LINEAR-STABILITY OF A DOUBLE-DIFFUSIVE LAYER WITH VARIABLE FLUID PROPERTIES

The linear stability of an infinite horizontal double diffusive layer stratified vertically by temperature and solute concentration is analy zed numerically for the case of temperature-dependent viscosity and sa lt diffusivity. The one-dimensional steady basic state associated with the variable properties is characterized by zero fluid velocity, a li near temperature profile and a non-linear salinity distribution. The h orizontal boundaries are shear-free and perfectly conducting. The eige nvalue problem for the linearized perturbation equations is resolved n umerically by the Galerkin method. The results for the direct mode ('f inger regime') show that, in contrast to the constant properties case, the critical wavenumber increases with the solute Rayleigh number (Ra -s) and the critical thermal Rayleigh number is reduced from its corre sponding constant properties value. The behavior of the oscillatory mo de ('diffusive regime') is more complex, and two different branches ex ist for Ra-s larger than some fixed value. The least stable branch is characterized by a high wavenumber while the second branch by a small wavenumber.