Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations

Abstract:

We propose to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields using direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987). We implement a robust phenomenological-based energy dissipation model in HOS to capture the effect of wave-breaking dissipation on the overall wave-field evolution (Xiao et al 2013). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events.

By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field δ(x,y,t), which provides the times, locations and intensity of wave breaking events (δ>δ_c). This is validated by comparison of HOS simulations with Airborne Terrain Mapper (ATM) measurements in the recent ONR Hi-Res field experiment. Figure (a) shows one frame of simulated wave-field (with dissipation model). Figure (b) is the corresponding measurement from ATM, where a large wave breaking event was captured. Figure (c) is the 3D view of the simulated wave-field with the colored region representing dissipation with δ>δ_c. The HOS predicted high-dissipation area is found to agree well with the measured breaking area. Based on HOS predicted high-dissipation area (δ>δ_c), we calculate Λ(c) (Phillips 1985), the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity c. Figure (d) shows the distribution Λ(c) calculated from HOS. For breaking speeds c greater than 5m/s, the simulated Λ(c) is in qualitative agreement with Phillips theoretical power-law of Λ(c)~c^-6.

From δ(x,y,t), we further quantify wave breaking by calculating the whitecap coverage rate W_r(t) and energy dissipation rate ΔE'(t), and study the evolution of W_r and ΔE' to understand the role of wave breaking in nonlinear wave-field evolution. We obtain HOS simulations starting with initial 3D wave-fields given by JONSWAP directional spectra with a range of peak enhancement factors and spreading angles. We find that both W_r and ΔE' evolve to their peak values over a short time (t/T_p~O(ε^-1), ε is wave steepness) and after longer evolution (t/T_p>O(ε^-2)) they reach a quasi-stationary state.