The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.
In this paper we propose a simple yet powerful vortex method to numerically approximate the dynamics of an incompressible flow. The idea is to sample the distribution of the initial vortices of the fluid flow in question then follow vortex dynamics along Taylor's Brownian fluid particles. The weak convergences of this approximation scheme are obtained for 2D and 3D cases, though only for small time in 3D case. Based on our method, the simulation results are quite attracting.
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian geometry can be applied to search for geodesics of constrained systems such as vortex flows, where the vortex motion is restricted by rotations that are expressed by vortex-related conservation laws. The Nambu formulation of incompressible, inviscid fluid dynamics provides a nilpotent Lie algebra for two- and three-dimensional fluids, called Vortex-Heisenberg a…
Vortex shedding by a swimming sphere in a viscous incompressible fluid is studied for surface modulation characterized by a superposition of dipolar and quadrupolar, as well as for quadrupolar and octupolar displacements, varying harmonically in time. The time-dependent swimming velocity and the flow velocity are calculated to second order in the amplitude of surface modulation for both models. The models are also useful for the discussion of bird flight.
Video of vortex shedding in the wake of a Naca0009 hydrofoil made of polyoxymethylene type C (POM C). This video was submitted as part of the Gallery of Fluid Motion 2011 which is showcase of fluid dynamics videos.
In 1894 M.J.M. Hill published an article describing a spherical vortex moving through a stationary fluid. Using cylindrical coordinates and assuming the azimuthal velocity component zero, Hill found a simple solution that described this flow. A similar modern problem in the MHD framework was put forth in 1987 by A. A. Bobnev and in 1995 by R. Kaiser and D. Lortz who applied the setup to model a ball lighting. We present a much simpler derivation of Hill's spherical vortex using the Bragg-Hawthorne equation. In particular, by using the moving frame of reference, the Euler equations reduce to eq…
Although traditional vortex identification methods such as Q, Delta, Lambda2, Lambdaci remain popular in the identification and visualization of vortices, these methods count on shearing and stretching as a part of vortex strength. However, shearing and stretching do not contribute to fluid rotation. In this paper, the contamination effects of stretching and shearing of these methods are investigated and compared with Liutex method. From our investigation, the Liutex is an exact definition of fluid rotation or vortex, while other vortex identification methods are contaminated by stretching and…
Vortex rings have the ability to transport fluid over long distances. They are usually produced by ejecting a volume of fluid through a circular orifice or nozzle. When the volume and velocity of the ejected fluid are known, the vortex' circulation, impulse, and energy can be estimated by the slug flow model. Vortex rings also form in the wake of accelerating axisymmetric bodies. In this configuration, the volume and velocity of the fluid that is injected into the vortex is not known a priori. Here, we present two models to predict the growth of the vortex behind disks or cones. The first mode…
We study the development and decay of vortex in viscoelastic fluids between coaxial cylinders by means of experiments with solutions of polyacrylamide and glycerin and numerical simulations. The transient process is triggered when the inner cylinder is either abruptly started or stopped while the outer is kept fixed. The azimuthal velocity, obtained by means of digital particle velocimetry, exhibits oscillations before reaching the stationary state. The development of the vortex is characterized by means of the overshoot, i.e. the difference between the maximum and the stationary velocity. Ana…
This study presents a numerical investigation of how fluid viscoelasticity influences the flow dynamics past a transversely forced oscillating cylinder in the laminar vortex shedding regime at a fixed Reynolds number of 100. In particular, we examine how fluid viscoelasticity influences the boundary between the lock-in and no lock-in zones and the associated wake topology compared to that seen in a simple Newtonian fluid. All in all, we find that the fluid viscoelasticity facilitates the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than that re…
The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of symmetry, and is therefore an equilibrium solution of Euler's equations. In a frame of reference moving with the system of vortex rings, the motion of passive fluid particles is investigated as a function of the two non-dimensional parameters that define this system: $\varepsilon = a/R$, the ratio of minor radius to major radius of the torus-shaped vortex rin…
Quantum vortex driven Kelvin wave in the thermal background of superfluid helium
Université Côte d’Azur（蔚蓝海岸大学）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；CNRS（法国国家科学研究中心）；Institut de Physique de Nice (INPHYNI)（尼斯物理研究所）；Istituto per le Applicazioni del Calcolo M. Picone, IAC-CNR（M. Picone计算应用研究所）
Collapse of Point Vortex Dipoles in a Bounded Fluid Layer and the Hydrodynamic Mechanism of Mutual Attraction of Like-Charged Micro-Particles in the Colloid or Dusty Plasma Systems
得到了理想不可压缩流体动力学方程组在两固体边界平板内有限层中的新的精确弱解。该解决方案满足一个设计的非线性有限维哈密顿动力系统的坐标和兰姆脉冲的N点涡偶极子（PVD），即非常小的固体球形颗粒，相对于流体移动。当N=2时，给出了两个PVD坍缩（或在有限时间内收敛于一点）的必要条件。在此基础上，引入了两个相同半径的小球形粒子会聚的新的流体力学机制，并用于解释在胶体和尘埃等离子体系统中观察到的具有相同电荷符号的微粒子吸引的矛盾效应。两个物理气相沉积的坍缩条件与实验观测数据的一致性，其中只有当从上方和下方对流体层深度施加明确的必要限制时，才能观察到在流体层中运动的两个带相同电荷的微球的会聚（J.C. Crocker，D. G. Grier，1996）。我们还指出了在无界流体极限中两个PVD的崩溃条件与已知的数值结果之间的对应性的可能性，即两个有限尺寸的涡旋偶极子在无界流体中散射时实现共振键态（和相应的随机动力学区域）的碰撞参量阈值。V. Manakov，L. N. Shchur，1983; L. Tophoj，H. Aref，2008）。在这里，我们表明，在后一个过程中，偶极子的大小是不是那么重要，因为它被认为是以前。
Herein, the Karman vortex system is considered to be a large recurrent neural network, and the computational capability is numerically evaluated by emulating nonlinear dynamical systems and the memory capacity. Therefore, the Reynolds number dependence of the Karman vortex system computational performance is revealed and the optimal computational performance is achieved near the critical Reynolds number at the onset of Karman vortex shedding, which is associated with a Hopf bifurcation. Our finding advances the understanding of the relationship between the physical properties of fluid dynamics…
In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique. The Monte-Carlo method based on this random vortex dynamic may be implemented, and several Monte-Carlo simulations are then carried out for the flows near the solid wall.
If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantised vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a non-equilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond time scales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortice…
We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross--Pitaevskii model. Despite the time-reversibility of the model, we report a clear evidence that the dynamics of the reconnection process is time-irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently in Proment and Krstulovic (arXiv:2005.02047), we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the pro…
The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as the projection of a virtual construct, a circular vortex with a symmetry axis that is tilted with respect to the direction of propagation. The resulting kinetic equation offers insights into how tilt and vortex velocity coevolve in few-body nonequilibrium settings such as vortex pair nucleation and annihilation. The model is developed and applied in associati…
Adding energy to a system through transient stirring usually leads to more disorder. In contrast, point-like vortices in a bounded two-dimensional fluid are predicted to reorder above a certain energy, forming persistent vortex clusters. Here we realize experimentally these vortex clusters in a planar superfluid: a $^{87}$Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long times, maintaining the superfluid system in a high energy state far from global equilibrium. Our experiments explore a regime of vortex matter at negative absolut…
