Effect of rotation on the stability of advective flow in a horizontal liquid layer with solid boundaries at small Prandtl numbers

Abstract

The limits of the existence of monotonous instability of an advective flow in a rotating horizontal layer of incompressible fluid with solid boundaries are investigated as the function of the Prandtl (Pr) and Taylor (Ta) numbers. The neutral curves, as the dependences of the Grashof number on the wave number, are constructed for different values of Ta and Pr. Two hydrodynamic instability modes are detected and their dependence on the rotation is studied on the range 0 ≤ Ta ≤ 105 at small Prandtl numbers. As the Taylor number increases from 0 to 200, the limits of the first monotonous mode reduce with respect to Pr from 0.34 to 0. With increase in Ta on the range 268 ≤ Ta ≤ 105, the limits of the second monotonous mode expand in Pr from 0.065 to zero and from 0.065 to 0.92.