Gravity-capillary flows over obstacles for the fifth-order forced Korteweg-de Vries equation

03/06/2021 ∙ by Marcelo V. Flamarion, et al. ∙ 0 ∙ share

The aim of this work is to investigate gravity-capillary waves resonantly excited by two topographic obstacles in a shallow water channel. By considering the weakly nonlinear regime the forced fifth-order Korteweg-de Vries equation arises as a model for the free surface displacement. The water surface is initially taken at rest and the initial value problem for this equation is computed numerically using a pseudospectral method. We study near-resonant flows with intermediate capillary effects. Details of the wave interactions are analysed for obstacles with different sizes. Our numerical results indicate that the flow is not necessarily governed by the larger obstacle.

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Gravity-capillary flows over obstacles for the fifth-order forced Korteweg-de Vries equation

Authors

Solitary water wave interactions for the Forced Korteweg-de Vries equation

Local on-surface radiation condition for multiple scattering of waves from convex obstacles

The Whitham Equation with Surface Tension

Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution

Numerical Algorithms for Water Waves with Background Flow over Obstacles and Topography

1D and 2D Flow Routing on a Terrain

A continuation method for building invisible obstacles in waveguides

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