非线性Kelvin-Helmholtz不稳定性

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Nonlinear Kelvin Helmholtz Instability

摘要: 本文用导数展开法对液体薄层与亚音速气流接壤时的界面稳定性作非线性分析.文中考虑了液体的表面张力与体积力,故非线性的Rayleigh-Taylor不稳定性可作为特例而导出;液体与气体均不计粘性.虽然Nayfeh^[1]曾算过这一情况,但其三阶方程有遗漏(如213页的式(2.29)).同时解也不自洽(如其一阶解(2.31)并不满足他的初始条件(2.20)),此外,在截止波数附近,对行波他并未考虑.本文弥补了这些,并得出了新的结论.

Abstract: A non-linear analysis is presented with derivative expansion method for the inter facial stability of a liquid film adjacent to a subsonic gas flow under the influence of body force and surface tension. The non-linear Rayleigh-Taylor instability is included as a special case. The gas and liquid are considered to be inviscid. Though Nayfeh (1971) gave consideration into this case, there is something omitted in his third-order equation (e.g. p. 213 expression (2.29)) and inconsistent with his solutions (e.g. the first-order solution (2.31) does not satisfy his initial conditions (2.20)). Besides, in this paper, our solution near the cut-off wave number is extended to include the case of travelling waves and a new conclusion is drawn.

[1]	Nayfeh, A, H, and W, S, Saric, J.Fluid Mech.46, 2(1971), 209.
[2]	Van Dyke,M.,Pertubation Methods in Fluid Mechanics,New York:Academic(1964).
[3]	柯青等,《理论流体力学》,第一卷第二分册,高等教育出版社,(1956) 454页.
[4]	柯青等,《理论流体力学》,第一卷第一分册,高等教育出版社(1956) 107页.
[5]	Chandrasekhar,S.,Hydrodynamic and Hydromagnetic Stability,Oxford University Press,Amen House, London, E, C, 4(1961) 431
[6]	Liepmann, H, W.and A, Roshko, Elements of Gasdenamics, New York; John Wiley(1957).
[7]	钱伟长,《奇异摄动理论》(讲义),清华大学基础部力学教研组,第六章(1980).