Onset of Unsteady Horizontal Convection in Rectangular Tank atPr= 1

Abstract

The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac = 5.5377 × 108 for the middle plume forcing at Pr = 1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's first hypotheses (J. Fluid Mech. 466 (2002) 205) about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.