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 - Chikulaev, Dmitriy Gennadievich; Shvarts, Konstantin Grigorievich (Computational Continuum Mechanics, 2014)
We investigate the effect of fast rotation at large Taylor number (Та=105) 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%3CPr%3C1.0) using a small perturbation method. In calculations, we apply the grid method for the one-dimensional problem and the differential sweep method. The system of equations and the necessary parameters of the numerical solution are presented for both methods. Neutral curves describing the dependence of the critical Grashof number on the wave number are obtained and their behavior at differentvalues 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 GrC=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.