中国物理B ›› 2003, Vol. 12 ›› Issue (1): 60-66.doi: 10.1088/1009-1963/12/1/311

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Numerical simulation for thermohaline multiple equilibrant system in non-rectangular domains

詹杰民1, 李毓湘2   

  1. (1)Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China; (2)Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong, China
  • 收稿日期:2002-05-10 修回日期:2002-08-30 出版日期:2003-01-20 发布日期:2003-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 40276011), and the Scientific Research Found-ation for the Returned Overseas Chinese Scholars from the Ministry of Education of China (Grant No [1998]679).

Numerical simulation for thermohaline multiple equilibrant system in non-rectangular domains

Zhan Jie-Min (詹杰民)a, Li Yok-Sheung (李毓湘)b   

  1. a Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China; b Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong, China
  • Received:2002-05-10 Revised:2002-08-30 Online:2003-01-20 Published:2003-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 40276011), and the Scientific Research Found-ation for the Returned Overseas Chinese Scholars from the Ministry of Education of China (Grant No [1998]679).

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摘要： 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.

Abstract: 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 J. Fluid Mech. 331 169) and Quon and Ghil (1992 J. Fluid Mech. 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 Int. J. Heat Mass Transfer 33 1619) qualitatively, but eddies mixing in the top left-hand corner near the curved wall affects the layered structure.

Key words: double-diffusive convection, high-order accurate difference scheme, multiple equilibrant system

中图分类号:  (Turbulent transport processes)

  • 47.27.T-
02.60.-x (Numerical approximation and analysis) 02.70.Bf (Finite-difference methods)