The stability of an infinite fluid layer subject to arbitrary horizontal flow and to arbitrary vertical temperature and salinity distributions is considered. Linear stability analysis is used to investigate the stability under general three-dimensional perturbations.
A general discussion of the properties of the stability chart, using only the governing equations, but not their solution for any particular case, is presented in [1]. This paper contributes a numerical scheme, based,on a combination of the Galerkin and the continuation methods, to obtain the stability chart from the characteristic equation. The method is applied to an example with a parabolic velocity distribution and linear temperature and salinity fields. The stability chart in the plane of the Rayleigh numbers is obtained for the region corresponding to solar ponds. * Ref.
[1] also includes a summary of the relevant literature dealing with stability of double-diffusive systems with and without a horizontal flow, which is not repeated here.
* This condition has been derived by Magen [2] for the marginal stability lines, i.e. Real(o) = 0; ref.
[2] also includes additional details of the mathematical treatment,