DYNAMICS OF TRIANGULAR TWO-LAYER VORTEX STRUCTURES WITH ZERO TOTAL INTENSITY

The problem of three vortex lines in a homogeneous layer of an ideal incompressible uid 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 dierent from zero, based on the phase portraits in trilinear coordinates, a classication 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 specically, 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 con guration triton, a discrete analog of the vortex structure modon+rider, 2) an unstable triangular conguration. 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 nite-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 nite-size vortex behavior is dicussed. Examples of formation of vortical congurations are given. Such congurations appear either after merging of vortices of the same layer or as a result of instability of the two-layer vortex structure