Nonlinear Kelvin Helmholtz Instability

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Chen Le-shan. Nonlinear Kelvin Helmholtz Instability[J]. Applied Mathematics and Mechanics, 1985, 6(11): 999-1012.

Citation:

Chen Le-shan. Nonlinear Kelvin Helmholtz Instability[J]. Applied Mathematics and Mechanics, 1985, 6(11): 999-1012.

Citation:

Chen Le-shan. Nonlinear Kelvin Helmholtz Instability[J]. Applied Mathematics and Mechanics, 1985, 6(11): 999-1012.

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.

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