Acoustic wave effect on a stability of convective flow in a horizontal channel subjected to the horizontal temperature gradient

The effect of acoustic wave propagating in longitudinal direction on stationary convective flow in a horizontal channel of rectangular cross-section in the presence of horizontal temperature gradient and its stability is studied. It is shown that in the presence of sufficiently intensive acoustic wave stationary flow is of coaxial character, the fluid moves in the direction of temperature gradient near sidewalls and in the opposite direction in the interior of the channel. At Pr < ∼0.2 hydrodynamic shear instability mode is most dangerous. This mode is strongly stabilized by acoustic wave at low Prandtl numbers. The range of Prandtl number values where acoustic wave can stabilize the basic flow becomes wider with the channel width growth. At high Prandtl number values the spiral instability modes are most dangerous. The oscillatory spiral mode is slightly stabilized by acoustics. The monotonic spiral mode is destabilized by acoustic wave, especially in the wide channels. In general, for all instability modes the sidewalls suppress the development of perturbations and stationary flow in the channel is more stable than that in plane horizontal layer. In the channel of square cross-section the oscillatory spiral mode is completely suppressed.