Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

Abstract

The paper discusses a class of exact solutions of the Oberbeck–Boussinesq equations suitable for describing three-dimensional nonlinear layered flows of a vertically swirling viscous incompressible fluid. An inhomogeneous distribution of the velocity field (there is a dependence of the field components on the horizontal coordinates) generates a vertical swirl in the fluid without external rotation (excluding Coriolis acceleration). Setting the linearly distributed heat field and the field of shear stresses at the boundaries of the flow region is one of the reasons inducing convection in a viscous incompressible fluid. The main attention is paid to the study of the properties of the temperature field. The effect of vertical twist on the distribution of isolines of this field is studied. It is shown that the homogeneous component of the temperature field can be stratified into several zones relative to the reference value, and the number of such zones does not exceed nine. The inclusion of inhomogeneous components of the temperature field can only decrease this number. It is also demonstrated that the class discussed in the paper allows one to generalize the previously obtained results on modeling convective flows of viscous incompressible fluids.

Keywords

• exact solution
• layered convection
• shear stress
• counterflow
• stratification
• system of oberbeck–boussinesq equations
• vertical twist