Shoaling of Nonlinear Surface Water Waves on Depth Uniform Current

This work presents the shoaling results of nonlinear surface water waves on depth uniform current through the classical integral approach. The Fourier approximation method that is verified to be accurate for steady water waves is used to compute and provide the integral properties for the conservation laws of shoaling waves. The calculations are performed up to the waves with amplitudes of 95% of the highest and up to the currents with the Fourde number equal to unity. The results are presented for different initial steepness and different dimensionless volume fluxes, and comparisons between the nonlinear shoaling and linear shoaling on different volume fluxes are also made. The effects of initial steepness and volume flux on the shoaling variations are numerically examined, conforming that the increasing initial steepness reduces the volume flux effect on the shoaling evolutions.