisymmetric oscillations”

1

Sanz, A., i J. Lopez Diez. "Non-axisymmetric oscillations of liquid bridges". Journal of Fluid Mechanics 205, nr -1 (sierpień 1989): 503. http://dx.doi.org/10.1017/s0022112089002120.

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Sotani, Hajime, i Kostas D. Kokkotas. "Non-axisymmetric Torsional Oscillations of Relativistic Stars". Journal of Physics: Conference Series 314 (22.09.2011): 012081. http://dx.doi.org/10.1088/1742-6596/314/1/012081.

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Dymova, M. V., i M. S. Ruderman. "Non-Axisymmetric Oscillations of Thin Prominence Fibrils". Solar Physics 229, nr 1 (czerwiec 2005): 79–94. http://dx.doi.org/10.1007/s11207-005-5002-x.

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Lyubimov, D. V., T. P. Lyubimova i S. V. Shklyaev. "Non-axisymmetric oscillations of a hemispherical drop". Fluid Dynamics 39, nr 6 (listopad 2004): 851–62. http://dx.doi.org/10.1007/s10697-004-0002-3.

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Lyubimov, D. V., T. P. Lyubimova i S. V. Shklyaev. "Non-axisymmetric oscillations of a hemispherical drop". Fluid Dynamics 39, nr 6 (listopad 2004): 851–62. http://dx.doi.org/10.1007/s10697-005-0021-8.

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Khudainazarov, Sh, B. Donayev i J. Yarashov. "Non-stationary oscillations of high-rise axisymmetric structures". IOP Conference Series: Materials Science and Engineering 883 (21.07.2020): 012195. http://dx.doi.org/10.1088/1757-899x/883/1/012195.

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Ruderman, Michael S. "Non-axisymmetric oscillations of thin twisted magnetic tubes". Proceedings of the International Astronomical Union 3, S247 (wrzesień 2007): 344–50. http://dx.doi.org/10.1017/s1743921308015068.

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AbstractIn this paper we study non-axisymmetric oscillations of thin twisted magnetic tubes taking the density variation along the tube into account. We use the approximation of the zero-beta plasma. The magnetic field outside the tube is straight and homogeneous, however it is twisted inside the tube. We assume that the azimuthal component of the magnetic field is proportional to the distance from the tube axis, and that the tube is only weakly twisted, i.e. the ratio of the azimuthal and axial components of the magnetic field is small. Using the asymptotic analysis we show that the eigenmodes and eigenfrequencies of the kink and fluting oscillations are described by a classical Sturm-Liouville problem for a second order ordinary differential equation. The main result is that the twist does not affect the kink mode.

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Narayanan, A. Satya. "Non-Radial Oscillations in an Axisymmetric MHD Incompressible Fluid". International Astronomical Union Colloquium 179 (2000): 361–64. http://dx.doi.org/10.1017/s0252921100064836.

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AbstractIt is well known from Helioseismology that the Sun exhibits oscillations on a global scale, most of which are non-radial in nature. These oscillations help us to get a clear picture of the internal structure of the Sun as has been demonstrated by the theoretical and observational (such as GONG) studies. In this study we formulate the linearised equations of motion for non-radial oscillations by perturbing the MHD equilibrium solution for an axisymmetric incompressible fluid. The fluid motion and the magnetic field are expressed as scalarsU,V,PandT, respectively. In deriving the exact solution for the equilibrium state, we neglect the contribution due to meridional circulation. The perturbed quantitiesU*,V*,P*,r*are written in terms of orthogonal polynomials. A special case of the above formulation and its stability is discussed.

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Bohdan, A. V., O. N. Petryschev, Yu I. Yakymenko Yakymenko i Yu Yu Yanovskaya. "Non-axisymmetric radial vibrations of thin piezoelectric disks". Electronics and Communications 16, nr 3 (28.03.2011): 195–99. http://dx.doi.org/10.20535/2312-1807.2011.16.3.266783.

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Lee, Umin, i Hideyuki Saio. "Angular-Momemtum Transfer by Nonradial Oscillations in Massive Main-Sequence Stars". International Astronomical Union Colloquium 137 (1993): 287–89. http://dx.doi.org/10.1017/s0252921100017942.

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Angular mementum distribution is one of the most important factors for stellar structutre and evolution. Among other mechanisms, angular momentum is transfered by non-axisymmetric oscillations (nonradial oscillations). In this mechanism the angular momentum is carried mainly by the Reynolds stress, which is proportional to the product between radial and azimuthal components of oscillation velocity; i.e., (Φ direction is the direction of rotation velocity). In the linear oscillation analysis, the phase difference between and is with A finite value of δ, which arises from excitation or damping of the oscillation, makes the time average of finite. Positive angular momentum is transfered from the driving zone to the damping zone by a prograde mode (Osaki 1986).

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Natarajan, Ramesh, i Robert A. Brown. "Third-order resonance effects and the nonlinear stability of drop oscillations". Journal of Fluid Mechanics 183 (październik 1987): 95–121. http://dx.doi.org/10.1017/s0022112087002544.

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The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small non-axisymmetric perturbations, as is demonstrated here for the three-and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, non-axisymmetric travelling-wave solutions are also obtained and their stability is investigated. A non-generic cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.

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Kato, Shoji. "Damping and Frequencies of Non-Axisymmetric Trappedg-Mode Oscillations". Publications of the Astronomical Society of Japan 55, nr 1 (25.02.2003): 257–65. http://dx.doi.org/10.1093/pasj/55.1.257.

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Narayanan, A. Satya. "Non-radial oscillations in an axisymmetric MHD incompressible fluid". Journal of Astrophysics and Astronomy 21, nr 3-4 (wrzesień 2000): 361–64. http://dx.doi.org/10.1007/bf02702425.

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Nasibullayev, I. Sh, E. Sh Nasibullaeva i O. V. Darintsev. "Dependence of the Piezoelectric Micropump Operating Mode on Its Geometry". Journal of Physics: Conference Series 2096, nr 1 (1.11.2021): 012081. http://dx.doi.org/10.1088/1742-6596/2096/1/012081.

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Abstract A mathematical and computer axisymmetric models in which periodic oscillations of ring piezoelectric actuators placed on an elastic tube of circular cross-section leads to radial deformations of the tube is constructed. The result of these displacements is a local compression of the microchannel, which leads to changes in its volume and the corresponding pushing of the fluid. If a non-symmetrical oscillation scheme is used, the average fluid flow over the period will be non-zero and the device can be used as a micropump. The aim of the work is a computer study of the geometric features of an axisymmetric piezoelectric micropump, taking into account the processes of heat transfer by a fluid in the channel. The dependence of the average fluid flow rate on the channel parameters and the frequency of oscillations of the piezoelectric actuators is determined by the method of factorial experiment. The parameters preventing heat backflow have been determinate, which makes it possible to use a device for supplying coolant to a microgripper cooling system.

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Kidambi, R. "Frequency and damping of non-axisymmetric surface oscillations of a viscous axisymmetric liquid bridge". Physics of Fluids 24, nr 4 (kwiecień 2012): 042103. http://dx.doi.org/10.1063/1.3703658.

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TRINH, E. H., D. B. THIESSEN i R. G. HOLT. "Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid: experimental results". Journal of Fluid Mechanics 364 (10.06.1998): 253–72. http://dx.doi.org/10.1017/s0022112098001153.

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Large-amplitude oscillations of drops and bubbles immersed in an immiscible liquid host have been investigated using ultrasonic radiation pressure techniques. Single levitated or trapped drops and bubbles with effective radius between 0.2 and 0.8 cm have been driven into resonant shape oscillations of the first few orders. The direct coupling of driven drop shape oscillations between the axisymmetric l=6 and l=3 modes has been documented as well as the interaction between axisymmetric and non-axisymmetric l=3 and l=2 modes. Effective resonant energy transfer from higher- to lower-order modes has been observed together with a much less efficient energy transfer in the reverse direction. The first three resonant modes for bubbles trapped in water have also been excited, and mode coupling during driven and free-decaying oscillations has been measured. The evidence gathered thus far indicates that efficient drop resonant coupling between a higher- and a lower-order mode occurs when the characteristic frequency of the latter mode roughly coincides with a harmonic resonance.

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Yang, Shuo, Guofeng Wang, Shanshan Ma i Yu Gao. "A new cognition on oscillatory thermocapillary convection for high Prandtl number fluids". Thermal Science, nr 00 (2020): 234. http://dx.doi.org/10.2298/tsci200324234y.

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A direct numerical simulations on the oscillatory thermocapillary convection in a non-axisymmetric liquid bridge of high Pr fluids under normal gravity has been conducted by using a new method of mass conserving Level Set method for capturing any micro-scale migrations of free surface. Against the former studies, the oscillatory behaviors of surface flow (the perturbation of velocity, temperature, and free surface) and flow pattern have been quantitatively investigated simultaneously for the first time. The present results show that the instability of thermocapillary convection originates from the oscillations of velocity, temperature, and free surface at the hot corner. The velocity oscillation responds slowly to the temperature oscillation, which are opposite in transfer direction for each other, resulting in the free surface oscillation. The oscillatory thermocapillary convection in the liquid bridge is eventually excited by the coupling effects of these three kinds of oscillations, which discloses clearly the oscillatory mechanism of thermocapillary convection for high Pr fluids.

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Enriquez, Oscar R., Ivo R. Peters, Stephan Gekle, Laura E. Schmidt, Detlef Lohse i Devaraj van der Meer. "Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water". Journal of Fluid Mechanics 701 (24.04.2012): 40–58. http://dx.doi.org/10.1017/jfm.2012.130.

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AbstractThe axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long-term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number $m$ and amplitude ${a}_{m} $. For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small-amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (Nature Phys., vol. 5, 2009, pp. 343–346) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (J. Fluid Mech., vol. 633, 2009b, pp. 381–409). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off.

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Leonovich, A. S., i V. A. Mazur. "Standing Alfvén waves with m ≫ 1 in an axisymmetric magnetosphere excited by a non-stationary source". Annales Geophysicae 16, nr 8 (31.08.1998): 914–20. http://dx.doi.org/10.1007/s00585-998-0914-z.

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Abstract. As a continuation of our earlier paper, we consider here the case of the excitation of standing Alfvén waves by a source of the type of sudden impulse. It is shown that, following excitation by such a source, a given magnetic shell will exhibit oscillations with a variable frequency which increases from the shell's poloidal to toroidal frequency. Simultaneously, the oscillations will also switch over from poloidally (radially) to toroidally (azimuthally) polarized. With a reasonably large attenuation, only the start of this process, the stage of poloidal oscillations, will be observed in the ionosphere.Key words. Ionosphere-magnetosphere interactions · Wave propagation · MHD waves and instabilities

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RACZ, J. P., i J. F. SCOTT. "Parametric instability in a rotating cylinder of gas subject to sinusoidal axial compression. Part 1. Linear theory". Journal of Fluid Mechanics 595 (8.01.2008): 265–90. http://dx.doi.org/10.1017/s0022112007009238.

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An analysis is presented of parametric instability in a finite-length rotating cylinder subject to periodic axial compression by small sinusoidal oscillations of one of its ends (the ‘piston’). The instability is due to resonant interactions between inertial-wave (Kelvin) modes of the cylinder and the oscillatory compression and is resisted by viscosity, acting both through thin boundary layers and throughout the volume, the two mechanisms proving crucial for a satisfactory description. Instability is found to take the form of either a single axisymmetric mode with frequency near to half that of compression, or a pair of non-axisymmetric modes of the same azimuthal and axial orders and oppositely signed frequencies, whose difference is close to the compression frequency. Thus, in the axisymmetric case, instability leads to spontaneous growth of a system of one or more oscillating toroidal vortices encircling the cylinder axis, while the differing frequencies of the two modes of non-axisymmetric instability implies an oscillatory aperiodic flow. The neutral curves giving the threshold for instability are determined for all modes/mode pairs. For a given mode or mode pair, the neutral curve shows a critical piston amplitude dependent on rotational Reynolds number and cylinder aspect ratio, below which instability does not occur, and above which there is instability provided the compression frequency is chosen to lie in a band centred on the exact resonance condition.

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PRIEDE, JĀNIS. "Oscillations of weakly viscous conducting liquid drops in a strong magnetic field". Journal of Fluid Mechanics 671 (10.02.2011): 399–416. http://dx.doi.org/10.1017/s0022112010005781.

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We analyse small-amplitude oscillations of a weakly viscous electrically conducting liquid drop in a strong uniform DC magnetic field. An asymptotic solution is obtained showing that the magnetic field does not affect the shape eigenmodes, which remain the spherical harmonics as in the non-magnetic case. A strong magnetic field, however, constrains the liquid flow associated with the oscillations and, thus, reduces the oscillation frequencies by increasing effective inertia of the liquid. In such a field, liquid oscillates in a two-dimensional (2D) way as solid columns aligned with the field. Two types of oscillations are possible: longitudinal and transversal to the field. Such oscillations are weakly damped by a strong magnetic field – the stronger the field, the weaker the damping, except for the axisymmetric transversal and inherently 2D modes. The former are overdamped because of being incompatible with the incompressibility constraint, whereas the latter are not affected at all because of being naturally invariant along the field. Since the magnetic damping for all other modes decreases inversely with the square of the field strength, viscous damping may become important in a sufficiently strong magnetic field. The viscous damping is found analytically by a simple energy dissipation approach which is shown for the longitudinal modes to be equivalent to a much more complicated eigenvalue perturbation technique. This study provides a theoretical basis for the development of new measurement methods of surface tension, viscosity and the electrical conductivity of liquid metals using the oscillating drop technique in a strong superimposed DC magnetic field.

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Loretero, M. E., i R. F. Huang. "Behaviors of Flame and Flow of Swirling Wake During Fuel Jet Oscillation Due to Acoustic Excitations". Journal of Mechanics 26, nr 3 (wrzesień 2010): 279–86. http://dx.doi.org/10.1017/s1727719100003828.

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AbstractThe flame and flow behaviors along with the fuel jet oscillations of non-premixed and axisymmetric swirling wake during acoustic excitations are studied experimentally. Visual observations on the reaction zones are carried out to identify the flame behaviors. Close-up images at the flame base as well as the whole flame images are captured and discussed. Traditional photography techniques are adopted to illustrate the dimensional characteristics of every flame mode. The central jet oscillations are diagnosed by a two component laser Doppler anemometer. Combined images of the flame and flow are gathered using the laser-light sheet assisted Mie scattering method. Results showed that the short and wide flame which was induced during acoustic forcing is principally because of the severe premixing at the tip of the burner tube. Wake recirculation bubble enhanced premixing at low swirl number while it damped the jet oscillation at higher swirl number. Mechanics of mixing at every flame mode during acoustic excitation are reported and discussed.

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HEIL, MATTHIAS, i JONATHAN BOYLE. "Self-excited oscillations in three-dimensional collapsible tubes: simulating their onset and large-amplitude oscillations". Journal of Fluid Mechanics 652 (13.04.2010): 405–26. http://dx.doi.org/10.1017/s0022112010000157.

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We employ numerical simulations to explore the development of flow-induced self-excited oscillations in three-dimensional collapsible tubes which are subject to boundary conditions (flow rate prescribed at the outflow boundary) that encourage the development of high-frequency oscillations via an instability mechanism originally proposed by Jensen & Heil (J. Fluid Mech., vol. 481, 2003, p. 235). The simulations show that self-excited oscillations tend to arise preferentially from steady equilibrium configurations in which the tube is buckled non-axisymmetrically. We follow the growing oscillations into the large-amplitude regime and show that short tubes tend to approach an approximately axisymmetric equilibrium configuration in which the oscillations decay, whereas sufficiently long tubes develop sustained large-amplitude limit-cycle oscillations. The period of the oscillations and the critical Reynolds number beyond which their amplitude grows are found to be in good agreement with theoretical scaling estimates.

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Shul'ga, N. A., A. Ya Grigorenko i T. L. Efimova. "Free non-axisymmetric oscillations of a thick-walled, nonhomogeneous, transversally isotropic, hollow sphere". Soviet Applied Mechanics 24, nr 5 (maj 1988): 439–44. http://dx.doi.org/10.1007/bf00883063.

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KIDAMBI, RANGACHARI. "Frequency and damping of non-axisymmetric surface oscillations of a viscous cylindrical liquid bridge". Journal of Fluid Mechanics 681 (29.06.2011): 597–621. http://dx.doi.org/10.1017/jfm.2011.225.

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We present a semi-analytic solution for the non-axisymmetric oscillations of a viscous cylindrical free-standing liquid bridge formed between two coaxial discs of radius R. Even though a streamfunction does not exist, a Helmholtz decomposition is used to obtain an analytic representation of the velocity field. An eigenvalue problem is formulated by projecting the free-surface boundary conditions onto a suitable space of test functions. This is then solved iteratively along with the dispersion relation obtained from the satisfaction of endwall boundary conditions. Extensive comparison with previous theoretical and numerical results, for a range of Reynolds number and bridge slenderness ratio, shows very good agreement in most cases. The present solution generalises that of Tsamopoulos, Chen & Borkar (J. Fluid Mech., vol. 235, 1992, p. 579), which employed a streamfunction formulation and was for the axisymmetric case.

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Shtemler, Yuri, i Michael Mond. "Vertical shear-induced resonant triads in Keplerian discs". Monthly Notices of the Royal Astronomical Society 488, nr 3 (25.07.2019): 4207–19. http://dx.doi.org/10.1093/mnras/stz2032.

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ABSTRACT The vertical-shear instability (VSI) is studied through weakly non-linear analysis of unmagnetized vertically isothermal thin Keplerian discs under small radial temperature gradients. Vertically global and radially local axisymmetric compressible perturbations are considered. The VSI excites three classes of quasi-resonant triads of non-linearly interacting modes characterized by distinct temporal evolution. Most of the triads belong to the two-mode regime of non-linear interaction. Such triads are comprised of one unstable non-linear mode that grows quasi-exponentially, and two other modes that practically decoupled from the former. The latter two modes perform non-linear oscillations around their either linear prototypes (class I) or respective initial values (class II). The rest of the resonant triads belong to class III where all three modes exhibit non-linear oscillations. The proposed model describes an intermediate non-linear stage of the VSI prior to its saturation.

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Subbotin, Stanislav. "Non-axisymmetric flow excited by fluid oscillations in a rotating cylinder with sloping ends". Journal of Physics: Conference Series 1809, nr 1 (1.02.2021): 012015. http://dx.doi.org/10.1088/1742-6596/1809/1/012015.

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Yoshida, Shin'ichirou. "Non-axisymmetric oscillations of a torus around a Schwarzschild black hole: a toy problem". Classical and Quantum Gravity 23, nr 23 (20.10.2006): 6899–917. http://dx.doi.org/10.1088/0264-9381/23/23/018.

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Oberleithner, Kilian, Lothar Rukes i Julio Soria. "Mean flow stability analysis of oscillating jet experiments". Journal of Fluid Mechanics 757 (19.09.2014): 1–32. http://dx.doi.org/10.1017/jfm.2014.472.

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AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

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HEIL, MATTHIAS, i SARAH L. WATERS. "How rapidly oscillating collapsible tubes extract energy from a viscous mean flow". Journal of Fluid Mechanics 601 (25.04.2008): 199–227. http://dx.doi.org/10.1017/s0022112008000463.

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We present a combined theoretical and computational analysis of three-dimensional unsteady finite-Reynolds-number flows in collapsible tubes whose walls perform prescribed high-frequency oscillations which resemble those typically observed in experiments with a Starling resistor. Following an analysis of the flow fields, we investigate the system's overall energy budget and establish the critical Reynolds number, Recrit, at which the wall begins to extract energy from the flow. We conjecture that Recrit corresponds to the Reynolds number beyond which collapsible tubes are capable of performing sustained self-excited oscillations. Our computations suggest a simple functional relationship between Recrit and the system parameters, and we present a scaling argument to explain this observation. Finally, we demonstrate that, within the framework of the instability mechanism analysed here, self-excited oscillations of collapsible tubes are much more likely to develop from steady-state configurations in which the tube is buckled non-axisymmetrically, rather than from axisymmetric steady states, which is in agreement with experimental observations.

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Gokhale, M. H. "Study of long period global oscillations of Sun through spherical harmonic Fourier analysis of sunspot activity". Symposium - International Astronomical Union 123 (1988): 219–22. http://dx.doi.org/10.1017/s0074180900158115.

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A spherical-harmonic-fourier analysis of the maximum areas of sunspot groups listed in Ledgers I and II of Greenwich photoheliographic results for 1933–1954 yield significant peaks at the 11y periodicity for some spherical harmonic modes: especially the mode (ℓ = 6, m = 0). A similar analysis of the daily areas of the spotgroups during 1944–1954 yields 11y periodicity peaks only for some non-axisymmetric modes. These results suggest that the sunspot activity may be physically related to long period global oscillations of the sun.

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Kato, Shoji. "Trapping of Non-Axisymmetric $g$-Mode Oscillations in Thin Relativistic Disks and kHz QPOs: Fig. 1". Publications of the Astronomical Society of Japan 53, nr 5 (25.10.2001): L37—L40. http://dx.doi.org/10.1093/pasj/53.5.l37.

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Fuller, J., D. W. Kurtz, G. Handler i S. Rappaport. "Tidally trapped pulsations in binary stars". Monthly Notices of the Royal Astronomical Society 498, nr 4 (22.09.2020): 5730–44. http://dx.doi.org/10.1093/mnras/staa2376.

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ABSTRACT A new class of pulsating binary stars was recently discovered, whose pulsation amplitudes are strongly modulated with orbital phase. Stars in close binaries are tidally distorted, so we examine how a star’s tidally induced asphericity affects its oscillation mode frequencies and eigenfunctions. We explain the pulsation amplitude modulation via tidal mode coupling such that the pulsations are effectively confined to certain regions of the star, e.g. the tidal pole or the tidal equator. In addition to a rigorous mathematical formalism to compute this coupling, we provide a more intuitive semi-analytic description of the process. We discuss three resulting effects: (1) Tidal alignment, i.e. the alignment of oscillation modes about the tidal axis rather than the rotation axis; (2) Tidal trapping, e.g. the confinement of oscillations near the tidal poles or the tidal equator; (3) Tidal amplification, i.e. increased flux perturbations near the tidal poles where acoustic modes can propagate closer to the surface of the star. Together, these phenomena can account for the pulsation amplitude and phase modulation of the recently discovered class of ‘tidally tilted pulsators.’ We compare our theory to the three tidally tilted pulsators HD 74423, CO Cam, and TIC 63328020, finding that tidally trapped modes that are axisymmetric about the tidal axis can largely explain the first two, while a non-axisymmetric tidally aligned mode is present in the latter. Finally, we discuss implications and limitations of the theory, and we make predictions for the many new tidally tilted pulsators likely to be discovered in the near future.

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NICHOLS, JOSEPH W., i PETER J. SCHMID. "The effect of a lifted flame on the stability of round fuel jets". Journal of Fluid Mechanics 609 (31.07.2008): 275–84. http://dx.doi.org/10.1017/s0022112008002528.

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The stability and dynamics of an axisymmetric lifted flame are studied by means of direct numerical simulation (DNS) and linear stability analysis of the reacting low-Mach-number equations. For light fuels (such as non-premixed methane/air flames), the non-reacting premixing zone upstream of the lifted flame base contains a pocket of absolute instability supporting self-sustaining oscillations, causing flame flicker even in the absence of gravity. The liftoff heights of the unsteady flames are lower than their steady counterparts (obtained by the method of selective frequency damping (SFD)), owing to premixed flame propagation during a portion of each cycle. From local stability analysis, the lifted flame is found to have a significant stabilizing influence at and just upstream of the flame base, which can truncate the pocket of absolute instability. For sufficiently low liftoff heights, the truncated pocket of absolute instability can no longer support self-sustaining oscillations, and the flow is rendered globally stable.

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Aubert, Julien, i Nicolas Gillet. "The interplay of fast waves and slow convection in geodynamo simulations nearing Earth’s core conditions". Geophysical Journal International 225, nr 3 (10.02.2021): 1854–73. http://dx.doi.org/10.1093/gji/ggab054.

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SUMMARY Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual timescale range where Earth’s core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth’s core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the relevance of the approach to describe Earth’s core dynamics. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfvén torsional waves, and non-axisymmetric, quasi-geostrophic Alfvén and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal timescales, thereby providing a constraint on the extent of the $f^{-4}$ range observed in the geomagnetic frequency power spectrum. As the model approaches Earth’s core conditions, this spectral broadening arises because the decreasing inertia allows for waves at increasing frequencies. Through non-linear energy transfers with convection underlain by Lorentz stresses, these waves also extract an increasing amount of energy from the underlying convection as their key timescale decreases towards a realistic value. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion timescale to the Alfvén timescale, highlighting the dominance of Alfvén waves in the signal and the stabilizing control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth’s core conditions supports the detectability of Alfvén waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.

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36

Mannix, P. M., i A. J. Mestel. "Weakly nonlinear mode interactions in spherical Rayleigh–Bénard convection". Journal of Fluid Mechanics 874 (9.07.2019): 359–90. http://dx.doi.org/10.1017/jfm.2019.440.

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In an annular spherical domain with separation $d$, the onset of convective motion occurs at a critical Rayleigh number $Ra=Ra_{c}$. Solving the axisymmetric linear stability problem shows that degenerate points $(d=d_{c},Ra_{c})$ exist where two modes simultaneously become unstable. Considering the weakly nonlinear evolution of these two modes, it is found that spatial resonances play a crucial role in determining the preferred convection pattern for neighbouring modes $(\ell ,\ell \pm 1)$ and non-neighbouring even modes $(\ell ,\ell \pm 2)$. Deriving coupled amplitude equations relevant to all degeneracies, we outline the possible solutions and the influence of changes in $d,Ra$ and Prandtl number $Pr$. Using direct numerical simulation (DNS) to verify all results, time periodic solutions are also outlined for small $Pr$. The $2:1$ periodic signature observed to be general for oscillations in a spherical annulus is explained using the structure of the equations. The relevance of all solutions presented is determined by computing their stability with respect to non-axisymmetric perturbations at large $Pr$.

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37

Boryseiko, O. V., V. I. Denysenko i Yu F. Didenko. "Vibrations of a cylindrical piezoshell filled with a fluid". Reports of the National Academy of Sciences of Ukraine, nr 11 (2020): 31–38. http://dx.doi.org/10.15407/dopovidi2020.11.031.

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Stationary oscillations of a piezoceramic cylindrical shell with thickness polarization under the action of a time-harmonic mechanical load in the form of an external pressure are considered. The shell has a finite length and is closed at the ends with rigid plates. The inner volume of the shell is filled with a non-viscous compressible liquid. A continuous thin electrode coating is applied to the cylindrical surfaces of the shell. Surface electrodes are considered open. The equations of axisymmetric oscillations and the corresponding boundary conditions at the ends are written in the problem statement for the shell. A problem is formulated also for determining the motion in the form of small oscillations of a liquid inside the shell, as well as the boundary conditions for the equality of velocities of liquid particles and the shell on their contact surfaces. An analytic expression is given for determining the distribution of the thickness component of the electric field strength, which arises due to the deformation of the shell element, depending on the frequency of oscillations of the external mechanical load. The results of numerical calculations are shown.

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38

JI, Jianghui, Shangli OU i Lin LIU. "Baroclinic generation of potential vorticity in an embedded planet-disk system". Proceedings of the International Astronomical Union 3, S249 (październik 2007): 407–12. http://dx.doi.org/10.1017/s1743921308016918.

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AbstractWe use a multi-dimensional hydrodynamics code to study the gravitational interaction between an embedded planet and a protoplanetary disk with emphasis on the generation of vortensity (Potential Vorticity or PV) through a Baroclinic Instability. We show that the generation of PV is very common and effective in non-barotropic disks through the Baroclinic Instability, especially within the coorbital region. Our results also complement previous work that non-axisymmetric Rossby-Wave Instabilities (RWIs) are likely to develop at local minima of PV distribution that are generated by the interaction between a planet and an inviscid barotropic disk. The development of RWIs results in non-axisymmetric density blobs, which exert stronger torques onto the planet when they move to the vicinity of the planet. Hence, large amplitude oscillations are introduced to the time behavior of the total torque acted on the planet by the disk. In current simulations, RWIs do not change the overall picture of inward orbital migration but cause a non-monotonic behavior to the migration speed. As a side effect, RWIs also introduce interesting structures into the disk. These structures may help the formation of Earth-like planets in the Habitable Zone or Hot Earths interior to a close-in giant planet.

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39

Moya-Torregrosa, I., A. Fuentes, J. M. Martí, J. L. Gómez i M. Perucho. "Magnetized relativistic jets and helical magnetic fields". Astronomy & Astrophysics 650 (czerwiec 2021): A60. http://dx.doi.org/10.1051/0004-6361/202037898.

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This is the first of a series of two papers that deepen our understanding of the transversal structure and the properties of recollimation shocks of axisymmetric, relativistic, superfast magnetosonic, overpressured jets. They extend previous work that characterized these properties in connection with the dominant type of energy (internal, kinetic, or magnetic) in the jet to models with helical magnetic fields with larger magnetic pitch angles and force-free magnetic fields. In this paper, the magnetohydrodynamical models were computed following an approach that allows studying the structure of steady, axisymmetric, relativistic (magnetized) flows using one-dimensional time-dependent simulations. In these approaches, the relevance of the magnetic tension and of the Lorentz force in shaping the internal structure of jets (transversal structure, radial oscillations, and internal shocks) is discussed. The radial Lorentz force controls the jet internal transversal equilibrium. Hence, highly magnetized non-force-free jets exhibit a thin spine of high internal energy around the axis. The properties of the recollimation shocks and sideways expansions and compressions of the jet result from the total pressure mismatch at the jet surface, which among other factors depends on the magnetic tension and the magnetosonic Mach number of the flow. Hot jets with low Mach number tend to have strong oblique shocks and wide radial oscillations. Highly magnetized jets with large toroidal fields tend to have weaker shocks and radial oscillations of smaller amplitude. In the second paper, we present synthetic synchrotron radio images of the magnetohydrodynamical models that are produced at a post-processing phase, focusing on the observational properties of the jets, namely the top-down emission asymmetries, spine brightening, the relative intensity of the knots, and polarized emission.

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40

Sivertsson, S., J. I. Read, H. Silverwood, P. F. de Salas, K. Malhan, A. Widmark, C. F. P. Laporte, S. Garbari i K. Freese. "Estimating the local dark matter density in a non-axisymmetric wobbling disc". Monthly Notices of the Royal Astronomical Society 511, nr 2 (8.02.2022): 1977–91. http://dx.doi.org/10.1093/mnras/stac094.

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ABSTRACT The density of dark matter near the Sun, ρDM, ⊙, is important for experiments hunting for dark matter particles in the laboratory, and for constraining the local shape of the Milky Way’s dark matter halo. Estimates to date have typically assumed that the Milky Way’s stellar disc is axisymmetric and in a steady-state. Yet the Milky Way disc is neither, exhibiting prominent spiral arms and a bar, and vertical and radial oscillations. We assess the impact of these assumptions on determinations of ρDM, ⊙ by applying a free-form, steady-state, Jeans method to two different N-body simulations of Milky Way-like galaxies. In one, the galaxy has experienced an ancient major merger, similar to the hypothesized Gaia–Sausage–Enceladus; in the other, the galaxy is perturbed more recently by the repeated passage and slow merger of a Sagittarius-like dwarf galaxy. We assess the impact of each of the terms in the Jeans–Poisson equations on our ability to correctly extract ρDM, ⊙ from the simulated data. We find that common approximations employed in the literature – axisymmetry and a locally flat rotation curve – can lead to significant systematic errors of up to a factor ∼1.5 in the recovered surface mass density ∼2 kpc above the disc plane, implying a fractional error on ρDM, ⊙ of the order of unity. However, once we add in the tilt term and the rotation curve term in our models, we obtain an unbiased estimate of ρDM, ⊙, consistent with the true value within our 95 per cent confidence intervals for realistic 20 per cent uncertainties on the baryonic surface density of the disc. Other terms – the axial tilt, 2nd Poisson and time-dependent terms – contribute less than 10 per cent to ρDM, ⊙ (given current data) and can be safely neglected for now. In the future, as more data become available, these terms will need to be included in the analysis.

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Pavliuk, A. V. "Dynamics of Three-layer Cylindrical Shells Elliptical Cross-Section With a Longitudinal-Transverse Discrete Ribbed Filler". Фізика і хімія твердого тіла 18, nr 2 (15.06.2017): 243–48. http://dx.doi.org/10.15330/pcss.18.2.243-248.

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In this paper, we consider the equations of non-axisymmetric oscillations of discretely reinforced multilayer cylindrical shells of elliptical section. When analyzing the elements of the elastic structure, a refinement model of the theory of shells and rods of the Timoshenko type is used. The numerical method of solving the dynamic equations is based on the integro- interpolation method of constructing the finite-difference schemes for equations with discontinuous coefficients. The problem of dynamic behavior of a three-layer longitudinal-transversal reinforced cylindrical shell of an elliptical section under a distributed nonstationary load is investigated. A solution of the problem on dynamic behaviour of the three-layered cylindrical shell with some discrete longitudinal-transverse ribbed filler is considered for distributed non-stationary loading.

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42

ZHANG, Wei, Zhiwei MA, Haowei ZHANG i Xin WANG. "Sawtooth-like oscillations and steady states caused by the m/n = 2/1 double tearing mode". Plasma Science and Technology 24, nr 3 (1.03.2022): 035104. http://dx.doi.org/10.1088/2058-6272/ac4bb4.

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Abstract The sawtooth-like oscillations resulting from the m / n = 2 / 1 double tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of the m / n = 2 / 1 DTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state with m / n = 2 / 1 magnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity of m / n = 2 / 1 . Like the steady state with m / n = 1 / 1 radial flow, which is beneficial for preventing the helium ash accumulation in the core, the steady state with m / n = 2 / 1 radial flow might also be a good candidate for the advanced steady state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry, which implies that the steady state with saturated m / n = 2 / 1 islands might exist in different tokamaks.

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43

Xiong, Junhao, Kaiyong Yang, Tao Xia, Jingyu Li, Yonglei Jia, Yunfeng Tao, Yao Pan i Hui Luo. "A High-Precision Method of Stiffness Axes Identification for Axisymmetric Resonator Gyroscopes". Micromachines 13, nr 10 (21.10.2022): 1793. http://dx.doi.org/10.3390/mi13101793.

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Axisymmetric resonators are key elements of Coriolis vibratory gyroscopes (CVGs). The performance of a CVG is closely related to the stiffness and damping symmetry of its resonator. The stiffness symmetry of a resonator can be effectively improved by electrostatic tuning or mechanical trimming, both of which need an accurate knowledge of the azimuth angles of the two stiffness axes of the resonator. Considering that the motion of a non-ideal axisymmetric resonator can be decomposed as two principal oscillations with two different natural frequencies along two orthogonal stiffness axes, this paper introduces a novel high-precision method of stiffness axes identification. The method is based on measurements of the phase difference between the signals detected at two orthogonal sensing electrodes when an axisymmetric resonator is released from all the control forces of the force-to-rebalance mode and from different initial pattern angles. Except for simplicity, our method works with the eight-electrodes configuration, in no need of additional electrodes or detectors. Furthermore, the method is insensitive to the variation of natural frequencies and operates properly in the cases of either large or small frequency splits. The introduced method is tested on a resonator gyroscope, and two stiffness axes azimuth angles are obtained with a resolution better than 0.1°. A comparison of the experimental results and theoretical model simulations confirmed the validity of our method.

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44

Cébron, D., S. Vantieghem i W. Herreman. "Libration-driven multipolar instabilities". Journal of Fluid Mechanics 739 (2.01.2014): 502–43. http://dx.doi.org/10.1017/jfm.2013.623.

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AbstractWe consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestrial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the libration-driven multipolar instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the nonlinear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration-driven elliptical instability simply corresponds to the particular case $n= 2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally.

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45

Maksat, Kalimoldayev, Kuspanova Kalipa, Baisalbayeva Kulyash, Mamyrbayev Orken i Abdildayeva Assel. "Numerical simulation of two-phase filtration in the near well bore zone". Open Engineering 8, nr 1 (19.04.2018): 77–86. http://dx.doi.org/10.1515/eng-2018-0010.

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Abstract On the basis of the fundamental laws of energy conservation, nonstationary processes of filtration of two-phase liquids in multilayered reservoirs in the near well bore zone are considered. Number of reservoirs, fluid pressure in the given reservoirs, reservoir permeability, oil viscosity, etc. are taken into account upon that. Plane-parallel flow and axisymmetric cases have been studied. In the numerical solution, non-structured meshes are used. Closer to the well, the meshes thicken. The integration step over time is defined by the generalized Courant inequality. As a result, there are no large oscillations in the numerical solutions obtained. Oil production rates, Poisson’s ratios, D-diameters of the well, filter height, filter permeability, and cumulative thickness of the filter cake and the area have been taken as the main inputs in numerical simulation of non-stationary processes of two-phase filtration.

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Passamonti, A., i N. Andersson. "Merger-inspired rotation laws and the low-T/W instability in neutron stars". Monthly Notices of the Royal Astronomical Society 498, nr 4 (10.09.2020): 5904–15. http://dx.doi.org/10.1093/mnras/staa2725.

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ABSTRACT Implementing a family of differential rotation laws inspired by binary neutron-star merger remnants, we consider the impact of the rotation profile on the low-T/W instability. We use time evolutions of the linearized dynamical equations, in Newtonian gravity, to study non-axisymmetric oscillations and identify the unstable modes. The presence and evolution of the low-T/W instability is monitored with the canonical energy and angular momentum, while the growth time is extracted from the evolved kinetic energy. The results for the new rotation laws highlight similarities with the commonly considered j-constant law. The instability sets in when an oscillation mode corotates with the star (i.e. whenever there is a point at which the mode’s pattern speed matches the bulk angular velocity) and grows faster deep inside the co-rotation region. However, the new profiles add features, like an additional co-rotation point, to the problem, and these affect the onset of instability. The rotation laws have the most drastic influence on the oscillation frequencies of the l = m = 2 f mode in fast-rotating models, but affect the instability growth time at some level for any rotation rate. We also identify models where the low-T/W instability appears to be triggered by inertial modes. We discuss to what extent the inferred qualitative behaviour is likely to be of observational relevance.

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Belvedere, Gaetano. "The effect of toroidal magnetic fields in the overshoot layer on the eigenfrequencies of stellar oscillations". Symposium - International Astronomical Union 123 (1988): 167–70. http://dx.doi.org/10.1017/s0074180900157997.

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The overshoot layer in stellar convection zones is slightly subadiabatic and can be considered as a stable region for storage of magnetic flux. Belvedere, Pidatella and Stix (1986) estimated the size of the overshoot layer and computed the magnetic field strength, beyond which toroidal flux tubes become unstable to buoyancy, for a number of main sequence spectral types ranging from F5 to K0. Here we estimate the relative frequency perturbation of high order acoustic modes due to the presence of a non-oblique axisymmetric magnetic field in the overshoot layer. We find that increases with the advancing spectral type, the predicted frequency splitting being large enough to be detected by observations, at least for the Sun.We conclude that magnetic field induced frequency splitting of high order acoustic modes may well be due to a toroidal field of relatively moderate strength just beneath the bottom of the convection zone.

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MAAS, LEO R. M., i UWE HARLANDER. "Equatorial wave attractors and inertial oscillations". Journal of Fluid Mechanics 570 (3.01.2007): 47–67. http://dx.doi.org/10.1017/s0022112006002904.

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Three different approximations to the axisymmetric small-disturbance dynamics of a uniformly rotating thin spherical shell are studied for the equatorial region assuming time-harmonic motion. The first is the standard β-plane model. The second is Stern's (Tellus, vol. 15, 1963, p. 246) homogeneous, equatorial β-plane model of inertial waves (that includes all Coriolis terms). The third is a version of Stern's equation extended to include uniform stratification. It is recalled that the boundary value problem (BVP) that governs the streamfunction of zonally symmetric waves in the meridional plane becomes separable only for special geometries. These separable BVPs allow us to make a connection between the streamfunction field and the underlying geometry of characteristics of the governing equation. In these cases characteristics are each seen to trace a purely periodic path. For most geometries, however, the BVP is non-separable and characteristics and therefore wave energy converge towards a limit cycle, referred to as an equatorial wave attractor. For Stern's model we compute exact solutions for wave attractor regimes. These solutions show that wave attractors correspond to singularities in the velocity field, indicating an infinite magnification of kinetic energy density along the attractor. The instability that arises occurs without the necessity of any ambient shear flow and is referred to as geometric instability.For application to ocean and atmosphere, Stern's model is extended to include uniform stratification. Owing to the stratification, characteristics are trapped near the equator by turning surfaces. Characteristics approach either equatorial wave attractors, or point attractors situated at the intersections of turning surfaces and the bottom. At these locations, trapped inertia–gravity waves are perceived as near-inertial oscillations. It is shown that trapping of inertia–gravity waves occurs for any monochromatic frequency within the allowed range, while equatorial wave attractors exist in a denumerable, infinite set of finite-sized continuous frequency intervals. It is also shown that the separable Stern equation, obtained as an approximate equation for waves in a homogeneous fluid confined to the equatorial part of a spherical shell, gives an exact description for buoyancy waves in uniformly but radially stratified fluids in such shells.

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Roy, Abhradeep, Arkadipta Sarkar, Anshu Chatterjee, Alok C. Gupta, Varsha Chitnis i P. J. Wiita. "Transient quasi-periodic oscillations at γ-rays in the TeV blazar PKS 1510-089". Monthly Notices of the Royal Astronomical Society 510, nr 3 (21.12.2021): 3641–49. http://dx.doi.org/10.1093/mnras/stab3701.

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ABSTRACT We present periodicity search analyses on the γ-ray light curve of the TeV blazar PKS 1510-089 observed by the Fermi Large Area Telescope. We report the detection of two transient quasi-periodic oscillations: A 3.6-d QPO during the outburst in 2009 that lasted five cycles (MJD 54906–54923); and a periodicity of 92 d spanning over 650 d from 2018 to 2020 (MJD 58200–58850), which lasted for seven cycles. We employed the Lomb–Scargle periodogram, Weighted Wavelet Z-transform, redfit, and the Monte Carlo light-curve simulation techniques to find any periodicity and the corresponding significance. The 3.6-d QPO was detected at a moderate significance of ∼3.5σ, while the detection significance of the 92-d QPO was ∼7.0σ. We explore a few physical models for such transient QPOs including a binary black hole system, precession of the jet, a non-axisymmetric instability rotating around the central black hole near the innermost stable circular orbit, the presence of quasi-equidistant magnetic islands inside the jet, and a geometric model involving a plasma blob moving helically inside a curved jet.

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RIBOUX, GUILLAUME, ÁLVARO G. MARÍN, IGNACIO G. LOSCERTALES i ANTONIO BARRERO. "Whipping instability characterization of an electrified visco-capillary jet". Journal of Fluid Mechanics 671 (7.02.2011): 226–53. http://dx.doi.org/10.1017/s0022112010005586.

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The charged liquid micro-jet issued from a Taylor cone may develop a special type of non-axisymmetric instability, usually referred to in the literature as a whipping mode. This instability usually manifests itself as a series of fast and violent lashes of the charged jet, which makes its characterization in the laboratory difficult. Recently, we have found that this instability may also develop when the host medium surrounding the Taylor cone and the jet is a dielectric liquid instead of air. When the oscillations of the jet occur inside a dielectric liquid, their frequency and amplitude are much lower than those of the oscillations taking place in air. Taking advantage of this fact, we have performed a detailed experimental characterization of the whipping instability of a charged micro-jet within a dielectric liquid by recording the jet motion with a high-speed camera. Appropriate image processing yields the frequency and wavelength, among the other important characteristics, of the jet whipping as a function of the governing parameters of the experimental set-up (flow rate and applied electric field) and liquid properties. Alternatively, the results can be also written as a function of three dimensionless numbers: the capillary and electrical Bond numbers and the ratio between an electrical relaxation and residence time.

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