Cross-shore Transformation of Breaking Random Waves in the Surfzone

Abstract

The transformation of breaking waves in the surfzone, including the evolution of the roller, the foamy air-water mixture on the surface of a breaking wave, and the turbulence, determines the wave-driven onshore-directed mass transport, the vertical structure of the compensating return flow (undertow), and the increase in the mean water level (setup). A two-phase Reynolds-Averaged Navier-Stokes (RANS) model and field and laboratory observations are used to study the cross-shore transformation of the roller, turbulence, and undertow resulting from irregular breaking waves. Modeled wave heights, wave spectra, setup, and undertow agree well with field and laboratory observations on barred and unbarred bathymetry. The roller forcing contributes 50% - 60% to the setup. The horizontal advection and turbulence each contribute ∼ 20% to the setup, whereas the contribution of bottom stress is largest (up to 20%) for shallow sandbar crest depths. The majority of the energy transferred to the roller is dissipated internally, while 15% - 25% of the energy in breaking waves first is transferred to the roller and then diffused back to the water column. Internal dissipation of roller energy increases with increasing depth of the sandbar crest, possibly indicating a change from plunging to spilling breakers. The momentum flux balance in the mid- and lowerwater column is between the wave, vertical turbulence transfers, vertical inertia, and setup, whereas near the surface the roller and pressure slope are important. Turbulence transports momentum downwards, while vertical inertia transfers momentum upwards. Turbulence production dominates the near-surface turbulence-energy-flux balance, and its penetration depth in the trough onshore of the sandbar is correlated with the local wave height. The roller thickness is related to the local wave height. Surfzone turbulence is more anisotropic than plane-wake turbulence, and is dominated by cross-shore normal stresses. Cross-shore vertical two-dimensional anisotropy is dependent on the cross-shore position in the surfzone, vertical shear of the cross-shore current, wave directional spread, frequency, and proximity to the seafloor. The three dimensional turbulence structure is related to the total vertical current shear, and to the directions of both mean currents and waves. Horizontal turbulence length scales are larger than the vertical length scales, consistent with prior studies.