On the persistence of non-axisymmetric vortices in inviscid two-dimensional flows
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Previous research has suggested that isolated, initially non-axisymmetric vortices in two-dimensional flows tend to become axisymmetric, in a coarse-grained sense, by purely inviscid mechanisms. That research, however, considered only vortices with broadly distributed vorticity. In this paper, it is shown that vortices with sufficiently steep edge gradients behave in a radically different way; in particular they can remain non-axisymmetric, apparently indefinitely. Such vortices, it is argued, are more typical in inviscid two-dimensional flows than the broadly distributed vortices previously considered, and hence the tendency for vortices to become axisymmetric is not generic to these flows.Keywords:
Inviscid flow
Inviscid flow
Barotropic fluid
Geophysical fluid dynamics
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Inviscid flow
Vortex stretching
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The interaction of two equal vortices under the influence of a gradient of background vorticity (β) is studied numerically and experimentally. If the initial shape and vorticity distribution of the vortices is fixed, two parameters determine the evolution: the normalized intercentroid distance d*=d/R, where R is the radius of the vortex; and the normalized gradient of background vorticity β*=βR/ω, where ω is the peak vorticity of the vortex. Alternate ways of identifying regimes of behavior in the parameter plane (d*,β*) are presented. These are applied to numerical simulations of interaction of vortices with steplike, steep and smooth vorticity profiles. It is found that the critical distance for merger decreases with increasing β* for all vortex types, and that vortices with smooth vorticity profile are the most merger-prone vortices. Laboratory experiments were done in a rotating water tank with a flat sloping bottom providing the β effect. The vortices produced have a smooth vorticity profile and show the same behavior observed in the simulations, except that, as a result of viscous effects, the critical merger distance is shifted towards larger values of d*.
Burgers vortex
Vortex stretching
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An analysis is performed of the evolution in time of the structure- and vorticity fields in viscousand inviscid-fluid numerically simulated wave-diffraction cases. It is shown that numerical integration of the Euler equations gives rather meaningful results in terms of structure- and vorticity fields in the cases considered, as compared with the physically rigorous approach represented by the solution of the full Navier−Stokes equations.
Inviscid flow
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The generation of topological domain structures can significantly influence the behaviors of ferroelectric materials, and, however, strategies and perspectives for treating and analyzing them are still lacking. Inspired by the fluid lines and vorticity in hydromechanics, a characterization method of polarization lines and polarization vorticity is proposed herein for characterizing the vortex structure evolution. The polarization vorticity has the same unit as charge density, and the polarization vortex size is identified as a structure for vorticity concentration. Observing the radius and vorticity of vortices, we find that the domain evolution can be divided into three stages and the vortices react to mechanical loading in two ways: increasing the vorticity and enlarging the radius. Moreover, vortices exhibit three-dimensional shape, just like the vortex tube, and their conservation is proved. This paper provides a basis for further research on topological domain structures and the mechanism of vortex evolution, which might help improve high energy density devices.
Vortex stretching
Burgers vortex
Vortex Tube
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Previous research has suggested that isolated, initially non-axisymmetric vortices in two-dimensional flows tend to become axisymmetric, in a coarse-grained sense, by purely inviscid mechanisms. That research, however, considered only vortices with broadly distributed vorticity. In this paper, it is shown that vortices with sufficiently steep edge gradients behave in a radically different way; in particular they can remain non-axisymmetric, apparently indefinitely. Such vortices, it is argued, are more typical in inviscid two-dimensional flows than the broadly distributed vortices previously considered, and hence the tendency for vortices to become axisymmetric is not generic to these flows.
Inviscid flow
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We report new features observed in two-dimensional interactions of discrete vortices either isolated in vacuum or immersed in a background vorticity. The vortices are strings of electron plasma which are produced with a newly developed cathode array and trapped in a Malmberg trap. We observe long-lasting orbital motion of discrete vortices in vacuum, consistent with kinetic equations of point vortices, while a rapid re-organization occurs in the spatial distribution of vorticity when discrete vortices are immersed in an extended distribution of the background vorticity. The main features of the new observation are accounted for by a recently-proposed theoretical model incorporating collective interaction between two vortices.
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General equations are derived for the rate of change of vorticity in compressible, inviscid flow into which fluid may be introduced, and in which nonuniform body forces may exist. Examples of vorticity transfer and change are given and analogies are drawn between these examples.
Inviscid flow
Compressible flow
Vortex stretching
Burgers vortex
Incompressible Flow
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We prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. One of the key steps is a reformulation of the problem into a symmetric quasilinear Klein-Gordon system, for which the global existence of classical solutions is then proved with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity.
Inviscid flow
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Inviscid flow
Burgers vortex
Vortex stretching
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