Analysis of the characteristic perturbations spectrum of the exact invariant solution of the microconvection equations

Abstract

The properties of an exact invariant solution of the equations of microconvection of isothermally incompressible liquids have been investigated. The solution describes a stationary fluid flow in a vertical channel. The temperature or heat flux can be given at the solid boundaries of the channel. A classification of the solutions and their physical interpretation are suggested. In accordance with the classification the solutions describe different types of flows. The solution of the stability problem of all classes of flows in the vertical channel with the given temperature on the walls is presented. The structure of the spectrum of small non-stationary spatial perturbations for the model medium (silicon dioxide melt) has been studied, depending on the configuration of the perturbation wave, thickness channel, thermal and gravitational effects. The formation regularities of different types of the thermal and hydrodynamic disturbances have been determined. The interaction of the thermal and hydrodynamic perturbations leads to the formation of various convective structures. Typical patterns of the velocity and temperature perturbations and relations of critical characteristics of the instability are presented, depending on the problem parameters. The most dangerous mechanisms change from hydrodynamic to thermal ones with the variation of the viscous and thermal liquid properties.