Wave breaking onset and strength for two-dimensional deep-water wave groups

2007 ◽  
Vol 585 ◽  
pp. 93-115 ◽  
Author(s):  
MICHAEL L. BANNER ◽  
WILLIAM L. PEIRSON
Keyword(s):  
Growth Rate ◽  
Energy Density ◽  
Deep Water ◽  
Wave Energy ◽  
Water Wave ◽  
Wave Group ◽  
Two Dimensional ◽  
Carrier Wave ◽  
Wave Groups ◽  
Deep Water Wave

The numerical study of J. Song & M. L. Banner (J. Phys. Oceanogr. vol. 32, 2002, p. 254) proposed a generic threshold parameter for predicting the onset of breaking within two-dimensional groups of deep-water gravity waves. Their parameter provides a non-dimensional measure of the wave energy convergence rate and geometrical steepening at the maximum of an evolving nonlinear wave group. They also suggested that this parameter might control the strength of breaking events. The present paper presents the results of a detailed laboratory observational study aimed at validating their proposals.For the breaking onset phase of this study, wave potential energy was measured at successive local envelope maxima of nonlinear deep-water wave groups propagating along a laboratory wave tank. These local maxima correspond alternately to wave group geometries with the group maximum occurring at an extreme carrier wave crest elevation, followed by an extreme carrier wave trough depression. As the nonlinearity increases, these crest and trough maxima can have markedly different local energy densities owing to the strong crest–trough asymmetry. The local total energy density was reconstituted from the potential energy measurements, and made dimensionless using the square of the local (carrier wave) wavenumber. A mean non-dimensional growth rate reflecting the rate of focusing of wave energy at the envelope maximum was obtained by smoothing the local fluctuations.For the cases of idealized nonlinear wave groups investigated, the observations confirmed the evolutionary trends of the modelling results of Song & Banner (2002) with regard to predicting breaking onset. The measurements confirmed the proposed common breaking threshold growth rate of 0.0014±0.0001, as well as the predicted key evolution times: the time taken to reach the energy maximum for recurrence cases; and the time to reach the breaking threshold and then breaking onset, for breaking cases.After the initiation and subsequent cessation of breaking, the measured wave packet mean energy losses and loss rates associated with breaking produced an unexpected finding: the post-breaking mean wave energy did not decrease to the mean energy level corresponding to maximum recurrence, but remained significantly higher. Therefore, pre-breaking absolute wave energy or mean steepness do not appear to be the most fundamental determinants of post-breaking wave packet energy density.However, the dependence of the fractional breaking energy loss of wave packets on the parametric growth rate just before breaking onset proposed by Song & Banner (2002) was found to provide a plausible collapse to our laboratory data sets, within the experimental uncertainties. Further, when the results for the energy loss rate per unit width of breaking front were expressed in terms of a breaker strength parameter b multiplying the fifth power of the wave speed, it is found that b was also strongly correlated with the parametric growth rate just before breaking. Measured values of b obtained in this investigation ranged systematically from 8 × 10−5 to 1.2 × 10−3. These are comparable with open ocean estimates reported in recent field studies.

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

2002 ◽  
Vol 32 (9) ◽  
pp. 2541-2558 ◽  
Author(s):  
Jin-Bao Song ◽  
Michael L. Banner
Keyword(s):  
Growth Rate ◽  
Nonlinear Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Group ◽  
Two Dimensional ◽  
Wave Groups ◽  
Average Growth ◽  
Deep Water Waves

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 two-dimensional 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.

Assessment of random wave energy dissipation due to submerged aquatic plants in shallow water using deep water wave conditions

2021 ◽  
pp. 147509022110399
Author(s):  
Dag Myrhaug ◽  
Pierre-Yves Henry
Keyword(s):  
Energy Dissipation ◽  
Shallow Water ◽  
Deep Water ◽  
Aquatic Plants ◽  
Wave Energy ◽  
Water Wave ◽  
Random Wave ◽  
Wave Energy Dissipation ◽  
Submerged Aquatic Plants ◽  
Deep Water Wave

This article addresses the random wave energy dissipation due to submerged aquatic plants in shallow water based on deep water wave conditions including estimation of wave damping. The motivation is to provide a simple engineering tool suitable to use when assessing random wave damping due to small patches of plants in shallow water. Examples of application for typical field conditions are provided. The present method versus common practice is discussed. A possible application of the outcome of this study is that it can be used as a parameterization of wave energy dissipation due to vegetation patches of limited size in operational estuarine and coastal circulation models.

Hindcast of Deep-Water Wave Energy Spectra for Hurricane Audrey of 1957

1973 ◽  
Author(s):  
Basil W. Wilson ◽  
Subrata K. Chakrabarti ◽  
Peter H. Feldhausen
Keyword(s):  
Deep Water ◽  
Wave Energy ◽  
Water Wave ◽  
Energy Spectra ◽  
Deep Water Wave

scholarly journals On Determining the Onset and Strength of Breaking for Deep Water Waves. Part II: Influence of Wind Forcing and Surface Shear

2002 ◽  
Vol 32 (9) ◽  
pp. 2559-2570 ◽  
Author(s):  
Michael L. Banner ◽  
Jin-Bao Song
Keyword(s):  
Growth Rate ◽  
Group Dynamics ◽  
Deep Water ◽  
Water Waves ◽  
Numerical Study ◽  
Wind Forcing ◽  
Vertical Shear ◽  
Wave Group ◽  
Wave Groups ◽  
Deep Water Waves

Abstract Part I of this study describes the authors' findings on a robust threshold variable that determines the onset of breaking for unforced, irrotational deep water waves and proposes a means of predicting the strength of breaking if the breaking threshold is exceeded. Those results were based on a numerical study of the unforced evolution of fully nonlinear, two-dimensional inviscid wave trains and highlight the fundamental role played by the nonlinear wave group dynamics. In Part II the scope of these calculations is extended to investigate the additional influence of wind forcing and background shear on the evolution to breaking. Using the methodology described in Part I, the present study focuses on the influence of wind forcing and vertical shear on long-term evolution toward breaking or recurrence of the maximum of the local energy density within a wave group. It investigates the behavior of a dimensionless local growth rate parameter that reflects the mean energy flux to the energy maximum in the wave group and provides a clearer physical interpretation of the evolution toward recurrence or breaking. Typically, the addition of the wind forcing and surface layer shear results in only small departures from the irrotational, unforced cases reported in Part I. This indicates that nonlinear hydrodynamic energy fluxes within wave groups still dominate the evolution to recurrence or breaking even in the presence of these other mechanisms. Further, the calculations confirm that the breaking threshold for this growth rate found for unforced irrotational wave groups in Part I is also applicable for cases with wind forcing and shear typical of open ocean conditions. Overall, this approach provides an earlier and more decisive indicator for the onset of breaking than previously proposed breaking thresholds and suggests a foundation for predicting the strength of breaking events.

Nonhydrostatic Modeling of Nonlinear Deep-Water Wave Groups

2010 ◽  
Vol 136 (2) ◽  
pp. 155-167 ◽  
Author(s):  
Chih-Chieh Young ◽  
Chin H. Wu
Keyword(s):  
Deep Water ◽  
Water Wave ◽  
Wave Groups ◽  
Deep Water Wave

scholarly journals Computational Fluid Dynamics Simulation of Deep-Water Wave Instabilities Involving Wave Breaking

2021 ◽  
Vol 144 (2) ◽  
Author(s):  
Yuzhu Li ◽  
David R. Fuhrman
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Wave ◽  
Class Ii ◽  
Dynamics Simulation ◽  
Class I ◽  
Wave Instabilities ◽  
Deep Water Wave

Abstract Instabilities of deep-water wave trains subject to initially small perturbations (which then grow exponentially) can lead to extreme waves in offshore regions. The present study focuses on the two-dimensional Benjamin–Feir (or modulational) instability and the three-dimensional crescent (or horseshoe) waves, also known as Class I and Class II instabilities, respectively. Numerical studies on Class I and Class II wave instabilities to date have been mostly limited to models founded on potential flow theory; thus, they could only properly investigate the process from initial growth of the perturbations to the initial breaking point. The present study conducts numerical simulations to investigate the generation and development of wave instabilities involving the wave breaking process. A computational fluid dynamics (CFD) model solving Reynolds-averaged Navier–Stokes (RANS) equations coupled with a turbulence closure model in terms of the Reynolds stress model is applied. Wave form evolutions, Fourier amplitudes, and the turbulence beneath the broken waves are investigated.

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