On Determining the Onset and Strength of Breaking for Deep Water Waves. Part I: Unforced Irrotational Wave Groups

Abstract

Finding a robust threshold variable that determines the onset of breaking for deep water waves has been an elusive problem for many decades. Recent numerical studies of the unforced evolution of two-dimensional nonlinear wave trains have highlighted the complex evolution to recurrence or breaking, together with the fundamental role played by nonlinear intrawave group dynamics. In Part I of this paper the scope of twodimensional nonlinear wave group calculations is extended by using a wave-group-following approach applied to a wider class of initial wave group geometries, with the primary goal of identifying the differences between evolution to recurrence and to breaking onset. Part II examines the additional influences of wind forcing and background shear on these evolution processes.The present investigation focuses on the long-term evolution of the maximum of the local energy density along wave groups. It contributes a more complete picture, both long-term and short-term, of the approach to breaking and identifies a dimensionless local average growth rate parameter that is associated with the mean convergence of wave-coherent energy at the wave group maximum. This diagnostic growth rate appears to have a common threshold for all routes to breaking in deep water that have been examined and provides an earlier and more decisive indicator for the onset of breaking than previously proposed breaking thresholds. The authors suggest that this growth rate may also provide an indicative measure of the strength of wave breaking events.

Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

“…If we accept the idea that the γ is the result of a resonance in the generation mechanism, why would the wind generate a narrow spectrum in frequency at the peak and a broad one in angle? It should also be mentioned that recently a direct connection between the breaking phenomena and the modulational instability has been discussed in Song & Banner (2002), therefore we believe that the present results may also represent a first step towards the development of a new dissipation source term in the energy balance equation.…”

Capillary effects on wave breaking

“…We are able to go continuously from one wave pattern to another by changing the Bond number and the initial steepness of the wave. For our initial conditions, we observe that when surface tension effects are small, a critical steepness c can be defined to distinguish breaking from non-breaking waves, as already discussed theoretically as well as through experiments and numerical studies (Rapp & Melville 1990;Peregrine et al 1993;Song & Banner 2002;Banner & Peirson 2007;Perlin et al 2013). When surface tension becomes important, its influence is quantified through two boundaries separating firstly gravity-capillary waves and breakers, and secontly spilling and plunging breakers.…”

“…Perlin et al (2013)). When breaking is triggered by modulational instabilities, plunging waves can be observed for initial slopes ≈ 0.11 (Melville 1982;Tulin & Waseda 1999;Song & Banner 2002;Banner & Peirson 2007;Iafrati et al 2013). In focusing experiments a critical slope of the same order is described when considering the dissipation by breaking, and ≈ 0.08 (Drazen et al 2008;Romero et al 2012).…”

Modulational Instability, Wave Breaking, and Formation of Large-Scale Dipoles in the Atmosphere

“…The sideband components are placed at ∆k = k 0 /5 and their amplitude is A 1 = 0.1A 0 . The conditions are essentially similar to those used in [12,23] and corresponds to the early stages of an Akhmediev breather [3].…”