Long-scale thermodiffusional convection

Abstract

Thermodiffusional convection in the presence of the Soret effect is considered under conditions of poor heat exchange when convective patterns with large aspect ratio are formed beyond the instability threshold. Three distinct long-scale equations are obtained for the description of long-scale patterns associated with stationary and oscillatory convection. The equation of stationary convection coincides, up to coefficients, with the respective equation derived for thermal convection in one-component fluids. Long-scale oscillatory instability is found to obey the Schrödinger equation with the amplitude modulated on a longer time scale. An equation retaining the widest variety of behavior and describing transitions to both stationary and oscillatory convection patterns is obtained in the vicinity of the degenerate bifurcation at double zero eigenvalue.