Elevation and velocity measurements of laboratory shoaling waves

Measurements of wave elevation and orbital velocity in the shoaling, breaking, and bore regime of single-frequency laboratory waves show that third-order Stokes theory, when energy flux is conserved, predicts the wave height change and harmonic growth in the regime where the Ursell number Ur = (H/ h)/(kh)2 is 0(1) or less. Shoreward of the Stokes region and up to the breakpoint, harmonic amplitudes are well described by the cnoidal theory. It is shown theoretically that a smooth transition regime exists between Stokes and cnoidal regions for waves which eventually break by plunging. The wave profile asymmetry about the vertical plane observed in near-breaking waves and bores is due to slow changes of phase of the harmonics relative to the primary wave as the wave train shoals. By contrast, only asymmetry about the horizontal plane is possible in the Stokes and cnoidal wave theories, since these classical solutions allow no relative phase shifts between harmonics. Velocity measurements made with hot-film anemometers show that ‘unorganized’ fluctuations at the bottom under breaking waves are of the order of half the rms amplitude of the wave-induced ‘organized’ flow. The correlation between surface elevation and bottom velocity under breakers and bores suggests that turbulence contributes more strongly to the unorganized flow at the bottom under plunging than under spilling waves.