A shallow water theory is developed which applies to surface wave propagation over structured bathymetry comprised of rapid abrupt fluctuations in depth between two smoothly-varying levels. Using a homogenisation approach coupled to the depth-averaging process which underpins shallow water modelling, governing equations for the wave elevation are derived which explicitly relate local spatially-varying anisotropy of wave speeds to properties of the microstructured bed. The model is applied to two water wave scattering problems to demonstrate both the complex wave propagation characteristics exhibited by structured beds and to provide examples of how to use structured beds to engineer bespoke wave propagation. This includes propagating waves with practically zero reflection and loss of form through circular bends in channels.
Code (Fortran 77)
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