Spectral Evolution of Directional Finite Amplitude Dispersive Waves in Shallow Water

Two different aspects of nearshore wave modelling are discussed. The first section details a model valid in deeper water than the usual shallow water wave models. We derive a mild-slope equation in which nonlinearity is retained to second order in ϵ and dispersion is retained to all orders. The resulting parabolic model is then simplified for expedient calculation. This simplified model is compared to the data of Whalin (1971) with favorable results. The second section concerns the role of vector-sum interactions as compared to colinear, near-resonant interactions. We use the angular spectrum model of Kirby (1990) to determine which sort of interaction is dominant in the nearshore wavefield. A steady wave solution of the model and a case of unsteady wave evolution were investigated. Two simplified data sets with different amounts of directional spread were then run through the model. All three tests indicate that vector-sum interactions contribute significantly to wave field evolution.