Wave statistics and energy dissipation of shallow-water breaking waves in a tank with a level bottom

Abstract

The present study focuses on two-dimensional direct numerical simulations of shallow-water breaking waves, specifically those generated by a wave plate at constant water depths. The primary objective is to quantitatively analyse the dynamics, kinematics and energy dissipation associated with wave breaking. The numerical results exhibit good agreement with experimental data in terms of free-surface profiles during wave breaking. A parametric study was conducted to examine the influence of various wave properties and initial conditions on breaking characteristics. According to research on the Bond number (

$Bo$

, the ratio of gravitational to surface tension forces), an increased surface tension leads to the formation of more prominent parasitic capillaries at the forwards face of the wave profile and a thicker plunging jet, which causes a delayed breaking time and is tightly correlated with the main cavity size. A close relationship between wave statistics and the initial conditions of the wave plate is discovered, allowing for the classification of breaker types based on the ratio of wave height to water depth,

$H/d$

. Moreover, an analysis based on inertial scaling arguments reveals that the energy dissipation rate due to breaking can be linked to the local geometry of the breaking crest

$H_b/d$

, and exhibits a threshold behaviour, where the energy dissipation approaches zero at a critical value of

$H_b/d$

. An empirical scaling of the breaking parameter is proposed as

$b = a(H_b/d - \chi _0)^n$

, where

$\chi _0 = 0.65$

represents the breaking threshold and

$n = 1.5$

is a power law determined through the best fit to the numerical results.