A note on breaking waves

Some simple general properties of wave breaking are deduced from the known behaviour of surface gravity waves in deep water, on the assumption that breaking occurs in association with wave groups. In particular we derive equations for the time interval, ז, between the onset of breaking of successive waves: ז ═ T / |1 – ( c ⋅ c g )/ c 2 |, and for the propagation vector c b (referred to as the ‘wave-breaking vector’) of the position at which breaking, once initiated, will proceed: c b ═ c (1 – c ⋅ c g / c 2 )+ c g . Here c is the phase velocity, and c g the group velocity, of waves of period T . Interfacial waves, internal gravity waves, inertial waves and planetary waves are considered as particular examples. The results apply not only to wave breaking, but to the movement of any property (e. g. fluid acceleration, gradient Richardson number) that is carried through a medium in association with waves. One application is to describe the distribution, in space and time, of regions of turbulent mixing, or transitional phenomena, in the oceans or atmosphere.

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Theoretical interpretation of fetch limited wind-drivensea observations

Nonlinear Processes in Geophysics ◽

10.5194/npg-12-1011-2005 ◽

2005 ◽

Vol 12 (6) ◽

pp. 1011-1020 ◽

Cited By ~ 30

Author(s):

V. E. Zakharov

Keyword(s):

Gravity Waves ◽

Wave Breaking ◽

Field Studies ◽

The Self ◽

Theoretical Interpretation ◽

Simple Analytical Model ◽

Surface Gravity Waves ◽

Interaction Terms ◽

Self Similar ◽

Observations of Breaking Waves and Energy Dissipation in Modulated Wave Groups

Journal of Physical Oceanography ◽

10.1175/jpo-d-17-0224.1 ◽

2018 ◽

Vol 48 (12) ◽

pp. 2937-2948 ◽

Cited By ~ 6

Author(s):

David W. Wang ◽

Hemantha W. Wijesekera

Keyword(s):

Energy Dissipation ◽

Wave Height ◽

Wave Breaking ◽

Dissipation Rate ◽

Breaking Waves ◽

Wave Groups ◽

Dissipation Rates ◽

Local Wave ◽

Tke Dissipation Rate ◽

The Impact

AbstractIt has been recognized that modulated wave groups trigger wave breaking and generate energy dissipation events on the ocean surface. Quantitative examination of wave-breaking events and associated turbulent kinetic energy (TKE) dissipation rates within a modulated wave group in the open ocean is not a trivial task. To address this challenging topic, a set of laboratory experiments was carried out in an outdoor facility, the Oil and Hazardous Material Simulated Environment Test Tank (203 m long, 20 m wide, 3.5 m deep). TKE dissipation rates at multiple depths were estimated directly while moving the sensor platform at a speed of about 0.53 m s−1 toward incoming wave groups generated by the wave maker. The largest TKE dissipation rates and significant whitecaps were found at or near the center of wave groups where steepening waves approached the geometric limit of waves. The TKE dissipation rate was O(10−2) W kg−1 during wave breaking, which is two to three orders of magnitude larger than before and after wave breaking. The enhanced TKE dissipation rate was limited to a layer of half the wave height in depth. Observations indicate that the impact of wave breaking was not significant at depths deeper than one wave height from the surface. The TKE dissipation rate of breaking waves within wave groups can be parameterized by local wave phase speed with a proportionality breaking strength coefficient dependent on local steepness. The characterization of energy dissipation in wave groups from local wave properties will enable a better determination of near-surface TKE dissipation of breaking waves.

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Numerical and the MU radar estimations of gravity wave enhancement and turbulent ozone fluxes near the tropopause

Annales Geophysicae ◽

10.5194/angeo-22-3889-2004 ◽

2004 ◽

Vol 22 (11) ◽

pp. 3889-3898 ◽

Cited By ~ 7

Author(s):

N. M. Gavrilov ◽

S. Fukao

Keyword(s):

Gravity Waves ◽

Wave Breaking ◽

Internal Gravity Waves ◽

Vertical Temperature ◽

Turbulent Diffusion Coefficient ◽

Middle Latitudes ◽

Mu Radar ◽

Different Seasons ◽

Ozone Fluxes ◽

Vertical Ozone

Abstract. It is shown with a numerical simulation that a sharp increase in the vertical temperature gradient and Brunt-Väisälä frequency near the tropopause may produce an increase in the amplitudes of internal gravity waves (IGWs) propagating upward from the troposphere, wave breaking and generation of stronger turbulence. This may enhance the transport of admixtures between the troposphere and stratosphere in the middle latitudes. Turbulent diffusion coefficient calculated numerically and measured with the MU radar are of 1-10m2/s in different seasons in Shigaraki, Japan (35° N, 136° E). These values lead to the estimation of vertical ozone flux from the stratosphere to the troposphere of (1-10)x1014, which may substantially add to the usually supposed ozone downward transport with the general atmospheric circulation. Therefore, local enhancements of IGW intensity and turbulence at tropospheric altitudes over mountains due to their orographic excitation and due to other wave sources may lead to the changes in tropospheric and total ozone over different regions.

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Breaking Surface Wave Effects on River Plume Dynamics during Upwelling-Favorable Winds

Journal of Physical Oceanography ◽

10.1175/jpo-d-12-0185.1 ◽

2013 ◽

Vol 43 (9) ◽

pp. 1959-1980 ◽

Cited By ~ 20

Author(s):

Gregory P. Gerbi ◽

Robert J. Chant ◽

John L. Wilkin

Keyword(s):

Gravity Waves ◽

Wave Breaking ◽

Deep Ocean ◽

River Plume ◽

Sea Floor ◽

Plume Dynamics ◽

Surface Gravity Waves ◽

Shear Dispersion ◽

Wave Effects ◽

Critical Richardson Number

Abstract This study examines the dynamics of a buoyant river plume in upwelling-favorable winds, concentrating on the time after separation from the coast. A set of idealized numerical simulations is used to examine the effects of breaking surface gravity waves on plume structure and cross-shore dynamics. Inclusion of a wave-breaking parameterization in the two-equation turbulence submodel causes the plume to be thicker and narrower, and to propagate offshore more slowly, than a plume in a simulation with no wave breaking. In simulations that include wave breaking, the plume has much smaller vertical gradients of salinity and velocity than in the simulation without breaking. This leads to decreased importance of shear dispersion in the plumes with wave breaking. Much of the widening rate of the plume is explained by divergent Ekman velocities at the off- and onshore edges. Some aspects of plume evolution in all cases are predicted well by a simple theory based on a critical Richardson number and an infinitely deep ocean. However, because the initial plume in these simulations is in contact with the sea floor in the inner shelf, some details are poorly predicted, especially around the time that the plume separates from the coast.

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Internal wave breaking and the fate of planets around solar-type stars

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311017807 ◽

2010 ◽

Vol 6 (S271) ◽

pp. 363-364

Author(s):

Adrian J. Barker ◽

Gordon I. Ogilvie

Keyword(s):

Gravity Waves ◽

Wave Breaking ◽

Internal Gravity Waves ◽

Amplitude Dependence ◽

Tidal Dissipation ◽

Short Period ◽

Central Regions ◽

Solar Type ◽

The Waves ◽

Solar Type Star

AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

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Transport by breaking internal gravity waves on slopes

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.723 ◽

2016 ◽

Vol 789 ◽

pp. 93-126 ◽

Cited By ~ 19

Author(s):

Robert S. Arthur ◽

Oliver B. Fringer

Keyword(s):

Gravity Waves ◽

Wave Breaking ◽

Internal Gravity Waves ◽

Length Scale ◽

Two Dimensional ◽

Turbulent Diffusivity ◽

Nepheloid Layer ◽

Molecular Diffusivity ◽

Tracking Model ◽

Offshore Transport

We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.

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Ensemble-Based Variational Method for Nonlinear Inversion of Surface Gravity Waves

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-19-0072.1 ◽

2020 ◽

Vol 37 (1) ◽

pp. 17-31 ◽

Cited By ~ 1

Author(s):

Wataru Fujimoto ◽

Takuji Waseda

Keyword(s):

Data Assimilation ◽

Gravity Waves ◽

Wave Model ◽

Surface Gravity ◽

Nonlinear Inversion ◽

Imaging Data ◽

Large Area ◽

Wave Groups ◽

Surface Gravity Waves ◽

Free Data

ABSTRACTFreak/rogue waves are considered to be the causes of marine accidents and their generation mechanism is closely related to the formation of wave groups. However, observations that capture the spatiotemporal evolution of coherent wave groups in directional windsea are rather limited. The paper presents a new technique known as the surface wave reconstruction by ensemble adjoint-free data assimilation (SWEAD) method that enables reconstruction of a spatiotemporal wave field covering a large area from wave records limited in observational density and spatial extent. We reconstructed spatiotemporal profiles of nonlinear surface gravity waves from virtual observational data using the adjoint-free four-dimensional variational data assimilation (a4DVar) scheme. The higher-order spectral method (HOSM) is used as a forward deep-water nonlinear wave model in a realistic sea state. The a4DVar scheme uses perturbed ensemble simulations to calculate the cost function gradient and Hessian; thus, construction of an adjoint model is not needed. A few extensions of the a4DVar scheme are proposed in this study. For efficient wave reconstruction, perturbed ensemble simulation results are reused by increasing the searching direction dimension at each iteration while assuring conformity to the perturbed model’s linearity. For regularization, Fourier coefficient magnitudes are constrained by a known power spectrum from the phase-averaged wave model. Twin experiments were conducted for a unidirectional wave with virtual wave gauge data and a multidirectional wave with virtual stereo camera imaging data. For both unidirectional and multidirectional cases, nonlinear freak wave–related wave groups were well reproduced, which is impossible using a linear model.

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Phase velocity and dispersion relations of surface gravity waves in shallow sea

Marine and Freshwater Research ◽

10.1071/mf9940993 ◽

1994 ◽

Vol 45 (6) ◽

pp. 993

Author(s):

VA Kalmykov

Keyword(s):

Phase Velocity ◽

Gravity Waves ◽

Experimental Studies ◽

Finite Depth ◽

Dispersion Relations ◽

Sea Surface ◽

Surface Gravity ◽

Linear Wave ◽

Shallow Sea ◽

Surface Gravity Waves

Phase velocity and dispersion relations of surface gravity waves on the sea have been modelled by two numerical methods and the results compared with previous experimental studies. Wave nonlinearities cause deviations from linear wave relations and these deviations are seen on the sea surface in the form of sharply crested waves. The effects are amplified if wave steepness increases or wave spectra become narrower. When the effects of finite depth of water are included in the calculations, the deviations from linearity are found to increase significantly.

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