Effect of rotation on the monotonic instability mode of advective flow in a horizontal incompressible fluid layer with rigid boundaries in the case of normal spiral perturbations - Chikulaev, Dmitriy Gennadievich; Shvarts, Konstantin Grigorievich (Computational Continuum Mechanics, 2016)
We study the monotonic instability mode of an advective flow in a rotating horizontal layer of incompressible fluid with rigid boundaries, which depend on the Prandtl number (Pr) and the Taylor number (Ta) in the case of spiral perturbations using a small perturbation method. In calculations, we apply the grid method to the one-dimensional problem. The system of equations and necessary parameters of the numerical solution are presented. The neutral curves of dependency the Grashof number on the wave number for different values of Ta and Pr are presented. Two hydrodynamic modes of instability are revealed. The effect of rotation on these modes is investigated in the range of 0 ≤ Ta ≤ 10^5 at Prandtl numbers in the range of 0 < Pr ≤ 20. The region of the first monotonic mode is expanded with respect to Pr in the range of 0 to 0.3 with increasing Taylor number from 4 to 370. The second monotonic mode arises in the range 0.3 < Pr ≤1 at Ta = 370, and the region of this mode is expanded with respect to Pr in the range from 0.3 to 0 and from 1 to 20 with increasing Ta. The curves describing the dependence of the Grashof number on the Taylor and Prandtl numbers are given. The first mode is more dangerous than the second mode for a fixed value of the Prandtl number at Pr ≤ 0,1. However, the second mode is more dangerous than the first monotonic mode in the range of 0.1 < Pr ≤ 0.3. The second mode is more dangerous than the first mode for a fixed value of Ta in the range of the simultaneous existence of both monotonic modes.