Thermocapillary Flows with Low Frequency g-Jitter

Abstract

A thermocapillary parallel flow is established in a fluid filled slot with an applied temperature gradient. Low frequency jitter is imposed in arbitrary directions. Vertical jitter proves to be relatively uninteresting, merely augmenting or opposing the basic thermocapillary flow. Streamwise jitter still produces parallel flows, but these now exhibit boundary layers or layered cellular structures for large Rayleigh number as the applied stratification alternates between stable and unstable. Runaways are possible for unstable stratification and these correspond to resonant excitation of stationary long wave Rayleigh-Benard modes. Spanwise jitter produces fully three dimensional motion. A spanwise-streamwise circulation results for weak spanwise jitter, which advects the interfacial temperature establishing a subsidiary spanwise thermocapillary flow. This flow is strong at small Biot number when advected temperature is trapped in the slot, and has a counter-intuitive dependence on the spanwise-streamwise aspect ratio.