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Scattering of gravity waves by a periodically structured ridge of finite extent. (English) Zbl 1419.76090
Summary: We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.
MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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