On Coherent and Stochastic Structures in Hydrodynamic Flows with a Velocity Shift

We described various structures formed during the stabilization of instability in wave and vortex flows of an ideal liquid. The problem of wave structures in an incompressible fluid flow stratified by density and velocity is considered in detail. Instability stabilization occurs as a result of the interaction of an unstable wave with waves forming a resonant triplet with it. In this case, structures of a regular and stochastic nature arise. We analyzed and described the scenario of the transition of the system to the stochastic mode. The formulation corresponds to atmospheric currents under wind shear, but the results can be used in other problems of the theory of nonlinear waves and vortices. In this paper we showed that structures of a similar nature also arise in vortex flows, both ideal and viscous liquids.