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Some Aspects of the Kinematics of Short Waves Over Longer Gravity Waves on Deep Water
Abstract Modulations in wave number and in amplitude of short waves propagating over the surface of longer gravity waves on deep water is known to be of main importance for various fundamental and applied problems. They can be studied either by integrating the ray equations coupled with the action conservation principle established by Bretherton and Garrett (1969) or by treating the stability of the long waves to superharmonic perturbations. The aim of this note is to check the validity of the former approach when the nonlinearity of the longer wave is taken into account together with the capillarity effect on the short waves. A system of first order differential equations is derived from approximate formulation and solved numerically along the characteristics. A numerical investigation of superharmonic normal mode perturbations of finite amplitude Stokes wave has been developed by using the QZ algorithm. The variations of wave number and amplitude of the short waves over the profile of the long wave, obtained by the two different methods are similar, showing that ray equations and action conservation principle can be applied for strongly nonlinear inhomogeneous moving media.
Some Aspects of the Kinematics of Short Waves Over Longer Gravity Waves on Deep Water
Abstract Modulations in wave number and in amplitude of short waves propagating over the surface of longer gravity waves on deep water is known to be of main importance for various fundamental and applied problems. They can be studied either by integrating the ray equations coupled with the action conservation principle established by Bretherton and Garrett (1969) or by treating the stability of the long waves to superharmonic perturbations. The aim of this note is to check the validity of the former approach when the nonlinearity of the longer wave is taken into account together with the capillarity effect on the short waves. A system of first order differential equations is derived from approximate formulation and solved numerically along the characteristics. A numerical investigation of superharmonic normal mode perturbations of finite amplitude Stokes wave has been developed by using the QZ algorithm. The variations of wave number and amplitude of the short waves over the profile of the long wave, obtained by the two different methods are similar, showing that ray equations and action conservation principle can be applied for strongly nonlinear inhomogeneous moving media.
Some Aspects of the Kinematics of Short Waves Over Longer Gravity Waves on Deep Water
Kharif, C. (author)
1990-01-01
15 pages
Article/Chapter (Book)
Electronic Resource
English
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