The effects of density extremum and rotation on the onset of thermal instability Available to Purchase

This paper addresses the onset of Be´nard convection on a rotating horizontally confined layer of water near the temperature of maximum density that is heated from below. A quadratic relation between temperature and density is assumed near the density extremum. A linear stability analysis is employed to determine the critical conditions for the onset of thermal instability. The resulting eigenvalue problem is numerically solved by expanding the amplitudes of the temperature and velocity perturbations in a truncated eigenfunction and power series. The validity of the principle of exchange of stabilities is proved analytically for a certain case and numerically investigated in general. Plots of the marginal stability curves as well as the variation of the critical Rayleigh number with other dimensionless parameters which naturally arise in the problem are also presented and discussed.