Showing papers on "Breaking wave published in 2007"

Global dissipative solutions of the camassa–holm equation

Abstract: This paper is devoted to the continuation of solutions to the Camassa–Holm equation after wave breaking. By introducing a new set of independent and dependent variables, the evolution problem is rewritten as a semilinear hyperbolic system in an L∞ space, containing a non-local source term which is discontinuous but has bounded directional variation. For a given initial condition, the Cauchy problem has a unique solution obtained as fixed point of a contractive integral transformation. Returning to the original variables, we obtain a semigroup of global dissipative solutions, defined for every initial data $\bar u\in H^1 ({\mathbb R})$, and continuously depending on the initial data. The new variables resolve all singularities due to possible wave breaking and ensure that energy loss occurs only through wave breaking.

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

Abstract: The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

Characteristics of the Atlantic Storm-Track Eddy Activity and Its Relation with the North Atlantic Oscillation

Abstract: This study focuses on feedbacks of the high-frequency eddy activity onto the quasi-stationary circulation, particularly with regard to the North Atlantic Oscillation (NAO). The methodology consists of analyzing NCEP–NCAR reanalysis data and sensitivity runs from a high-resolution nonhydrostatic regional model. Consistent with recent studies, results show that the jet displacement characteristic of the NAO phenomenon depends strongly on the dynamics of the synoptic-scale waves and the way they break. Positive and negative phases of the NAO are closely related to anticyclonic and cyclonic wave breaking, respectively. Indeed, the high-frequency momentum flux whose sign is directly related to the type of wave breaking is correlated with the NAO index over the Atlantic. The peak of the momentum flux signal precedes that of the NAO by a few days suggesting that wave breaking is triggering NAO events. Two examples illustrate the significant impact of single storms, in particular those occurring in the e...

Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation

Abstract: In this paper we mainly study the problem of the development of singularities for solutions to the periodic Degasperis-Procesi equation. Firstly, we show that the first blow-up of strong solution to the equation must occur only in the form of wave breaking and shock waves possibly appear afterwards. Secondly, we established two new blow-up results. Thirdly, we investigate the blow-up rate for all non-global strong solutions and determine the blow-up set of blowing-up strong solutions to the equation for a large class of initial data. We finally give an explicit example of weak solutions to the equation, which may be considered as periodic shock waves.

A particle image velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach

Abstract: Particle image velocimetry (PIV) measurements were performed in a wave tank under water waves propagating and breaking on a 1/15 sloping beach. The wave transformation occurred in the surf zone over a large domain covering several wavelengths from incipient breaking to swash zone beyond the shoreline. PIV spatial interrogation windows must be small enough to obtain accurate velocities, and one window covers only a small part of the domain. To overcome this problem and to measure the instantaneous velocity field over the whole surf zone area, we have split the full field into 14 overlapping smaller windows of the same size. Local measurements were synchronized with each other using pulsed TTL triggers and wave gauge data. The full velocity field was then reconstructed at every time step by gathering the 14 PIV fields. We then measured the complete space–time evolution of the velocity field over the whole surf zone. We determined also the ensemble-period-average and phase-average components of the flow with their associated fluctuating parts. We used the PIV images and velocity measurements to estimate the void fraction in each point of the surf zone. Special attention was given to the calculation of the spatial derivatives in order to obtain relevant information on vorticity and on the physical terms that appear in the fluctuating kinetic energy transport equation.

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

Abstract: 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

Blocking and Rossby Wave Breaking on the Dynamical Tropopause in the Southern Hemisphere

Abstract: Rossby wave breaking on the dynamical tropopause in the Southern Hemisphere (the −2-PVU surface) is investigated using the ERA-40 dataset. The indication of wave breaking is based on reversal in the meridional gradient of potential temperature, and persistent large-scale wave breaking is taken as a strong indication that blocking may be present. Blocking in the midlatitudes is found to occur predominantly during wintertime in the Pacific and is most vigorous in the east Pacific, while during summertime, the frequency of blocking weakens and its extent becomes confined to the west Pacific. The interannual variability of blocking is found to be high. Wave breaking occurs most frequently on the poleward side of the polar jet and has some, but not all, of the signatures of blocking, so it is referred to as high-latitude blocking. In general, cyclonic wave breaking occurs on the poleward side of the polar jet, otherwise anticyclonic breaking occurs. However, at least in wintertime, wave breaking in th...

Void fraction measurements in breaking waves

Abstract: This paper describes detailed measurements and analysis of the time-varying distribution of void fractions in three different breaking waves under laboratory conditions. The measurements were made with highly sensitive optical fibre phase detection probes and document the rapid spatial and temporal evolutions of both the bubble plume generated beneath the free surface and the splashes above. Integral properties of the measured void fraction fields reveal a remarkable degree of similarity between characteristics of the two-phase flow in different breaker types as they evolve with time. Depending on the breaker type, the energy expended in entraining air and generating splash accounts for a minimum of between 6.5 and 14% of the total energy dissipated during wave breaking.

Gravity wave turbulence in a laboratory flume

Abstract: We present experimental results for water wave turbulence excited by piston-like programmed wavemakers in a water flume with dimensions 6 × 12 × 1.5 meters. Our main finding is that for a wide range of excitation amplitudes the energy spectrum has a power-law scaling, E! ∼ ! −� . These scalings were achieved in up to one-decade wide frequency range, which is significantly wider than the range available in field observa- tions and in numerical simulations. However, exponentappears to be non-universal. It depends on the wavefield intensity and ranges from about 6.5 for weak forcing to about 3.5 for large levels of wave excitations. We discuss our results in the context of the key theoretical predictions, such as Zakharov-Filonenko spectrum � = −4, Phillips spectrum � = −5, Kuznetsov's revision of Phillips spectrum (leading to � = −4) and Nazarenko's prediction � = −6 for weak turbulence in finite basins. We measured Probability Density Function of the surface elevation and good agreement with the Tayfun shape except values near the maximum which we attribute to an anisotropy and inhomogeneity caused by the finite flume size. We argue that the wavenumber dis- creteness, due to the finite-size of the flume, prevents four-wave resonant interactions. Therefore, statistical evolution of the water surface in the laboratory is significantly different than in the open ocean conditions.

The evolution of large ocean waves: the role of local and rapid spectral changes

Abstract: This paper concerns the formation of large-focused or near-focused waves in both unidirectional and directional sea-states. When the crests of wave components of varying frequency superimpose at one point in space and time, a large, transient, focused wave can occur. These events are believed to be representative of the largest waves arising in a random sea and, as such, are of importance to the design of marine structures. The details of how such waves form also offer an explanation for the formation of the so-called freak or rogue waves in deep water. The physical mechanisms that govern the evolution of focused waves have been investigated by applying both the fully nonlinear wave model of Bateman et al . (Bateman et al . 2001 J. Comput. Phys . 174 , 277–305) and the Zakharov's evolution equation (Zakharov 1968 J. Appl. Mech. Tech. Phys . 9 , 190–194). Aspects of these two wave models are complementary, and their combined use allows the full nonlinearity to be considered and, at the same time, provides insights into the dominant physical processes. In unidirectional seas, it has been shown that the local evolution of the wave spectrum leads to larger maximum crest elevations. In contrast, in directional seas, the maximum crest elevation is well predicted by a second-order theory based on the underlying spectrum, but the shape of the largest wave is not. The differences between the evolution of large waves in unidirectional and directional sea-states have been investigated by analysing the results of Bateman et al . (2001) using a number of spectral analysis techniques. It has been shown that during the formation of a focused wave event, there are significant and rapid changes to the underlying wave spectrum. These changes alter both the amplitude of the wave components and their dispersive properties. Importantly, in unidirectional sea-states, the bandwidth of the spectrum typically increases; whereas, in directional sea-states it decreases. The changes to the wave spectra have been investigated using Zakharov's equation (1968). This has shown that the third-order resonant effects dominate changes to both the amplitude of the wave components and the dispersive properties of the wave group. While this is the case in both unidirectional and directional sea-states, the consequences are very different. By examining these consequences, directional sea-states in which large wave events that are higher and steeper than second-order theory would predict have been identified. This has implications for the types of sea-states in which rogue waves are most likely to occur.

The Intermediate Water Depth Limit of the Zakharov Equation and Consequences for Wave Prediction

Abstract: Finite-amplitude deep-water waves are subject to modulational instability, which eventually can lead to the formation of extreme waves. In shallow water, finite-amplitude surface gravity waves generate a current and deviations from the mean surface elevation. This stabilizes the modulational instability, and as a consequence the process of nonlinear focusing ceases to exist when kh 1.363. This is a well-known property of surface gravity waves. Here it is shown for the first time that the usual starting point, namely the Zakharov equation, for deriving the nonlinear source term in the energy balance equation in wave forecasting models, shares this property as well. Consequences for wave prediction are pointed out.

A Seasonal Climatology of Rossby Wave Breaking in the 320–2000-K Layer

Abstract: Differential advection in Rossby waves can lead to potential vorticity (PV; P) contours on isentropic surfaces folding over in latitude (Py < 0) in a process called Rossby wave breaking (RWB). Exploring the properties of RWB may shed light on underlying dynamics and enable quantification of irreversible transport. A seasonal climatology of Py and RWB statistics is presented for the 320–850-K layer using NCEP reanalysis data during 1979–2005 and for the 320–2000-K layer using the Met Office (UKMO) data during 1991–2003. A primary goal is to depict the spatial extent and seasonality of RWB maxima. This analysis shows seven distinct RWB regimes: poleward and equatorward of the subtropical westerly jets, poleward and equatorward of the stratospheric polar night jets, flanking the equator in the stratosphere and mesosphere, equatorward of subtropical monsoon anticyclones, and the summertime polar stratosphere. A striking PV gradient maximum exists at the equator throughout the layer 360–2000 K, flanke...

Wave–Current Interaction: A Comparison of Radiation-Stress and Vortex-Force Representations

Abstract: The vortex-force representation of the wave-averaged effects on currents is compared to the radiation-stress representation in a scaling regime appropriate to coastal and shelf waters. Three-dimensional and vertically integrated expressions for the conservative current equations are obtained in both representations. The vortex-force representation decomposes the main wave-averaged effects into two physically understandable concepts—a vortex force and a Bernoulli head. The vortex force is shown to be the dominant wave-averaged effect on currents. This effect can occur at higher order than the apparent leading order for the radiation-stress representation. Excluding nonconservative effects such as wave breaking, the lowest-order radiation or interaction stress can be completely characterized in terms of wave setup, forcing of long (infragravity) waves, and an Eulerian current whose divergence cancels that of the primary wave Stokes drift. The leading-order, wave-averaged dynamical effects incorpora...

Wave-follower field measurements of the wind-input spectral function: part III: parameterization of the wind-input enhancement due to wave breaking

Abstract: This is the third in a series of papers describing wave-follower observations of the aerodynamic coupling between wind and waves on a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). It focuses on the long-standing problem of the aerodynamic consequences of wave breaking on the wind–wave coupling. Direct field measurements are reported of the influence of wave breaking on the wave-induced pressure in the airflow over water waves, and hence the energy flux to the waves. The level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, covered the range of 3–7. The propagation speeds of the dominant waves were limited by the water depth and the waves were correspondingly steep. These measurements allowed an assessment of the magnitude of any breaking-induced enhancement operative for these field conditions and provided a basis for parameterizing the effect. Overall, appreciable levels of wave breaking occurred for the strong win...

Effects of wave rollers and bottom stress on wave setup

Abstract: [1] Setup, the increase in the mean water level associated with breaking waves, observed between the shoreline and about 6-m water depth on an ocean beach is predicted well by a model that includes the effects of wave rollers and the bottom stress owing to the mean flow. Over the 90-day observational period, the measured and modeled setups are correlated (squared correlation above 0.59) and agree within about 30%. Although rollers may affect setup significantly on beaches with large-amplitude (several meters high) sandbars and may be important in predicting the details of the cross-shore profile of setup, for the data discussed here, rollers have only a small effect on the amount of setup. Conversely, bottom stress (calculated using eddy viscosity and undertow formulations based on the surface dissipation, and assuming that the eddy viscosity is uniform throughout the water column) significantly affects setup predictions. Neglecting bottom stress results in underprediction of the observed setup in all water depths, with maximum underprediction near the shoreline where the observed setup is largest.

Predicting the breaking onset of surface water waves

Abstract: [1] Why do ocean waves break? Understanding this important and obvious property of the ocean surface has been elusive for decades. This paper investigates causes which lead deep-water two-dimensional initially monochromatic waves to break. Individual wave steepness is found to be the single parameter which determines whether the wave will break immediately, never break or take a finite number of wave lengths to break. The breaking will occur once the wave reaches the Stokes limiting steepness. The breaking probability and the location of breaking onset can be predicted, properties of incipient breakers measured. Potential applications to field conditions are discussed.

Liquid sloshing and wave breaking in circular and square-base cylindrical containers

Abstract: Near resonance sloshing in containers, filled with a liquid to a given depth h, depends on three parameters, which are the viscous damping, the frequency offset that contains the forcing amplitude and the fluid depth. Experiments have been conducted with low-viscosity liquids mainly in circular cylindrical containers of radius R subjected to harmonic horizontal forcing; complementary experiments on wave breaking have been performed in a square-base container. The fluid depth was kept large (h/R > 1) so that it was no longer a variable parameter. The bounds of existence of the different wave regimes, namely planar waves, swirling waves, chaotic sloshing as well as breaking waves, have been determined as a function of forcing frequencies relative to the lowest natural frequency ω1 and for a wide range of forcing amplitudes. It is shown that when the forcing frequency ω is slightly larger than the lowest natural frequency ω1, planar wave motion bifurcates to a swirling wave mode at finite wave amplitude, the value of which depends on the offset parameter. The swirl wave amplitude grows exponentially and saturates at a certain value. The swirl has a hard-spring behaviour, is very robust and can generate a vortical flow of the liquid column. Chaotic sloshing and wave breaking occur quasi-periodically: growth of planar wave amplitude at a rate depending on the forcing amplitude, collapse, irregular swirl and again growth of planar wave amplitude. The details and periodicity of the chaotic behaviour and breaking depend on the frequency-offset parameter. Close to the natural frequency, chaotic wave motion is possible without breaking. Planar wave breaking is, in general, associated with spilling caused by the encounter of nearly freely falling lumps of fluid with the upward moving wave crest, in a way demonstrated previously in two-dimensional wave breaking. In three dimensions, the wave crest is destabilized in the crosswise direction so that spilling is not uniform along the wave crest and an irregular swirl is generated following breaking; free fall of fluid lumps occurs over many wave periods. The complementary experiments, performed in a square-base container of base dimension L, show four different wave patterns of wavelengths L and L/2 crosswise to the primary wave. This cross-wave instability is interpreted in terms of parametric instability.

On the extreme statistics of long‐crested deep water waves: Theory and experiments

Abstract: [1] Quasi-resonant four-wave interactions may influence the statistical properties of deep water long-crested surface gravity waves. As a consequence, the wave height exceedance probability can substantially deviate from the expected distribution obtained by assuming that waves are linear. Here the occurrence probability of extreme events recently derived by N. Mori and P. Janssen (2006) is compared with wave tank data, where strong departures from Gaussian behavior are observed. Experimental wave height, maximum wave height distribution, and probability of occurrence of freak waves are compared with theoretical expectations. The theory well predicts extreme waves in nonlinear wavefields.

Stability properties of steady water waves with vorticity

Abstract: We present two stability analyses for exact periodic traveling water waves with vorticity. The first approach leads in particular to linear stability properties of water waves for which the vorticity decreases with depth. The second approach leads to a formal stability property for long water waves that have small vorticity and amplitude although we do not use a small-amplitude or long-wave approximation. © 2006 Wiley Periodicals, Inc.

Synoptic Analysis of the Pacific-North American Teleconnection Pattern

Abstract: In this study, we use various diagnostic techniques to investigate the synoptic evolution of the Pacific–North American teleconnection pattern (PNA). National Center for Environment Prediction/National Center for Atmospheric Research reanalysis data are used. These data cover the years 1948–2008 for the months of November–March. It is found that the positive PNA is initiated by enhanced convection over the western tropical Pacific and weakened convection over the tropical Indian Ocean. The excitation of the negative PNA exhibits opposite features. For both phases, the response to tropical convection excites a small-amplitude PNA about 8–12 days prior to the pattern attaining its maximum amplitude. This is followed by slow, steady growth for about 5 days, after which driving by synoptic scale waves, via their eddy vorticity flux, together with stationary eddy advection lead to much more rapid growth and the establishment of the full PNA. For the positive PNA, the synoptic scale waves propagate eastward into the midlatitude northeastern Pacific, where they are observed to undergo cyclonic wave breaking. For the negative PNA, the synoptic scale waves first amplify over the midlatitude northeastern Pacific and then propagate equatorward into the Subtropics where they undergo anticyclonic wave breaking. Once established, for both phases, the PNA appears to be maintained through a positive feedback that involves a succession of wave breakings. These results suggest that preconditioning may play an important role in the formation of the PNA. For the positive PNA, in its early development, the strengthening and eastward extension of the subtropical jet result in an increase in the cyclonic shear and a decrease in the meridional potential vorticity gradient, features that are known to favour cyclonic wave breaking. For the negative PNA, opposite changes were observed for the background flow, which favour equatorward wave propagation and anticyclonic wave breaking. The role of optimal growth is also discussed. Our results also suggest that the PNA is potentially predictable 1–2 weeks in advance. Copyright © 2011 Royal Meteorological Society

Real-time Breaking Waves for Shallow Water Simulations

Abstract: We present a new method for enhancing shallow water simulations by the effect of overturning waves. While full 3D fluid simulations can capture the process of wave breaking, this is beyond the capabilities of a pure height field model. 3D simulations, however, are still too expensive for real-time applications, especially when large bodies of water need to be simulated. The extension we propose overcomes this problem and makes it possible to simulate scenes such as waves near a beach, and surf riding characters in real-time. In a first step, steep wave fronts in the height field are detected and marked by line segments. These segments then spawn sheets of fluid represented by connected particles. When the sheets impinge on the water surface, they are absorbed and result in the creation of particles representing drops and foam. To enable interesting applications, we furthermore present a two-way coupling of rigid bodies with the fluid simulation. The capabilities and efficiency of the method will be demonstrated with several scenes, which run in real-time on today's commodity hardware.

Vertical Structure of Dissipation in the Nearshore

Abstract: The vertical structure of the dissipation of turbulence kinetic energy was observed in the nearshore region (3.2-m mean water depth) with a tripod of three acoustic Doppler current meters off a sandy ocean beach. Surface and bottom boundary layer dissipation scaling concepts overlap in this region. No depth-limited wave breaking occurred at the tripod, but wind-induced whitecapping wave breaking did occur. Dissipation is maximum near the surface and minimum at middepth, with a secondary maximum near the bed. The observed dissipation does not follow a surfzone scaling, nor does it follow a “log layer” surface or bottom boundary layer scaling. At the upper two current meters, dissipation follows a modified deep-water breaking-wave scaling. Vertical shear in the mean currents is negligible and shear production magnitude is much less than dissipation, implying that the vertical diffusion of turbulence is important. The increased near-bed secondary dissipation maximum results from a decrease in the tu...

Dynamics of Convectively Driven Banded Jets in the Laboratory

Abstract: The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

The interaction between an internal gravity wave and the planetary boundary layer. Part II: Effect of the wave on the turbulence structure

Abstract: An atmospheric internal gravity wave was measured over a two-hour period by a microbarograph array and a series of fast response wind and temperature sensors deployed along a 300m tower. the particularly monochromatic nature of the pressure signal at the ground enabled an explicit separation of the velocity field into mean, wave, and turbulent components. Large wave-frequency fluctuations were observed in the turbulent Reynolds stresses. Their significance is discussed at length with special regard to their role in the budget of wave kinetic energy. It is shown that the quadrature relationship which they maintain with the components of wave-shear, limits their effectiveness in reducing the wave amplitude. Analysis of the important time scales in the budget of turbulent kinetic energy reveals that the energy containing eddies have time scales longer than the wave period, and consequently the turbulence cannot remain in equilibrium with large, wave-frequency fluctuations in shear production. the result is a boundary layer which never attains a true equilibrium state.

Influence of energetic wind and waves on gas transfer in a large wind–wave tunnel facility

Abstract: Air–water gas exchange experiments were carried out in a large wind wave tunnel in Marseille, France, to investigate gas transfer processes under energetic wind and wave fields, where macroscale breaking waves create bubble plumes (white caps) and turbulence on the water surface. We measured the gas transfer velocities of N2O, DMS, He, SF6, CH3Br, and total air. Their diffusivity and solubility span a large range, allowing us to investigate gas transfer mechanisms under a variety of physical conditions. We observed that the gas transfer velocities varied with friction velocity in a linear manner. Gas transfer in the presence of pure wind waves is generally consistent with the surface renewal model, as the gas transfer velocity has a strong dependence on diffusivity with an exponent of 0.53(±0.02). Contrary to expectations, the bubble plumes generated by breaking waves contributed relatively little in our pure wind wave experiments. Superposition of mechanically generated waves onto the wind waves in the high wind regime attenuated DMS gas transfer (as a function of friction velocity) across the air–water interface by ~20% compared with gas transfer under pure wind waves, implying suppression of gas transfer directly across the sheared water surface. Greater transfer of less soluble gases may result from bubble-mediated gas transfer.

Modeling of surf zone processes on a natural beach using Reynolds‐Averaged Navier‐Stokes equations

Abstract: [1] The use of an advanced volume of fluid (VOF)-type model (COBRAS-UC), based on the Reynolds-Averaged Navier-Stokes (RANS) equations, is proposed in this work with the aim of improving the current state of understanding of surf zone processes on natural beaches. Previous studies have suggested that it is important to consider contributions from terms traditionally neglected when assuming a uniform velocity and pressure distribution and a simple turbulence parameterization in surf zone hydrodynamics. In contrast with the Boussinesq and Nonlinear Shallow Water (NSW) equations models, in the RANS models none of the above-mentioned limiting assumptions is required, since no wave theory is imposed and the initiation of wave breaking is predicted by using an advanced turbulence model. Although the model has been widely validated in the laboratory, there is no previous study, to the best of the authors' knowledge, which addresses the applicability of this model to random waves on natural beaches. Free-surface elevation and wave-induced velocity observations, from the SwashX field experiment, are used to validate this model. The model is able to satisfactorily predict the wave evolution and flow characteristics across the surf zone. The model provides a means to obtain high spatial and time resolution information of magnitudes which are difficult or impossible to measure in the field and therefore may contribute to improve our understanding on the physics of surf zone hydrodynamics. Moreover, it is also an excellent tool to obtain useful information of magnitudes involved in different kinds of modeling that require parameterization.