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This article is cited in 15 scientific papers (total in 15 papers)
Dynamics of Triangular Two-Layer Vortex Structures with Zero Total Intensity
M. A. Sokolovskiya, J. Verronb a Water Problems Institute of the
Russian Academy of Sciences,
3, Gubkina Str., 119991, Moscow,
GSP-1, Russia
b Laboratoire des Ecoulements
Géophysiques et Industriels,
UMR 5519, CNRS, BP53 X,
38041, Grenoble Cedex, France
Abstract:
The problem of three vortex lines in a homogeneous layer of an ideal incompressible fluid is generalized to the case of a two-layer liquid with constant density values in each layer. For zero-complex-momentum systems the theory of the roundabout two-layer tripole is built. When the momentum is different from zero, based on the phase portraits in trilinear coordinates, a classification of possible relative motions of a system composed of three discrete (or point) vortices is provided. One vortex is situated in the upper layer, and the other two in the lower layer; their total intensity is zero. More specifically, a model of a two-layer tripole is constructed, and existence conditions for stationary solutions are found. These solutions represent a uniform translational motion of the following vortex structures: 1) a stable collinear configuration triton, a discrete analog of the vortex structure modon+rider, 2) an unstable triangular configuration. Features of the absolute motion of the system of three discrete vortices were studied numerically.
We compared the dynamics of a system of three point vortices with the dynamics of three finite-core vortices (vortex patches). In studying the evolution of the vortex patch system, a two-layer version of the Contour Dynamics Method (CDM) was used. The applicability of discrete-vortex theory to the description of the finite-size vortex behavior is dicussed. Examples of formation of vortical configurations are given. Such configurations appear either after merging of vortices of the same layer or as a result of instability of the two-layer vortex structure.
Received: 28.06.2002
Citation:
M. A. Sokolovskiy, J. Verron, “Dynamics of Triangular Two-Layer Vortex Structures with Zero Total Intensity”, Regul. Chaotic Dyn., 7:4 (2002), 435–472
Linking options:
https://www.mathnet.ru/eng/rcd828 https://www.mathnet.ru/eng/rcd/v7/i4/p435
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