Исследование стратификации гидродинамических полей для слоистых течений вертикально завихренной жидкости

Abstract

The article proposes an approach to estimating the number of stratification points in hydrodynamic fields. The article provides a method allowing one to estimate from above the number of zero points of hydrodynamic fields (points and stratification zones). The application of the proposed methodology is illustrated by several examples of the analysis of the exact solution to the problem of describing steady laminar flows of a viscous incompressible fluid in an infinite horizontal layer. In example 1, convection is induced by setting the shear stress field at one of the layer boundaries. The features of the background temperature profile, which is a seventh-degree polynomial, are discussed. It is shown that this component of the temperature field is a nonmonotonic function and that the obtained exact solution for the temperature field can describe the stratification of the considered fluid layer into one, two or three zones relative to the reference value. Example 2 illustrates evaluating the number of the zero points of the velocity field components in a vertically swirling fluid, in which convective flows are initiated by thermocapillary forces at the upper boundary of the layer. The exact solution studied in this example is a sixth-degree polynomial, which can have at most two zeros inside the region under consideration. This means that this exact solution is able to describe the stratification of the fluid layer into three zones, in each of which the test speed takes values of the same sign.