Invariant Submodels of the Generalized Leith Model of Wave Turbulence in a Medium with Nonstationary Viscosity

Abstract

A generalized phenomenological Leith model of wave turbulence in a medium with unsteady viscosity is under study. Group analysis methods are used to obtain the main models possessing nontrivial symmetries. All invariant submodels are determined for each model. Invariant solutions describing these submodels are either determined in explicit form or satisfy the integral equations obtained. The main models are used to study turbulent processes. At an initial instance and with a fixed value of the wave number modulus, either turbulence energy spectrum and its gradient or turbulence energy spectrum and the rate of its variation are specified for the above-mentioned models. It is determined that solutions of the problems describing these processes exist and are unique under certain conditions.