Advective Thermoacoustic Flow in a Rotating Horizontal Liquid Layer

Exact analytical solution of the Navier–Stokes equations, that describes, in the Boussinesq approximation, the flow of an incompressible liquid in the horizontal, plane layer with solid boundaries, rotating about a vertical axis, is presented. The flow of the liquid in this layer is advective and thermoacoustic in nature, and it is due to the constant longitudinal temperature gradient at the boundaries of the layer and to the acoustic wave propagating in it. The length of this wave is assumed to be comparable with the thickness of the layer, and the period of acoustic vibrations of the liquid in it is small compared to the characteristic convection times. Because of this, it is advantageous to define the averaged liquid flow in the layer. The properties of the solution obtained are investigated and the influence of the Taylor number of the liquid flow on its velocity and temperature profiles at constant Grashof, Reynolds, and Prandtl numbers is determined.