Waves in coastal regions can be affected by the bottom, by currents and by the local wind. The traditional approach in numerical modelling of these waves is to compute the wave propagation with so-called wave rays for mono-chromatic waves (one constant period and one deep water direction) and to supplement this with computations of bottom dissipation. This approach has two important disadvantages. Firstly, spectral computations, e.g. to determine a varying mean wave period or varying shortcrestedness, would be rather inefficient in this approach. Secondly, interpretation of the results of the refraction computations is usually cumbersome because of crossing wave rays. The model presented here has been designed to correct these shortcomings: the computations are carried out efficiently for a large number of wave components and the effects of currents, bottom friction, local wind and wave breaking are added. This requires the exploitation of the concept of the spectral action balance equation and numerical wave propagation on a grid rather than along wave rays. The model has been in operation for problems varying from locally generated waves over tidal flats to swell penetration into Norwegian fjords. A comparison with extensive measurements is described for young swell under high wind penetrating the Rhine estuary.
Modular forms in the spectral action of Bianchi IX gravitational instantons