Wave Energy Dissipation of Spilling and Plunging Breaking Waves in Spectral Models

Yana Saprykina,Burak Aydogan,Berna Ayat

doi:10.3390/jmse10020200

Abstract

On the basis of field experiments and modeling, the dependence of the dissipation of the energy of waves breaking by plunging and spilling on the frequency of wave spectra was investigated. It was shown that the modeling of wave breaking should take into account the compensation of the nonlinear growth of higher wave harmonics, which occurs in different ways for waves breaking with different types and for different methods of modeling a nonlinear source term. The study revealed that spilling breaking waves have a frequency selectivity of energy dissipation at frequencies of second and third harmonics for the Boussinesq and SWAN models for any method of modeling a nonlinear source term. Plunging breaking waves have a quadratic dependence of the dissipation coefficient on frequency in the Boussinesq model and SWAN model with the SPB approximation for a nonlinear source term. The SWAN model with default LTA approximation for plunging breaking waves also assumes frequency-selective energy dissipation. The discrepancy between the LTA default method and others can be explained by the overestimation of the contribution of the second nonlinear harmonic and by inaccurate approximation for the biphase. It is possible to improve the accuracy of LTA and SPB methods by tuning SWAN model coefficients.

Highlights

Almost all modeling of the dynamic processes occurring in the coastal zone of the sea begin with estimates of the wave parameters
The results revealed that the SPB model with trfac = 0.05 parametrization returned the most homogenous outputs for both spilling and plunging breaking waves, allowing the use of non-frequency-dependent energy dissipation formulations
We studied the necessary dissipation term for waves breaking by different types for modeling wave spectrum through phase-resolving and phase-averaged models with recommended default nonlinear terms

Summary

Introduction

Almost all modeling of the dynamic processes occurring in the coastal zone of the sea begin with estimates of the wave parameters. Changes in the steepness of waves and their asymmetry, occurring both due to linear and nonlinear processes and due to breaking, lead to a change in the higher statistical moments of wave motion, which determine the magnitude and the direction of sediment flow in the coastal zone [1]. There are a number of models that describe, with high accuracy, the linear and nonlinear transformation of waves over the real bottom topography in the coastal zone. Some phase resolving wave models are solved by spectral methods in the frequency domain that are less time-consuming in modeling as compared to the time domain simulation. Spectral method modeling results in the complex amplitudes of wave harmonics (deterministic models [3,4,5]) or the modulus of complex amplitudes and biphases (stochastic models [6])

Objectives

Methods

Discussion

Conclusion