Modeling of quasi-equilibrium states of a two-dimensional ideal fluid

Abstract

Contrary to a viscous fluid at high Reynolds numbers, the equations of a two-dimensional ideal fluid have an infinite number of invariants, the presence of which complicates both its statistical description and the numerical modeling. In this study, the numerical modeling of quasi-equilibrium states of an ideal fluid is carried out at a high resolution of 8192² within the framework of two models: the Arakawa approximations with two quadratic invariants and the approximations of the equations for a viscous fluid in the asymptotic case of low viscosity. The possibility of application of the theory of Cesaro convergence (time averaging) for the solution of the problem of unsteadiness of final states and the problem of achievement of equilibrium states are considered.