Lateral Vortex Dynamics behind Ahmed body

The flow-field in the wake of Ahmed body was studied experimentally. The study is oriented on unsteady behavior of the lateral vortex pair arising in the wake as well as on the wake itself. The time-mean characteristics of the wake flow are presented. The dynamical behavior of the longitudinal vortex pair is studied in details. The Stereo Time-Resolved PIV method was applied in the wake plane perpendicular to the mean flow. Two variants of Ahmed Body with slat angle 25 and 35 degrees are investigated respectively. Comparison shows considerable differences in the vortex pair topology and dynamics of the cases in question. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective Dynamics of a Magnetic Vortex in a Local Potential

We study a simplified mean field model of superconductor dynamics in the presence of impurities or for variable superconductor depth. This model is given by the gradient-flow version of the Ginzburg-Landau equations (Gorkov-Eliashberg equations) with an addition of a potential term. We find a dynamical law of motion of the vortex center, involving the potential, such that for datum close to a (static) magnetic vortex the solution is close, for all times, to a magnetic vortex whose center obeys this law.     

周期扰动下卫星运动系统的动力学性质

本文运用Melnikov方法对平面卫星运动系统在周期扰动下所表现出来的动力学性质进行了探讨.首先运用次谐Melnikov方法给出了卫星轨道在周期扰动下存在次谐周期轨道的条件,并进一步运用同宿.Melnikov方法证实了该系统存在Smale马蹄意义下的混沌性质.     

On Tzitzéica Vortex Streets and Their Reciprocals in Subsonic Gas Dynamics

Hydrodynamic vortex street solutions are generated based on an elliptic Tzitzéica model. A multiparameter class of reciprocal transformations is coupled with the action of a Bäcklund transformation to construct compressible vortex solutions of breather type valid in subsonic flow régimes of a generalized Kármán–Tsien gas.     

Dynamics of a Local Perturbation in the X-Y Model II—Excitations

Excitations of a single spin embedded in the X Y chain are studied. We find that the magnetization does not approach equilibrium, even if the external magnetic field approaches a non-zero limit, and that oscillatory excitation resonates with the edge of the one-particle spectrum band.     

The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics

We investigate the regularization of Moore’s singularities by surface tension in the evolution of vortex sheets and its dependence on the Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing up at finite time t ₀, grows exponentially fast up to a O(We) limiting value close to t ₀. We describe the analytic structure of the solutions and their self-similar features and characteristic scales in terms of the Weber number in a O(We⁻¹) neighborhood of the time at which, in absence of surface tension effects, Moore’s singularity would appear. Our arguments rely on asymptotic techniques and are supported by full numerical simulations of the PDEs describing the evolution of vortex sheets.     

Field Theory Approach to the Dynamics of a Continuous Medium: A Perturbation Theory

We propose a perturbation theory that allows solving the equations of motion for the displacement vector in the body of the Earth in the framework of the linear theory of elasticity. We show that tectonic processes are primarily determined by tidal actions. We analyze the tidal effects in the Earth–Moon–Sun system.     

A Novel Formulation of Point Vortex Dynamics on the Sphere: Geometrical and Numerical Aspects

In this paper, we present a novel Lagrangian formulation of the equations of motion for point vortices on the unit 2-sphere. We show first that no linear Lagrangian formulation exists directly on the 2-sphere but that a Lagrangian may be constructed by pulling back the dynamics to the 3-sphere by means of the Hopf fibration. We then use the isomorphism of the 3-sphere with the Lie group SU(2) to derive a variational Lie group integrator for point vortices which is symplectic, second-order, and preserves the unit-length constraint. At the end of the paper, we compare our integrator with classical fourth-order Runge–Kutta, the second-order midpoint method, and a standard Lie group Munthe-Kaas method.     

Dynamics of a Local Perturbation in the XY Model. I—Approach to Equilibrium

The magnetisation and spin correlation functions of the X–Y model are analysed exactly when the system is subjected to a local perturbation of the magnetic field in the z-direction. When such a perturbation is removed, these quantities approach their equilibrium values asymptotically as (time)^?1.     

Perturbation models

A Markov chain (with a discrete state space and a continuous parameter) is perturbed by forcing a chain to return to “permissible” states whenever it happens to enter “forbidden” states, with returns governed by a replacement distribution.The compensation method is employed to obtain the distribution for the modified chain, in terms of the original chain and the perturbation mechanism.Emphasis is placed on ergodic chains, and interpretation of results in terms of perturbation theory of semi-groups and the ergodic potential theory (based on the fundamental matrix of a chain) is mentioned.     

Perturbation in eigenvalues

We study the dependence of the eigenvalues of a tridiagonal matrix upon off-diagonal entries. The change in the eigenvalues when a cross-diagonal product approaches zero or infinity is estimated.     

Vortex Filament Method

In this paper, the convergence of the vortex filament methodfor three-dimensional incompressible and inviscid fluid flowis proved. Properties of consistency and stability are analysed.The foundation for studying these properties is based on thecubature formulae with lines as well as on the specific useof the vector measure that transports the vorticity by the flow,preserving the filament structure of the solution of the problem.In this way, the method takes into account the stretching termimplicitly.     

伴有边界摄动二阶非线性系统的奇摄动

讨论了伴有边界摄动的含积分算子的二阶非线性微分方程组边值问题的奇摄动.在适当的假设条件下,通过对角化技巧,证明了解的存在,并估计了余项.     

Vortex design problem

In this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity. The problem is formulated as a PDE-constrained optimization in which the solutions are found using a gradient-based descent method. Recognizing such Euler flows as free-boundary problems, the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients. In explicit tracking of interfaces (vortex boundaries) this method offers an alternative to grid-based techniques, such as the level-set methods, and represents a natural optimization formulation for vortex problems computed using the contour dynamics technique. We develop and validate this approach using the design of 2D equilibrium Euler flows with finite-area vortices as a model problem. It is also discussed how the proposed methodology can be applied to Euler flows featuring other vorticity distributions, such as vortex sheets, and to time-dependent phenomena.