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Academic literature on the topic 'Rotating singular interactions'
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Journal articles on the topic "Rotating singular interactions"
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SUTYRIN, GEORGI G., JAMES C. McWILLIAMS, and R. SARAVANAN. "Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores." Journal of Fluid Mechanics 357 (February 25, 1998): 321–49. http://dx.doi.org/10.1017/s0022112097008136.
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We investigate the evolution of nearby like-sign vortices whose centres are at different vertical levels in a stably stratified rotating fluid. We employ two differently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The first is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contour-dynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime.In the EM model we classify the co-rotating stationary states which exist always for vertically offset thin-core vortices. However, the mutual strain field among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex configurations, and our interpretive assumption is that such configurations will rapidly evolve in non-singular QG solutions towards a more aligned configuration through significantly non-conservative reorganizations of the potential vorticity field. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and significant filamentation and splitting in the CD solutions.
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Luo, Songrong, Junsheng Cheng, and Kexiang Wei. "A Fault Diagnosis Model Based on LCD-SVD-ANN-MIV and VPMCD for Rotating Machinery." Shock and Vibration 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/5141564.
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The fault diagnosis process is essentially a class discrimination problem. However, traditional class discrimination methods such as SVM and ANN fail to capitalize the interactions among the feature variables. Variable predictive model-based class discrimination (VPMCD) can adequately use the interactions. But the feature extraction and selection will greatly affect the accuracy and stability of VPMCD classifier. Aiming at the nonstationary characteristics of vibration signal from rotating machinery with local fault, singular value decomposition (SVD) technique based local characteristic-scale decomposition (LCD) was developed to extract the feature variables. Subsequently, combining artificial neural net (ANN) and mean impact value (MIV), ANN-MIV as a kind of feature selection approach was proposed to select more suitable feature variables as input vector of VPMCD classifier. In the end of this paper, a novel fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD is proposed and proved by an experimental application for roller bearing fault diagnosis. The results show that the proposed method is effective and noise tolerant. And the comparative results demonstrate that the proposed method is superior to the other methods in diagnosis speed, diagnosis success rate, and diagnosis stability.
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Achatz, Ulrich. "Modal and Nonmodal Perturbations of Monochromatic High-Frequency Gravity Waves: Primary Nonlinear Dynamics." Journal of the Atmospheric Sciences 64, no. 6 (June 2007): 1977–94. http://dx.doi.org/10.1175/jas3940.1.
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The primary nonlinear dynamics of high-frequency gravity waves (HGWs) perturbed by their most prominent normal modes (NMs) or singular vectors (SVs) in a rotating Boussinesq fluid have been studied by direct numerical simulations (DNSs), with wave scales and values of viscosity and diffusivity characteristic for the upper mesosphere. The DNS is 2.5D in that it has only two spatial dimensions, defined by the direction of propagation of the HGW and the direction of propagation of the perturbation in the plane orthogonal to the HGW phase direction, but describes a fully 3D velocity field. Many results of the more comprehensive fully 3D simulations in the literature are reproduced. So it is found that statically unstable HGWs are subject to wave breaking ending in a wave amplitude with respect to the overturning threshold near 0.3. It is shown that this is a result of a perturbation of the HGW by its leading transverse NM. For statically stable HGWs, a parallel NM has the strongest effect, quite in line with previous results on the predominantly 2D instability of such HGWs. This parallel mode is, however, not the leading NM but a larger-scale pattern, seemingly driven by resonant wave–wave interactions, leading eventually to energy transfer from the HGW into another gravity wave with steeper phase propagation. SVs turn out to be less effective in triggering HGW decay but they can produce turbulence of a strength that is (as that from the NMs) within the range of measured values, however with a more pronounced spatial confinement.
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Lott, François, Riwal Plougonven, and Jacques Vanneste. "Gravity Waves Generated by Sheared Potential Vorticity Anomalies." Journal of the Atmospheric Sciences 67, no. 1 (January 1, 2010): 157–70. http://dx.doi.org/10.1175/2009jas3134.1.
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Abstract The gravity waves (GWs) generated by potential vorticity (PV) anomalies in a rotating stratified shear flow are examined under the assumptions of constant vertical shear, two-dimensionality, and unbounded domain. Near a PV anomaly, the associated perturbation is well modeled by quasigeostrophic theory. This is not the case at large vertical distances, however, and in particular beyond the two inertial layers that appear above and below the anomaly; there, the perturbation consists of vertically propagating gravity waves. This structure is described analytically, using an expansion in the continuous spectrum of the singular modes that results from the presence of critical levels. Several explicit results are obtained. These include the form of the Eliassen–Palm (EP) flux as a function of the Richardson number N 2/Λ2, where N is the Brunt–Väisälä frequency and Λ the vertical shear. Its nondimensional value is shown to be approximately exp(−πN/Λ)/8 in the far-field GW region, approximately twice that between the two inertial layers. These results, which imply substantial wave–flow interactions in the inertial layers, are valid for Richardson numbers larger than 1 and for a large range of PV distributions. In dimensional form they provide simple relationships between the EP fluxes and the large-scale flow characteristics. As an illustration, the authors consider a PV disturbance with an amplitude of 1 PVU and a depth of 1 km, and estimate that the associated EP flux ranges between 0.1 and 100 mPa for a Richardson number between 1 and 10. These values of the flux are comparable with those observed in the lower stratosphere, which suggests that the mechanism identified in this paper provides a substantial gravity wave source, one that could be parameterized in GCMs.
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Caillol, Philippe. "A singular vorticity wave packet within a rapidly rotating vortex: spiralling versus oscillating motions." Journal of Fluid Mechanics 873 (June 27, 2019): 688–741. http://dx.doi.org/10.1017/jfm.2019.374.
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This paper considers a free vorticity wave packet propagating within a rapidly rotating vortex in the quasi-steady regime, a long time after the wave packet strongly and unsteadily interacted with the vortex. We study a singular, nonlinear, helical and asymmetric shear mode inside a linearly stable, columnar and axisymmetric vortex on the $f$-plane. The amplitude-modulated mode enters resonance with the vortex at a certain radius $r_{c}$, where the phase angular speed is equal to the rotation frequency. The singularity in the modal equation at $r_{c}$ strongly modifies the flow in the three-dimensional helical critical layer, the region around $r_{c}$ where the wave/vortex interaction occurs. This interaction generates a vertically sheared three-dimensional mean flow of higher amplitude than the wave packet. The chosen envelope regime assumes the formation of a mean radial velocity of the same order as the wave packet amplitude, leading to the streamlines exhibiting a spiral motion in the neighbourhood of the critical layer. Radar images frequently show such spiral bands in tropical cyclones or tornadoes. Through matched asymptotic expansions, we find an analytical solution of the leading-order equations inside the critical layer. The generalized Batchelor integral condition applied to the quasi-steady, three-dimensional motion inside the separatrices yields a leading-order, non-uniform three-dimensional vorticity. The critical-layer pattern, strongly deformed by the mean radial velocity, loses its symmetries with respect to the azimuthal and radial directions, which makes the leading-order mean radial wave fluxes non-zero. Finally, a stronger wave/vortex interaction occurs with respect to previous studies where a steady neutral vortical mode or an envelope of larger extent was involved.
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Pan, Xiao-Yin, Yin Chen, Yu-Qi Li, Aaron G. Kogan, and Juhao Wu. "On the gauge transformation for the rotation of the singular string in the Dirac monopole theory." International Journal of Modern Physics A 36, no. 03 (January 30, 2021): 2150019. http://dx.doi.org/10.1142/s0217751x21500196.
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In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function [Formula: see text] which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, [Formula: see text] is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.
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Sakajo, Takashi. "Vortex crystals on the surface of a torus." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2158 (September 30, 2019): 20180344. http://dx.doi.org/10.1098/rsta.2018.0344.
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Vortex crystals are equilibrium states of point vortices whose relative configuration is unchanged throughout the evolution. They are examples of stationary point configurations subject to a logarithmic particle interaction energy, which give rise to phenomenological models of pattern formations in incompressible fluids, superconductors, superfluids and Bose–Einstein condensates. In this paper, we consider vortex crystals rotating at a constant speed in the latitudinal direction on the surface of a torus. The problem of finding vortex crystals is formulated as a linear null equation A Γ = 0 for a non-normal matrix A whose entities are derived from the locations of point vortices, and a vector Γ consisting of the strengths of point vortices and the latitudinal speed of rotation. Point configurations of vortex crystals are obtained numerically through the singular value decomposition by prescribing their locations and/or by moving them randomly so that the matrix A becomes rank deficient. Their strengths are taken from the null space corresponding to the zero singular values. The toroidal surface has a non-constant curvature and a handle structure, which are geometrically different from the plane and the spherical surface where vortex crystals have been constructed in the preceding studies. We find new vortex crystals that are associated with these toroidal geometry: (i) a polygonal arrangement of point vortices around the line of longitude; (ii) multiple latitudinal polygonal ring configurations of point vortices that are evenly arranged around the handle; and (iii) point configurations along helical curves corresponding to the fundamental group of the toroidal surface. We observe the strengths of point vortices and the behaviour of their distribution as the number of point vortices gets larger. Their linear stability is also examined. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.
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Zhao, Le, Shaopu Yang, and Yongqiang Liu. "Weak Fault Feature Extraction of Axle Box Bearing Based on Pre-Identification and Singular Value Decomposition." Machines 10, no. 12 (December 14, 2022): 1213. http://dx.doi.org/10.3390/machines10121213.
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The axle box bearing is one of the core rotating components in high-speed trains, having served in complex working conditions for a long time. With the fault feature extraction of the vibration signal, the noise interference caused by the interaction between the wheels and rails becomes apparent. Especially when there is a shortwave defect in the rail, the interaction between wheels and rails will produce high-amplitude impulse interference. To solve the problem of the collected vibration signals of axle box bearings containing strong noise interference and high amplitude impact interference caused by rail shortwave irregularities, this paper proposes a method based on pre-identification via singular value decomposition technology to select the signals in sections and filter the noise, followed by feature extraction and fault diagnosis. The method is used to analyze the axle box bearing fault simulation signal and the weak fault signal collected by the railway bearing comprehensive experimental platform, and these signals are then compared with the random screening signal and the manual screening signal to verify the effectiveness of the method.
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Lonigro, Davide. "Generalized spin-boson models with non-normalizable form factors." Journal of Mathematical Physics 63, no. 7 (July 1, 2022): 072105. http://dx.doi.org/10.1063/5.0085576.
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Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models, which can accommodate non-normalizable form factors provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such “singular” GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation: for this model, the result is improved via a nonperturbative approach that enables us to further extend the class of admissible form factors as well as to compute its resolvent and characterize its self-adjointness domain.
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Samelson, R. M. "Lyapunov, Floquet, and singular vectors for baroclinic waves." Nonlinear Processes in Geophysics 8, no. 6 (December 31, 2001): 439–48. http://dx.doi.org/10.5194/npg-8-439-2001.
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Abstract. The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector f1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent l ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to f1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to f1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wave-dynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors.
Conference papers on the topic "Rotating singular interactions"
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Quinn, D. Dane, Curtis B. Clemons, and Kevin M. Dempsey. "The Singular Nature of Rotating Circular Rings With Symmetry." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0071.
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Abstract We study the S𝒪(2) symmetric deformation of circular rings. The equations of motion are based on general partial differential equations governing the elastodynamics of geometrically exact rings, which have been formulated by Dempsey [2], based on the work of Libai and Simmonds [6]. Thus, the formulation is valid for arbitrary pressure forcing, large deformations, and finite strains, although the results are tempered by a linear constitutive relation and an assumption of plane strain. With the assumption that the deformation retains S𝒪(2) symmetry, the partial differential equations are reduced to a set of coupled ordinary differential equations. Within this restricted space of solutions, we study the existence and stability of relative equilibria and discuss the effects of constant hydrostatic pressure on the dynamical response. Specifically, we find that interaction between inertial effects arising from rotational motion and the combined elastic and external pressure forces can produce unexpected behavior, including the existence of a “buckled” state which retains the symmetry, yet physically implies that material planes do not lie in the radial direction. Such a state is shown to effect the large-amplitude response of the system in a singular limit of the governing equations.
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Yang, Wei, Shuhong Liu, and Yulin Wu. "Application of CFD in the Design of Contra-Rotating Kaplan Turbine." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98119.
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A new type turbine which can be called contra-rotating Kaplan turbine has been designed in this paper. This new turbine, which can make power on both directions of the water flow, is mainly used in tidal power station. In this paper we discuss the feasibility of the new turbine by analyzing the velocity triangle of the inlet and outlet of the runner. According to this, we advance that two group of “S” type blades must be used to constitute the contra-rotating runner. Method of singular point distribution is used to design front-runner and rear runner based on the triangle velocity. Then the CFD simulation is used to validate and optimize the new turbine in different axial distances and different ratios of revolution speed between the front-runner and the rear runner. We simulate the internal flow field and the interaction between the front and rear runners using a three-dimensional steady turbulent flow with k-ε model and SIMPLEC method. Standard wall function is used in the turbulent calculation. From the simulation the hydraulic performance of the turbine is discussed.
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Georgiou, Ioannis T. "Experimental Investigation With Wireless Sensors of the Nonlinear Interaction Between Rotational Motions and Torsional Vibrations in a Coupled Rigid Rotor-Flexible Rotor System." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12813.
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This work presents an experimental study focused on a challenging signal interpretation issue arising in using wireless tri-axial sensors to measure acceleration components in rotating flexible rotor systems. Experiments with state of-the-art (modern technology microsystems) wireless accelerometers reveal that the dynamics of a rotating and-at the same time torsionally vibrating-flexible rotor system is perceived by the rotating sensor as a fast amplitude modulation of a slowly varying vibration. It is observed that the typical signal furnished by the rotating sensor consists of two distinct zones of harmonics: one is a broad band low frequency zone and is associated with the rigid body rotational motion, whereas the other zone contains distinct higher frequencies associated with torsional vibrations. The interesting result is the fact that in the frequency domain the fast torsional vibrations can be extracted sharply from the overall sensor signal. This is due to fact that the dynamics of the sensor output are characterized by slow and fast time scales. It turns out that the high harmonics of the rotating-and-vibrating system (generic motion) are very close to those of the non-rotating-but-torsionally vibrating system. A definite answer to a physics interpretation of the typical output of a rotating accelerometer (oscillator-based) is established by modeling the whole flexible rotor-sensor system as a singular perturbation coupled oscillators problem. This geometric mechanics modeling-analysis approach presents a global picture of the acceleration sensing property of stiff linear oscillators attached on rotating structures.
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Shabana, A. A., J. H. Choi, and H. C. Lee. "Nonlinear Dynamics and Vibrations of Three Dimensional Multibody Tracked Vehicles." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1186.
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Abstract A three dimensional model that includes significant details is developed for the nonlinear dynamic analysis of large scale multi-body tracked vehicle systems. In this model, the joint articulations of the track chains are taken into consideration so as to allow the developement of a computational procedure for the analysis of the vibrations and the contact forces of the multibody tracked vehicles. The three dimensional vehicle system is assumed to consist of three kinematically decoupled subsystems which include the chassis subsystem, and two track subsystems. A recursive approach for formulating the nonlinear equations of the vehicle based on the velocity transformation is used in this investigation in order to reduce the number of equations, avoid the solution of a system of differential and algebraic equations, and avoid the use of nonholonomic constraints to describe the rotations of the sprockets. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach to define the constraint forces at selected secondary joints of the tracks. Detailed three dimensional nonlinear contact force models that describe the interaction between the track links and the vehicle components such as the rollers, sprockets, and idlers as well as the interaction between the track links and the ground are developed and used to define the generalized contact forces associated with the vehicle generalized coordinates. In particular, body and surface coordinate systems are introduced in order to define the spatial contact conditions that describe the dynamic interaction between the teeth of the sprockets and the track link pins. These conditions provide the forces necessary for driving the tracked vehicle. The effect of the tangential friction forces on the stability of the motion of the vehicle is also discussed in this investigation. A computer simulation of a tracked vehicle that consists of one hundred and six bodies and has one hundred and twenty degrees of freedom is presented in order to demonstrate the use of the formulations presented in this study. A simple formula that can be used to predict the steady state velocity of the vehicle when the sprockets rotate with a constant angular velocity is presented and used to verify the numerical results obtained from the nonlinear dynamic simulation of the multibody vehicle.