Effects of non-uniform temperature gradient and Coriolis force on Bénard-Marangoni's instability

The effects of a non-uniform temperature gradient and the Coriolis force on the onset of convection driven by combined surface-tension and buoyancy force in a horizontal layer of Boussinesq fluid with upper boundary free and adiabatic and the lower boundary rigid and isothermal is studied by means of linear stability analysis. The Galerkin technique is used to obtain the eigenvalues. A mechanism for suppressing or augmenting convection is discussed in detail. It is found that as the rotation increases the coupling between the two agencies causing instability becomes weaker even in the presence of a non-uniform temperature gradient. A discontinuous change in cell size occurs at a certain value of Rayleigh number as a result of sudden change over from convection dominated by one of the two agencies to that dominated by the other. The results obtained in the limiting case of uniform temperature gradient or in the absence of rotation agree with the existing ones and found that even a single-term Galerkin expansion gives reasonable results with minimum mathematics. © 1986 Springer-Verlag