Küppers–Lortz Instability in the Rotating Brinkman–Bénard Problem

Abstract

We investigate the Kuppers–Lortz (KL) instability in the rotating Brinkman–Benard convection problem by assuming that there is local thermal non-equilibrium (LTNE) between the Newtonian liquid and the high-porosity medium that it has occupied to the point of saturation. The effects of local thermal non-equilibrium parameters on the threshold value of the Taylor number and the angle between the rolls at which KL-instability sets in are presented. The four routes through which the local thermal equilibrium situation can be approached are presented with the help of asymptotic analyses. The corresponding results of the rotating Darcy–Benard problem are extracted as a limiting case from the present problem with the help of another asymptotic analysis. The problem identifies the specific range of values of parameters within which LTNE effect is discernible and also clearly shows that the onset of KL-instability is delayed by the ratio of thermal conductivities. The heat transfer coefficient, however, has a dual effect on $${\mathrm{Ta}}_{\mathrm{c}}$$. Such a dual nature is seen, perhaps, due to the heat transport equations being of the hyperbolic type when local thermal non-equilibrium effect is significant. The results show that LTNE in the presence of rotation favors hexagonal pattern.