On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

Abstract

The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments' characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slowdown of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.

Crest speeds of unsteady surface water waves

“…In Banner et al (2014), our preliminary numerical study of chirped wave groups provides an overview of the gravity wave crest slowdown phenomenon, and has already been verified against observations of wave groups in the laboratory and in the open ocean field (see also Fedele 2014 a ). This generic crest slowdown phenomenon has been recently observed by other researchers (Shemer & Liberzon 2014; Itay & Liberzon 2017; Khait & Shemer 2018; Craciunescu & Christou 2019 a , b ). It is investigated in much greater detail in the present paper.…”

Microscale wave breaking in stratified air-water pipe flow

“…Wave breaking is characterized by fluid elements near the wave crest which achieve a velocity greater than the propagation speed of the wave, resulting in a reduction of the wave amplitude and increased turbulence levels in the liquid phase [1][2][3] . Here we consider wave breaking at deep or intermediate depths, as discussed by Perlin, Choi, and Tian 4 , as opposed to depth-limited breaking, typically observed as water waves approach a beach 5 .…”

“…This region disrupts the parasitic capillaries closest to the crest, while the smaller capillary waves located upstream of the toe of the spilling region may prevail during the breaking event 14 . Recently, the kinematic breaking criterion, which states that breaking occurs when fluid particles at the wave crest moves faster than the representative wave velocity, has received significant support 3,15,16 . Investigations of the initiation of breaking is however outside the scope of the present work, as we focus on detecting actively breaking waves and evaluating the properties of the liquid flow below actively breaking and nonbreaking waves.…”

Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties

“…Since the seminal work of Longuet-Higgins and Cokelet [75], increasingly efficient and generic numerical models were developed to simulate nonlinear ocean waves based on fully nonlinear potential flow (FNPF) equations, i.e., Euler equations for irrotational flows, in two-(2D), e.g., [2,13,19,21,22,35,37,38,40,43,44,46,47,58,65,66,81,84,88,111] or three-dimensions (3D), e.g., [5,11,25,26,34,55,82,83,94,114]. When simulating overturning waves in these models, as first proposed by [75], the free surface motion is typically described by an Eulerian-Lagrangian formulation.…”