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Title: Free surface flow under gravity and surface tension due to an Applied Pressure Distribution II bond number less then one-third
Authors: Maleewong, Montri
Grimshaw, Roger H.J.
Asavanant, Jack
Keywords: Depression wave
Elevation wave
Trapped bubble
NLS
Gravity-capillary
Issue Date: 2004
Abstract: We consider steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of a constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behaviour of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, τ < 1/3, and the magnitude and sign of the pressure forcing term ǫ. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F < Fm < 1 where Fm is a certain critical value where the phase and group velocities for linearized waves coincide, linear theory gives a good prediction for the numerical solution of the nonlinear problem in the case of a bifurcation from the uniform flow. As F approaches Fm, however, some nonlinear terms need to be taken in the problem. In this case the forced nonlinear Schr¨odinger equation is found to be an appropriate model to describe bifurcations from an unforced envelope solitary wave. In general, it is found that for given values of F < Fm and τ < 1/3, there exist both elevation and depression waves.
Description: This pre-print has been submitted, and accepted, to the journal, European Journal of Mechanics B-Fluids. The definitive version: MALEEWONG, M., GRIMSHAW, R. and ASAVANANT, J., 2005. Free surface flow under gravity and surface tension due to an Applied Pressure Distribution II bond number less then one-third. European Journal of Mechanics B-Fluids, 24 (4), pp.502-521 is available at http://www.sciencedirect.com/science/journal/09977546.
URI: https://dspace.lboro.ac.uk/2134/239
Appears in Collections:Pre-prints (Maths)

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