Stochastic modelling of nonlinear waves in shallow water
In this paper we shall study and model the nonlinear transformation of
frequency wave spectra using two different types of stochastic models.
The nonlinear processes considered include triad wave interaction and
dissipation due to depth-induced wave breaking. The two stochastic models
are the two-equation model proposed by Kofoed-Hansen and Rasmussen (1998)
and the one-equation Lumped Triad Approximation (LTA) originally proposed
by Eldeberky and Battjes (1995). Model results are compared with
laboratory experiments and results obtained by the underlying
deterministic time-domain Boussinesq model. The two stochastic models are
found in good agreement with measurements of wave height (Hm0) and wave
period (T01). In case of wave transformation on a horizontal bottom, the
LTA model fails as the rapid oscillations are neglected. The two-equation
model predicts the energy transfer to sub-harmonics and non-resonant
interaction excellently. In the inner surf zone and where the
nonlinearity is strong, only the underlying deterministic model predicts
the spectra and higher order wave statistics accurately.