Numerical study of the fast rotation effect on the stability of advective flow in a horizontal fluid layer with rigid boundaries at small Prandtl numbers

We investigate the effect of fast rotation at large Taylor number (Та=10 5) on the hydrodynamic instability mode of an advective flow in the horizontal layer of an incompressible fluid with rigid boundaries at small Prandtl number (0 values is analyzed. The relationship between the critical Grashof number and corresponding wave number and the Prandtl number is given. It is shown that when the Pr value increases from 0 to 0.3 the flow stability decreases and when it lies within the interval 0.3-0.93 the flow stability increases. For the monotonic instability mode Gr C =40839.42, the critical Grashof number reaches its lowest value at Pr=0.3. The boundary of monotonic instability mode at large Taylor number is determined.