Two-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids at Arbitrary Atwood Numbers
WANG Li-Feng1,4, YE Wen-Hua2,3,4, LI Ying-Jun1
1State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology, Beijing 1000832Department of Physics, Zhejiang University, Hangzhou 3100283Center for Applied Physics and Technology, Peking University,Beijing 1008714 Laboratory of Computational Physics, Institute of Applied Physics andComputational Mathematics, Beijing 100088
Two-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids at Arbitrary Atwood Numbers
WANG Li-Feng1,4, YE Wen-Hua2,3,4, LI Ying-Jun1
1State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology, Beijing 1000832Department of Physics, Zhejiang University, Hangzhou 3100283Center for Applied Physics and Technology, Peking University,Beijing 1008714 Laboratory of Computational Physics, Institute of Applied Physics andComputational Mathematics, Beijing 100088
摘要The Rayleigh-Taylor instability in two-dimensional incompressible fluids at arbitrary Atwood numbers is studied by expanding the perturbation velocity potential to third order. The second and third harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The mode coupling coefficients are dependent on the Atwood numbers. Our simulations support the weakly nonlinear results. We find that the ratio of the nonlinear saturation amplitude ηs and the perturbation wavelength λ is dependent on the Atwood number AT and the relation is ηs/λ=(1/π)[√2/5/√(1+3AT2 )].
Abstract：The Rayleigh-Taylor instability in two-dimensional incompressible fluids at arbitrary Atwood numbers is studied by expanding the perturbation velocity potential to third order. The second and third harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The mode coupling coefficients are dependent on the Atwood numbers. Our simulations support the weakly nonlinear results. We find that the ratio of the nonlinear saturation amplitude ηs and the perturbation wavelength λ is dependent on the Atwood number AT and the relation is ηs/λ=(1/π)[√2/5/√(1+3AT2 )].
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2010, Vol. 27 
