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Article Dans Une Revue Regular and Chaotic Dynamics Année : 2002

Dynamics of triangular two-layer vortex structures with zero total intensity

Résumé

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.
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hal-00230201 , version 1 (21-02-2020)

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Mikhail Sokolovskiy, Jacques Verron. Dynamics of triangular two-layer vortex structures with zero total intensity. Regular and Chaotic Dynamics, 2002, 7 (4), pp.435-472. ⟨10.1070/RD2002v007n04ABEH000221⟩. ⟨hal-00230201⟩

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