The method of "Large particles" in mathematical modeling of Kelvin–Helmholtz instability in air

The application of the well–known "Large particles" method in mathematical modeling of the simplest type of shear flows - a two-dimensional unsteady plane mixing layer is considered. The results of direct numerical simulation of the Kelvin-Helmholtz instability development at the interface of two layers of air of different densities moving with a tangential velocity shift in a field of strong external acceleration are described. The reliability of the calculation results is confirmed by comparing them with analytical calculations, with the results of numerical solution of a similar problem, as well as with experimental data. Based on the results of calculations, a new functional dependence of the increase in the width of the mixing layer on time, external acceleration, the difference in the densities of the air layers and the velocity difference at the contact boundary is obtained. This dependence is obtained for large values of acceleration values, velocity differences, and density at the gap. It will be useful for predicting the expansion of mixing zones in various currents with a tangential velocity gap, which are ubiquitous both in technology and in the atmosphere – for example, at the initial section of the jet, at the initial stage of mixing in a cylindrical vortex, with the development of wavy clouds or instability of a clear sky in the atmosphere.