Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Abstract

The stability of a liquid layer with an undeformable interface open to the atmosphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature difference applied on the system. Depending on the liquid depth, this basic flow is destabilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturbations are driven by the basic flow and therefore one must distinguish between convective and absolute thresholds. The instability mechanisms as well as the di¤erent regimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr ¼ 10Þ. In particular,it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally.