Method of building a mathematical model of layered flows

Abstract

The method of constructing mathematical models for plane-parallel layered flows is considered. Given that the flow structure implies simplification and splitting of the problem, it is shown that, for planar parallel fluxes, it is possible to construct a layered flow model in which the problem solution is constructed by the method of separating variables. It is shown that for each layer of flow it is possible to distinguish a function whose derivatives determine the velocity distribution in the layer and which can be interpreted as "flow potential in the layer". But the potential representation for the velocity field distribution in a layer has a parametric dependence on a variable that is orthogonal to the plane currents. Although there is a function that can be interpreted as the "potential" of a flow in a layer, the most common layered flow (as a whole) is not potential. Only a stream the averaged of a layer thickness can be considered as a potential flow. When constructing models, the viscosity, non-stationarity and inertia of the flow are taken into account (by taking into account nonlinear dynamic components). It is shown that the mathematical models constructed, of some cases of the stream, represent the classical solutions for layered flows.