Showing papers on "Breaking wave published in 2015"

Destructive tsunami-like wave generated by surf beat over a coral reef during Typhoon Haiyan.

Abstract: Storm surges cause coastal inundation due to setup of the water surface resulting from atmospheric pressure, surface winds and breaking waves. Here we show that during Typhoon Haiyan, the setup generated by breaking waves near the fringing-reef-protected town of Hernani, the Philippines, oscillated with the incidence of large and small wave groups, and steepened into a tsunami-like wave that caused extensive damage and casualties. Though fringing reefs usually protect coastal communities from moderate storms, they can exacerbate flooding during strong events with energetic waves. Typical for reef-type bathymetries, a very short wave-breaking zone over the steep reef face facilitates the freeing of infragravity-period fluctuations (surf beat) with little energy loss. Since coastal flood planning relies on phase-averaged wave modelling, infragravity surges are not being accounted for. This highlights the necessity for a policy change and the adoption of phase-resolving wave models for hazard assessment in regions with fringing reefs.

Field Measurements of Surface and Near-Surface Turbulence in the Presence of Breaking Waves

Abstract: Wave breaking removes energy from the surface wave field and injects it into the upper ocean, where it is dissipated by viscosity. This paper presents an investigation of turbulent kinetic energy (TKE) dissipation beneath breaking waves. Wind, wave, and turbulence data were collected in the North Pacific Ocean aboard R/P FLIP, during the ONR-sponsored High Resolution Air-Sea Interaction (HiRes) and Radiance in a Dynamic Ocean (RaDyO) experiments. A new method for measuring TKE dissipation at the sea surface was combined with subsurface measurements to allow estimation of TKE dissipation over the entire wave-affected surface layer. Near the surface, dissipation decayed with depth as z−1, and below approximately one significant wave height, it decayed more quickly, approaching z−2. High levels of TKE dissipation very near the sea surface were consistent with the large fraction of wave energy dissipation attributed to non-air-entraining microbreakers. Comparison of measured profiles with large-eddy s...

Surface Wave Effects in the NEMO Ocean Model: Forced and Coupled Experiments ∗

Abstract: The NEMO general circulation ocean model is extended to incorporate three physical processes related to ocean surface waves, namely the surface stress (modified by growth and dissipation of the oceanic wavefield), the turbulent kinetic energy flux from breaking waves, and the Stokes-Coriolis force. Experiments are done with NEMO in ocean-only (forced) mode and coupled to the ECMWF atmospheric and wave models. Ocean-only integrations are forced with fields from the ERA-Interim reanalysis. All three effects are noticeable in the extratropics, but the sea-state-dependent turbulent kinetic energy flux yields by far the largest difference. This is partly because the control run has too vigorous deep mixing due to an empirical mixing term in NEMO. We investigate the relation between this ad hoc mixing and Langmuir turbulence and find that it is much more effective than the Langmuir parameterization used in NEMO. The biases in sea surface temperature as well as subsurface temperature are reduced, and the total ocean heat content exhibits a trend closer to that observed in a recent ocean reanalysis (ORAS4) when wave effects are included. Seasonal integrations of the coupled atmosphere-wave-ocean model consisting of NEMO, the wave model ECWAM, and the atmospheric model of ECMWF similarly show that the sea surface temperature biases are greatly reduced when the mixing is controlled by the sea state and properly weighted by the thickness of the uppermost level of the ocean model. These wave-related physical processes were recently implemented in the operational coupled ensemble forecast system of ECMWF.

Upper atmospheric gravity wave details revealed in nightglow satellite imagery

Abstract: Gravity waves (disturbances to the density structure of the atmosphere whose restoring forces are gravity and buoyancy) comprise the principal form of energy exchange between the lower and upper atmosphere. Wave breaking drives the mean upper atmospheric circulation, determining boundary conditions to stratospheric processes, which in turn influence tropospheric weather and climate patterns on various spatial and temporal scales. Despite their recognized importance, very little is known about upper-level gravity wave characteristics. The knowledge gap is mainly due to lack of global, high-resolution observations from currently available satellite observing systems. Consequently, representations of wave-related processes in global models are crude, highly parameterized, and poorly constrained, limiting the description of various processes influenced by them. Here we highlight, through a series of examples, the unanticipated ability of the Day/Night Band (DNB) on the NOAA/NASA Suomi National Polar-orbiting Partnership environmental satellite to resolve gravity structures near the mesopause via nightglow emissions at unprecedented subkilometric detail. On moonless nights, the Day/Night Band observations provide all-weather viewing of waves as they modulate the nightglow layer located near the mesopause (∼90 km above mean sea level). These waves are launched by a variety of physical mechanisms, ranging from orography to convection, intensifying fronts, and even seismic and volcanic events. Cross-referencing the Day/Night Band imagery with conventional thermal infrared imagery also available helps to discern nightglow structures and in some cases to attribute their sources. The capability stands to advance our basic understanding of a critical yet poorly constrained driver of the atmospheric circulation.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

Abstract: The scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Combined infragravity wave and sea‐swell runup over fringing reefs by super typhoon Haiyan

Abstract: Super typhoon Haiyan struck the Philippines on 8 November 2013, marking one of the strongest typhoons at landfall in recorded history. Extreme storm waves attacked the Pacific coast of Eastern Samar where the violent typhoon first made landfall. Our field survey confirmed that storm overwash heights of 6–14 m above mean sea level were distributed along the southeastern coast and extensive inundation occurred in some coastal villages in spite of natural protection by wide fringing reefs. A wave model based on Boussinesq-type equations is constructed to simulate wave transformation over shallow fringing reefs and validated against existing laboratory data. Wave propagation and runup on the Eastern Samar coast are then reproduced using offshore boundary conditions based on a wave hindcast. The model results suggest that extreme waves on the shore are characterized as a superposition of the infragravity wave and sea-swell components. The balance of the two components is strongly affected by the reef width and beach slope through wave breaking, frictional dissipation, reef-flat resonances, and resonant runup amplification. Therefore, flood characteristics significantly differ from site to site due to a large variation of the two topographic parameters on the hilly coast. Strong coupling of infragravity waves and sea swells produces extreme runup on steep beaches fronted by narrow reefs, whereas the infragravity waves become dominant over wide reefs and they evolve into bores on steep beaches.

Capillary effects on wave breaking

Abstract: We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier-Stokes equations for a two-phase air-water flow. A parametric study in terms of the Bond number, Bo, and the initial wave steepness, , is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of (, Bo) is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness c defines the wave stability. At low Bond number, the influence of surface tension is quantified through two boundaries separating, firstly gravity-capillary waves and breakers, and secondly spilling and plunging breakers; both boundaries scaling as ∼ (1 + Bo) −1/3. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter b is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at high Reynolds number

Abstract: Motivated by the importance of small-scale turbulent diapycnal mixing to the closure of the large-scale meridional overturning circulation (MOC) of the oceans, we focus on a model problem which allows us to address the fundamental fluid mechanics that is expected to be characteristic of the oceanographic regime. Our model problem is one in which the initial conditions consist of a stably stratified parallel shear flow which evolves into the turbulent regime through the growth of a Kelvin–Helmholtz wave to finite amplitude followed by transition to turbulence. Through both linear stability analysis and direct numerical simulations (DNS), we investigate the secondary instabilities and the turbulent mixing at a fixed high Reynolds number and for a range of Prandtl numbers. We demonstrate that the oceanographically expected high value of the Prandtl number has a profound influence on the nature of the secondary instabilities that govern the transition process. Specifically through non-separable linear stability analysis, we discover new characteristics for the shear-aligned convective instability such that it is modified into a mixed mode that is driven both by static instability and by shear. The growth rate and ultimate strength of this mode are both strongly enhanced at higher while the growth rate and ultimate strength of the stagnation point instability (SPI), which may compete for control of the transition process, are simultaneously impeded. Of equal importance is the fact that, for higher , the characteristic length scales associated with the dominant mixed mode of instability decrease and therefore there ceases to be a strong scale selectivity. In the limit of much higher , we conjecture that a wide range of spatial scales become equally unstable so as to support an ‘ultraviolet catastrophe’, in which a direct injection of energy occurs into a broad range of scales simultaneously. We further establish the validity of these analytical results through a series of computationally challenging DNS analyses, and provide a detailed analysis of the efficiency of the turbulent mixing of the density field that occurs subsequent to transition and of the entrainment of fluid into the mixing layer from the high-speed flanks of the shear flow. We show that the mixing efficiency decreases monotonically with increase of the molecular value of the Prandtl number and the expansion of the shear layer is reduced as such entrainment diminishes.

Surface roughness and breaking wave properties retrieved from polarimetric microwave radar backscattering

Abstract: Ocean surface roughness and wave breaking are the two main contributors of radar backscattering from the ocean surface. The relative weightings of the two contributions vary with the microwave polarization: the VV (vertical transmit vertical receive) is dominated by the Bragg resonance scattering mechanism, and the HH (horizontal transmit horizontal receive) and VH (horizontal transmit vertical receive or vertical transmit horizontal receive) contain nontrivial non-Bragg contributions mainly produced by breaking features. A method is developed to obtain the short-scale properties of ocean surface roughness and wave breaking from Ku, C, and L band polarimetric sea returns. The results are used for quantitative evaluation of the ocean surface roughness spectral models and for deriving understanding of the breaking contribution important to microwave ocean remote sensing, in particular its dependence on wind speed, microwave frequency, and incidence angle. Implications of the results to air-sea interaction applications are discussed.

Nonlocal resonances in weak turbulence of gravity-capillary waves.

Abstract: We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space-resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve three-wave resonant interactions. By studying the solutions of the resonance conditions, we show that the nonlinear interaction is dominantly one dimensional and involves collinear wave vectors. Furthermore, taking into account the spectral widening due to weak nonlinearity explains why nonlocal interactions are possible between a gravity wave and high-frequency capillary ones. We observe also that nonlinear three-wave coupling is possible among gravity waves, and we raise the question of the relevance of this mechanism for oceanic waves.

Wave Boundary Layer Turbulence over Surface Waves in a Strongly Forced Condition

Abstract: Accurate predictions of the sea state–dependent air–sea momentum flux require a thorough understanding of the wave boundary layer turbulence over surface waves. A set of momentum and energy equations is derived to formulate and analyze wave boundary layer turbulence. The equations are written in wave-following coordinates, and all variables are decomposed into horizontal mean, wave fluctuation, and turbulent fluctuation. The formulation defines the wave-induced stress as a sum of the wave fluctuation stress (because of the fluctuating velocity components) and a pressure stress (pressure acting on a tilted surface). The formulations can be constructed with different choices of mapping. Next, a large-eddy simulation result for wind over a sinusoidal wave train under a strongly forced condition is analyzed using the proposed formulation. The result clarifies how surface waves increase the effective roughness length and the drag coefficient. Specifically, the enhanced wave-induced stress close to the ...

New computational methods in tsunami science

Abstract: Tsunamis are rare events with severe consequences. This generates a high demand on accurate simulation results for planning and risk assessment purposes because of the low availability of actual data from historic events. On the other hand, validation of simulation tools becomes very difficult with such a low amount of real-world data. Tsunami phenomena involve a large span of spatial and temporal scales-from ocean basin scales of [Formula: see text] to local coastal wave interactions of [Formula: see text] or even [Formula: see text], or from resonating wave phenomena with durations of [Formula: see text] to rupture with time periods of [Formula: see text]. The scale gap of five orders of magnitude in each dimension makes accurate modelling very demanding, with a number of approaches being taken to work around the impossibility of direct numerical simulations. Along with the mentioned multi-scale characteristic, the tsunami wave has a multitude of different phases, corresponding to different wave regimes and associated equation sets. While in the deep ocean, wave propagation can be approximated relatively accurately by linear shallow-water theory, the transition to a bore or solitary wave train in shelf areas and then into a breaking wave in coastal regions demands appropriate mathematical and numerical treatments. The short duration and unpredictability of tsunami events pose another challenging requirement to tsunami simulation approaches. An accurate forecast is sought within seconds with very limited data available. Thus, efficiency in numerical solution processes and at the same time the consideration of uncertainty play a big role in tsunami modelling applied for forecasting purposes. Language: en

Infragravity-wave dynamics in a barred coastal region, a numerical study

Abstract: This paper presents a comprehensive numerical study into the infragravity-wave dynamics at a field site, characterized by a gently sloping barred beach. The nonhydrostatic wave-flow model SWASH was used to simulate the local wavefield for a range of wave conditions (including mild and storm conditions). The extensive spatial coverage of the model allowed us to analyze the infragravity-wave dynamics at spatial scales not often covered before. Overall, the model predicted a wavefield that was representative of the natural conditions, supporting the model application to analyze the wave dynamics. The infragravity-wave field was typically dominated by leaky waves, except near the outer bar where bar-trapped edge waves were observed. Relative contributions of bar-trapped waves peaked during mild conditions, when they explained up to 50% of the infragravity variance. Near the outer bar, the infragravity-wave growth was partly explained by nonlinear energy transfers from short waves. This growth was strongest for mild conditions, and decreased for more energetic conditions when short waves were breaking at the outer bar. Further shoreward, infragravity waves lost most of their energy, due to a combination of nonlinear transfers, bottom friction, and infragravity-wave breaking. Nonlinear transfers were only effective near the inner bar, whereas near the shoreline (where losses were strongest) the dissipation was caused by the combined effect of bottom friction and breaking. This study demonstrated the model's potential to study wave dynamics at field scales not easily covered by in situ observations.

Dynamics of Wave Setup over a Steeply Sloping Fringing Reef

Abstract: High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdow...

Nonlinear infragravity–wave interactions on a gently sloping laboratory beach

Abstract: A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy transfers to investigate energy flows within the spectra. Energy flows are identified by dividing transfers into four types of triad interactions, with triads including one, two, or three infragravity–frequency components, and triad interactions solely between short-wave frequencies. In the shoaling zone, the energy transfers are generally from the spectral peak to its higher harmonics and to infragravity frequencies. While receiving net energy, infragravity waves participate in interactions that spread energy of the short-wave peaks to adjacent frequencies, thereby cre- ating a broader energy spectrum. In the short-wave surf zone, infragravity–infragravity interactions develop, and close to shore, they dominate the interactions. Nonlinear energy fluxes are compared to gradients in total energy flux and are observed to balance nearly completely. Overall, energy losses at both infragravity and short-wave frequencies can largely be explained by a cascade of nonlinear energy transfers to high frequencies (say, f . 1.5 Hz) where the energy is presumably dissipated. Infragravity–infragravity interactions seem to induce higher harmonics that allow for shape transformation of the infragravity wave to symmetric. The largest decrease in infragravity wave height occurs close to the shore, where infragravity–infragravity in- teractions dominate and where the infragravity wave is asymmetric, suggesting wave breaking to be the dominant mechanism of infragravity wave dissipation.

Mountain waves and wakes generated by South Georgia: implications for drag parametrization

Abstract: High-resolution simulations of flows over South Georgia (South Atlantic) are used to increase understanding of the likely influence of small isolated mountainous islands on the large-scale flow and to ascertain the extent to which parametrization schemes can account for the missing drag in models where such islands are only partially resolved. Long-duration (1 month) austral winter forecasts with a horizontal grid spacing of 1.5 km are used to quantify the mountain-wave momentum fluxes generated by the island and the low-level drag associated with flow-blocking dynamics. The characteristics of the drag, such as the occurrence of high and low drag states, its dependence on wind direction and the spectral contributions to the mountain-wave momentum flux, are considered. Flow splitting and low-level wave breaking are shown to be responsible for wake regions that extend for hundreds of kilometres from the island. Regions of deceleration are also evident in the stratosphere, due to mountain-wave dissipation. The extent to which an orographic drag parametrization scheme can reproduce the drag is investigated by comparison with coarse-resolution (15 km grid spacing) simulations in which the orography is poorly resolved and a large proportion of the drag is parametrized. It is demonstrated that the total of the resolved plus parametrized drag in these simulations closely resembles that at high resolution, although it is underpredicted during instances of high drag. Simple modifications to the scheme, which enhance the drag when the low-level flow is approximately normal to the major axis of the subgrid orography, are shown to rectify this. The study demonstrates that, at least for relatively simple isolated mountain ranges, the drag and mountain-wave momentum fluxes can be predicted in a deterministic sense by a well-tuned parametrization scheme of suitable complexity, although inclusion of stochastic effects might lead to yet further improvements.

New wave generation

Abstract: We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (2007). This mechanism, which involves a tunable source comprised of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential has yet to be realized. Our studies reveal that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.

Experimental study on plunging breaking waves in deep water

Abstract: This study presents a unique data set that combines measurements of velocities and void fraction under an unsteady deep water plunging breaker in a laboratory. Flow properties in the aerated crest region of the breaking wave were measured using modified particle image velocimetry (PIV) and bubble image velocimetry (BIV). Results show that the maximum velocity in the plunging breaker reached 1.68C at the first impingement of the overturning water jet with C being the phase speed of the primary breaking wave, while the maximum velocity reached 2.14C at the beginning of the first splash-up. A similarity profile of void fraction was found in the successive impinging and splash-up rollers. In the highly foamy splashing roller, the increase of turbulent level and vorticity level were strongly correlated with the increase of void fraction when the range of void fraction was between 0 and 0.4 (from the trough level to approximately the center of the roller). The levels became constant when void fraction was greater than 0.5. The mass flux, momentum flux, kinetic energy, potential energy, and total energy were computed and compared with and without the void fraction being accounted for. The results show that all the mean and turbulence properties related to the air-water mixture are considerably overestimated unless void fraction is considered. When including the density variation due to the air bubbles, the wave energy dissipated exponentially a short distance after breaking; about 54% and 85% of the total energy dissipated within one and two wavelengths beyond the breaking wave impingement point, respectively.

Influences of source conditions on mountain wave penetration into the stratosphere and mesosphere

Abstract: We present atmospheric gravity wave (GW) measurements obtained by a Rayleigh/Raman lidar at Lauder, New Zealand (45∘ S, 170∘ E) during and after the DEEPWAVE campaign. GW activity and characteristics are derived from 557 hours of high-resolution lidar data recorded between June and November 2014 in an altitude range between 28 and 76 km. In this period, strong GW activity occurred in sporadic intervals lasting a few days. Enhanced stratospheric GW potential energy density is detected during periods with high tropospheric wind speeds perpendicular to New Zealand's Southern Alps. These enhancements are associated with the occurrence of quasi-stationary GW (mountain waves). Surprisingly, the largest response in the mesosphere is observed for conditions with low to moderate lower tropospheric wind speeds (2–12 m/s). On the other hand, large-amplitude mountain waves excited by strong tropospheric forcings often do not reach mesospheric altitudes, either due to wave breaking and dissipation in the stratosphere or refraction away from New Zealand.

Passive buoyant tracers in the ocean surface boundary layer: 1. Influence of equilibrium wind‐waves on vertical distributions

Abstract: This paper is the first of a two part series that investigates passive buoyant tracers in the ocean surface boundary layer. The first part examines the influence of equilibrium wind-waves on vertical tracer distributions, based on large eddy simulations (LES) of the wave-averaged Navier-Stokes equation. The second part applies the model to investigate observations of buoyant microplastic marine debris, which has emerged as a major ocean pollutant. The LES model captures both Langmuir turbulence (LT) and enhanced turbulent kinetic energy input due to breaking waves (BW) by imposing equilibrium wind-wave statistics for a range of wind and wave conditions. Concentration profiles of LES agree well with analytic solutions obtained for an eddy diffusivity profile that is constant near the surface and transitions into the K-Profile Parameterization (KPP) profile shape at greater depth. For a range of wind and wave conditions, the eddy diffusivity normalized by the product of water-side friction velocity and mixed layer depth, h, mainly depends on a single nondimensional parameter, the peak wavelength (which is related to Stokes drift decay depth) normalized by h. For smaller wave ages, BW critically enhances near-surface mixing, while LT effects are relatively small. For greater wave ages, both BW and LT contribute to elevated near-surface mixing, and LT significantly increases turbulent transport at greater depth. We identify a range of realistic wind and wave conditions for which only Langmuir (and not BW or shear driven) turbulence is capable of deeply submerging buoyant tracers.

Turbulence in breaking mountain waves and atmospheric rotors estimated from airborne in situ and Doppler radar measurements

Abstract: Atmospheric turbulence generated in flow over mountainous terrain is studied using airborne in situ and cloud radar measurements over the Medicine Bow Mountains in southeast Wyoming, USA. During the NASA Orographic Clouds Experiment (NASA06) in 2006, two complex mountain flow cases were documented by the University of Wyoming King Air research aircraft carrying the Wyoming Cloud Radar. The structure of turbulence and its intensity across the mountain range are described using the variance of vertical velocity σw2 and the cube root of the energy dissipation rate ɛ1/3 (EDR). For a quantitative analysis of turbulence from the cloud radar, the uncertainties in the Doppler wind retrieval have to be taken into account, such as the variance of hydrometeor fall speed and the contamination of vertical Doppler velocity by the horizontal wind. A thorough analysis of the uncertainties shows that 25% accuracy or better can be achieved in regions of moderate to severe turbulence in the lee of the mountains, while only qualitative estimates of turbulence intensity can be obtained outside the most turbulent regions. Two NASA06 events exhibiting large-amplitude mountain waves, mid-tropospheric wave breaking, and rotor circulations are examined. Moderate turbulence is found in a wave-breaking region with σw2 and EDR reaching 4.8 m2 s−2 and 0.25 m2/3 s−1, respectively. Severe turbulence is measured within the rotor circulations with σw2 and EDR respectively in the ranges of 7.8–16.4 m2 s−2 and 0.50–0.77 m2/3 s−1. A unique result of this study is the quantitative estimation of the intensity of turbulence and its spatial distribution in the interior of atmospheric rotors, provided by the radar-derived turbulence fields.

Wave breaking in the Whitham equation

Abstract: We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg-de Vries type for a range of fractional dispersion.

Observations of runup and energy flux on a low‐slope beach with high‐energy, long‐period ocean swell

Abstract: The transformation of surface gravity waves from 11 m depth to runup was observed on the low-sloped (1/80) Agate Beach, Oregon, with a cross-shore transect of current meters, pressure sensors, and a scanning lidar. Offshore wave heights H0 ranged from calm (0.5 m) to energetic (>7 m). Runup, measured with pressure sensors and a scanning lidar, increases linearly with (H0L0)1/2, with L0 the deep-water wavelength of the spectral peak. Runup saturation, in which runup oscillations plateau despite further increases in (H0L0)1/2, is not observed. Infragravity wave shoaling and nonlinear energy exchanges with short waves are included in an infragravity wave energy balance. This balance closes for high-infragravity frequencies (0.025–0.04 Hz) but not lower frequencies (0.003–0.025 Hz), possibly owing to unmodeled infragravity energy losses of wave breaking and/or bottom friction. Dissipative processes limit, but do not entirely damp, increases in runup excursions in response to increased incident wave forcing.