Non-modal Stability Analysis of Thermocapillary Liquid Layers

The sensitivity of subcritical thermocapillary liquid layers to initial disturbances and external excitations is investigated by the non-modal stability analysis. The amplifications of initial disturbances and external excitations are measured by the growth function and response function, respectively. Results show that at small Prandtl numbers (Pr), the subcritical flows are sensitive to both initial disturbances and external excitations. The maximum amplifications are approximately proportional to the square of Reynolds number (Re). At large Pr, large amplifications to external excitations are found in the return flow. The maximum response increases linearly with Re⁵ and Pr⁵. When the frequency increases, the total wave number of the optimal response decreases. The flow and temperature fields indicate that the magnitudes of output temperature and velocity are far larger than those of input, which is significantly different from the pipe flow.