Shallow-water spectral shapes

Laboratory flume observations and Boussinesq model simulations of wave transformation are used to investigate the evolution of spectral shapes in shallow water. Wave spectra of nonlinear, shallow-water waves both inside and outside the surf zone evolve to the same equilibrium shape (single-peak, double-peak, broad, and narrow incident spectra). The equilibrium shape consists of two slopes, k(-4/3) for kd < 1 and k(-5/2) for kd > 1. Broad incident spectra or multi-peaked spectra evolve to equilibrium over shorter distances than narrow incident spectra. Likewise, the evolution distances shorten as nonlinearity increases. The one-dimensional, time-domain Boussinesq model of Nwogu and Demirbilek (2001) reproduced the spectral evolution both inside and outside the surf zone. The model also simulated the equilibrium range spectral shapes for kd < 1.5. Similar to deepwater spectral evolution, the equilibrium range in shallow water is driven by the nonlinear wave-wave interactions. The evolution in spectral shape from strong harmonic peaks to an equilibrium shape reflects the change in wave shape from a vertical asymmetry to a horizontal asymmetry.