Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom

The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenarios near the onset of rotating convection of low Prandtl number fluids are not well understood. Here, we investigate the transition scenario in rotating Rayleigh-Bénard convection with no-slip boundary conditions by performing 3D direct numerical simulations (DNS) and low-dimensional modeling. The governing parameters, namely, the Taylor number (Ta), Rayleigh number (Ra), and Prandtl number (Pr), are varied in the ranges 0 < Ta ≤ 8 × 10 3, 0 < Ra < 1 × 10 4, and 0 < Pr ≤ 0.35, where convection appears as a stationary cellular pattern. In DNS, for Pr < 0.31, the supercritical or subcritical onset of convection appears, according as Ta > Ta c (Pr) or Ta < Ta c (Pr), where Ta c (Pr) is a Pr dependent threshold of Ta. On the other hand, only supercritical onset of convection is observed for Pr ≥ 0.31. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as Ra is increased beyond the onset of convection, the system becomes time dependent and depending on Pr, standing and traveling wave solutions are observed. For very small Pr (≤ 0.045), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher Ta.