Stability analysis of double-diffusive solar ponds with non-constant temperature and salinity gradients

In this communication, the stability of the double-diffusive solar ponds with non-uniform temperature and salinity gradients has been investigated. This is a further generalization of our approach to this problem initiated in Ref. [7]. Using a stochastic approach, the linearized system of basic equations of motion is reduced to a single integro-differential equation. For convective motion, this equation reduces to a time-independent Schrödinger equation for a particle moving in a potential field ƒ(Z) characterized by the non-uniform temperature and salinity gradients. This equation can, in general, be solved (exactly or approximately depending on the form of the gradient profile) by methods commonly used in quantum mechanics.

In the Appendix, we show that, for a quadratic gradient profile, the above equation has an analytical solution similar to that obtained by Zangrando using numerical computations.