Conditionally Euler–Lagrange method on the example of the problem on the dynamics of an intra thermocline vortex lens

A new conditionally Eulerian-Lagrangian numerical method has been developed for solving a number of problems in which the object of study is concentrated in a region of changing configuration, and the movement within the region is described by a system of equations of a two-dimensional continuous medium. A modification of the computational scheme of "particles in cells" on adaptive Euler grids is presented on the example of solving the problem of the dynamics of an intrathermocline vortex lens. The basic equations are equations of the "shallow water" type. The area in which the fields of the lens parameters are determined is the desired one and is determined in the course of the solution. A study of the artificial viscosity of the numerical scheme is carried out, the results of testing the method and examples of computational experiments are presented.