Nonlinear dynamic behavior of non-convective zone in salt gradient solar pond

Non-Convective Zone (NCZ) of salt gradient solar pond is a typical double diffusive system of salinity and temperature, and it is subjected to instable effects of adverse temperature gradient. The onset of instability may occur as an oscillatory motion because of the stabilizing effect of the salinity. In this paper, the marginal state between the steady state and the convection of the NCZ is studied. The stability of the Boussinesq approximation of the Navier–Stokes equations is analyzed by a perturbation approach. The marginal states for the onset of convection are obtained by analytical method, which is based on the linearization of the ordinary differential equations, and then numerical method is used to solve the nonlinear ordinary differential equations. Numerical results provide the trajectories of the temperature and velocity coefficients in the three-dimensional phase space, as well as the two-dimensional temperature, salinity and velocity fields in NCZ. The results demonstrate that the numerical study is in agreement with the marginal stability and the critical Rayleigh number Rc a derived from linear stability analysis. Both the linear and nonlinear studies indicate that oscillation is a narrow region above the stable region; however, the nonlinear numerical results indicate that the linear stability analysis leans to a larger upper boundary in the oscillatory regions. 2011 Elsevier Ltd. All rights reserved