Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid
WANG Li-Feng1,2, YE Wen-Hua1,3,4, FAN Zheng-Feng2, LI Ying-Jun1
1School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 1000832Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 1000883Department of Physics, Zhejiang University, Hangzhou 3100284Center for Applied Physics and Technology, Peking University, Beijing 100871
Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid
WANG Li-Feng1,2, YE Wen-Hua1,3,4, FAN Zheng-Feng2, LI Ying-Jun1
1School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 1000832Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 1000883Department of Physics, Zhejiang University, Hangzhou 3100284Center for Applied Physics and Technology, Peking University, Beijing 100871
摘要A weakly nonlinear model is proposed for multimode Kelvin-Helmholtz instability. The second-order mode coupling formula for Kelvin-Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not.
Abstract：A weakly nonlinear model is proposed for multimode Kelvin-Helmholtz instability. The second-order mode coupling formula for Kelvin-Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not.
WANG Li-Feng;YE Wen-Hua;;FAN Zheng-Feng;LI Ying-Jun. Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid[J]. 中国物理快报, 2009, 26(1): 14701-014701.
WANG Li-Feng, YE Wen-Hua, , FAN Zheng-Feng, LI Ying-Jun. Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid. Chin. Phys. Lett., 2009, 26(1): 14701-014701.
[1] Chandrasekhar S 1961 Hydrodynamic and HydromagneticStability (London: Oxford University Press) chap 10 [2] Hasegawa1 H et al 2004 Nature 430 755 [3] Lobanov A P and Zensus J A 2001 Science 294128 [4] Gamexo V N et al 2003 Science 299 77 [5] Price D J and Rosswog S 2006 Science 312 719 [6] Ye W H et al 2002 Phys. Rev. E 65 57401 [7] Ye W H et al 2000 Acta Phys. Sin. 49 762 (inChinese) [8] Fan Z F et al 2007 Chin. Phys. Lett. 24 2308 [9] Fan Z F and Luo J S 2008 Chin. Phys. Lett. 25624 [10] Ferrari A et al 1978 Astron. Astrophys. 64 43 [11] Payne D G and Cohn H 1985 Astrophys. J. 291655 [12] Nayffh A H and Saric W S1970 J. Fluid Mech. 46 209 [13] Walker J S 1993 Phys. Fluids A 5 1466 [14] Bau H H 1982 Phys. Fluids 25 1719 [15] Tauber W et al 2002 Phys. Fluids 14 2871 [16] Keskinen M J 1995 Phys. Plasmas 3 1259 [17] Drazin P G 1969 J. Fluid Mech. 42 321 [18] Bodo G 2004 Phys. Rev. E 70 36304 [19] Miura A 1999 Phys. Rev. Lett 83 1586 [20] Horton W et al 2005 Phys. Plasmas 12 22303 [21] Lawrence G A et al 1991 Phys. Fluids A 3 2360 [22] Wang L F et al 2008 Acta Phys. Sin. 57 3038(in Chinese) [23] Wang L F et al 2008 Chin Phys. B 17 3792 [24] Haan S W 1991 Phys. Fluids B 3 2349
2009, Vol. 26 
