Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1
SUN Liang1,2, MA Dong-Jun3, ZHANG Wei3, SUN De-Jun3
1School of Earth and Space Sciences, University of Science and Technology of China, Hefei 2300272LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 1000293Dept of Modern Mechanics, University of Science and Technology of China, Hefei 230027
Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1
SUN Liang1,2;MA Dong-Jun3;ZHANG Wei3;SUN De-Jun3
1School of Earth and Space Sciences, University of Science and Technology of China, Hefei 2300272LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 1000293Dept of Modern Mechanics, University of Science and Technology of China, Hefei 230027
摘要The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac=5.5377×108 for the middle plume forcing at Pr=1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's first hypotheses [J. Fluid Mech. 466(2002)205] about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.
Abstract：The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac=5.5377×108 for the middle plume forcing at Pr=1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's first hypotheses [J. Fluid Mech. 466(2002)205] about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.
SUN Liang;MA Dong-Jun;ZHANG Wei;SUN De-Jun. Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1[J]. 中国物理快报, 2008, 25(6): 2121-2124.
SUN Liang, MA Dong-Jun, ZHANG Wei, SUN De-Jun. Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1. Chin. Phys. Lett., 2008, 25(6): 2121-2124.
[1] Paparella F and Young W R 2002 J. Fluid Mech. 466 205 [2] Mullarney J C, Griffiths R W and Hughes G O 2004 J. FluidMech. 516 181 [3] Wang W and Huang R X 2005 J. Fluid Mech. 540 49 [4] Hughes G O, Griffiths R W, Mullarney J C and Peterson W H 2007 J. Fluid Mech. 581 251 [5] Rossby H T 1965 Deep-Sea Research 12 9 [6] Rossby H T 1998 Tellus A 50242 [7] Siggers J H, Kerswell R R and Balmforth N J 2004 J. FluidMech. 517 55 [8] Sun L, Sun Y F, Sun D J and Yin X Y 2006 J. Hydrodyn. A 21 252 (in Chinese) [9] Sun L, Sun Y F, Ma D J and Sun D J 2007 Acta Phys. Sin. 56 6503 (in Chinese) [10] Quon C and Ghil M 1992 J. Fluid Mech. 245 449 [11] Arakawa A 1966 J. Comput. Phys. 1 119 [12] Orlandi P 2000 Fluid Flow Phenomena (Dordrecht: Kluwer)
2008, Vol. 25 
