The response to external excitations in thermocapillary liquid layers

Abstract

The responses to external excitations in thermocapillary liquid layers are investigated by non-modal stability theory. The maximum amplification of input signals is measured by a response function depending on the perturbation velocity and temperature. There can be rather large amplifications in subcritical flows at both small and large Prandtl numbers (Pr). For small Pr, the response increases significantly with both the Reynolds number (R) and the Biot number (Bi) but decreases with Pr. The optimal response is achieved when the perturbation is almost a spanwise wave. The response properties for the linear flow and the return flow are similar. The amplification is caused by a combination of the lift-up mechanism, Orr mechanism, and external forcing. However, for large Pr, large amplifications could only be found in the return flow, while the variations of response with Pr and Bi are opposite to those at small Pr. The optimal response propagates in the streamwise direction. The amplification is caused by the thermocapillary effect.