Nonlinear Effects in Gravity Waves Propagating in Shallow Water

Abstract

Nonlinear energy transfers due to triad interactions change the characteristics of the wave-field in the shoaling region. The degree of nonlinear coupling is examined using numerical simulations based on an accurate set of deterministic evolution equations for the propagation of fully dispersive weakly nonlinear waves. The model validation, using existing experimental measurements for wave transformation over a shoal, showed that it accurately predicts nonlinear energy transfer for irregular waves with large wave-numbers. The bound higher harmonics and nonlinear statistical measures, i.e. the wave skewness and asymmetry, are well simulated by the model in both the shoaling and deshoaling regions. Numerical simulation of steep waves in shallow water with the Ursell number O(1), showed that nonlinear dispersion and phase locking lead to triad interactions even on a horizontal bottom. Nonlinear energy transfers in monochromatic waves lead to rapid spatial recurrence of the primary wave amplitudes. This is in contrast to the case of irregular waves where the Fourier coefficients of the wave-field do not recur due to the presence of innumerable interactions, which are expected to cancel resulting in no spatial evolution of the wave spectrum.