温盐双扩散均衡场中的振荡现象

Oscillation phenomena in a thermohaline double-diffusive convection system

在一种简单的边界加密的坐标变换下 ,用高精度的差分法研究了温盐双扩散系统 .为了保证求解的稳定性和精确性 ,对流项采用了四阶精度的迎风格式 ,扩散项和涡量方程的浮力项则采用四阶精度的中心差 .首先针对温度占优 (Rρ=0 32 )和盐度占优 (Rρ=1 6 8)的情形进行了计算 ,得到了与文献 [2 ]和 [12 ]一致的结果 ,从而验证方法的正确性 .其次系统地给出了不同Lewis数下的流动形态 ,包括稳定的对称结构。

The incompressible, double diffusive convection has been simulated using finite difference schemes. The Navier Stokes equations are expressed in terms of stream function and vorticity. Because of the existence of large velocity, temperature and salinity gradients in boundary layers, a simple coordinate transformation is used to concentrate the grid points near the wall. The finite difference methods used include the high order accurate upwind difference scheme. It is shown that the scheme is a good candidate for direct simulations of double diffusive convection flows. The boundary fitted coordinate is used so that finer grids can be used to resolve the flow in the boundary layers. The proposed method is first applied to the symmetric states of a salinity dominated flow with R ρ =1 68 and a temperature dominated flow with R ρ =0 32. The numerical results agree well with those by Quon & Ghil( 1992 J.Fluid Mech. 245 449). Then our work concentrates on the study of the flow characteristic of the two dimensional thermosolutal equilibrant regime for different Lewis numbers. It can be found that there are several different states in this system, which could be the symmetric states, the periodic oscillations or non periodic (random) states.