Mathematical modeling of the vortices couple dynamics in a stratified fluid

Abstract The problem of the dynamics of the vortex couple in stratified fluid is considered. The couple is two vortexes, arranged symmetrically relative to the vertical axis, but with the opposite direction of rotation, so that it begins to rise upwards. The mathematical model of a couple of vortices in a viscous stratified medium was studied. Salinity is chosen as a stratifying component, just as it can be implemented in the laboratory. The task is described by the Navier-Stokes equations in the Boussinesq approximation. To solve the problem, the SMIF method is used, of course, the finite different scheme of which has such properties as the second order of approximation on spatial variables, minimal scheme dissipation and dispersion, performance in wide range of Reynolds and Froude numbers and, most importantly, when solving wave processes are a property of monotony. The dynamics of such a couple are studied depending on its geometric sizes, the intensity of the vortexes and the depth of their initial immersion.