Hydrodynamic modes and light scattering near the convective instability

Abstract

An analysis is presented of the behavior of the hydrodynamic modes in a horizontal fluid layer subject to a downward-directed temperature gradient which, when reaching a critical value, drives the system into convective instability. It is found that the combination of this thermal constraint and gravity gives rise to a coupling between the heat-diffusion mode and the transverse mode ${\left(\mathrm{curl}\mathrm{curl}\overrightarrow{\mathrm{v}}\right)}_z$, with $\overrightarrow{\mathrm{v}}$, the velocity field, and the $z$ axis pointing in the vertical direction. As a result of this mode coupling, which is absent in a fluid at equilibrium, the damping factor of one of the coupled modes goes to zero when the temperature gradient increases to its critical value. On the basis of this mode analysis, the spectral distribution of the light scattered by the nonequilibrium fluid is then computed. The main features of the light-scattering spectrum consist of the appearance of an additional central component and the respective narrowing and broadening of the spectral components corresponding to the coupled modes as the instability critical point is approached.