%A Zhan Jie-Min, Li Yok-Sheung
%T Numerical simulation for thermohaline multiple equilibrant system in non-rectangular domains
%0 Journal Article
%D 2003
%J Chin. Phys. B
%R 10.1088/1009-1963/12/1/011
%P 60-66
%V 12
%N 1
%U {http://cpb.iphy.ac.cn/CN/abstract/article_20425.shtml}
%8 2003-01-20
%X In this paper, incompressible, double-diffusive convection is 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 boundary-fitted coordinate system is used
to concentrate the grid points near the wall and fit complex
boundaries. 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 proposed method is first
applied to symmetry breaking and overturning states in
thermohaline-driven flows in trapezoid basins. The basic phenomena
agree well with those by Dijkstra and Molemaker (1997 {\em J. Fluid
Mech.} {\bf 331} 169)
and Quon and Ghil (1992 {\em J. Fluid Mech.} {\bf 245} 449), but symmetry breaking and
overturning states can occur in an asymmetric geometrical region
without perturbations. Then the method is applied to double-diffusive
convections in a cavity with opposing horizontal temperature and
concentration gradients at large thermal ($Rt$), solutal ($Rs$)
Rayleigh numbers and Lewis number. There are three straight sides
and a sine curve side in the cavity. Basically, numerical results
are in agreement with those of Lee and Hyun (1990 {\em Int. J. Heat
Mass Transfer} {\bf 33} 1619) qualitatively, but eddies mixing in the
top left-hand corner near the curved wall affects the layered structure.