Wave Breaking Dissipation Research Articles

Numerical simulations of ocean surface waves under hurricane conditions: Assessment of existing model performance

Using the well-observed hurricane case Ivan (2004) as an example, we investigate and intercompare the performance of two wave models under hurricane conditions. One is the WAVEWATCH III model (WW3) and the other is the University of Miami Wave Model (UMWM). Within WW3, four different source term packages (ST2/3/4/6) of wind input, wave breaking dissipation and swell decay are chosen for comparison purposes. Based on the comparisons between model results and measurements from various platforms, we concluded that UMWM shows less accuracy than WW3 in specification of bulk wave parameters. This is possibly because (i) UMWM-estimated drag coefficient does not clearly show a saturation trend when wind speeds are beyond ∼ 35 m s−1 and (ii) the four-wave interaction term of UMWM disagrees evidently with the full solution of the Boltzmann integral in detail. Among the four WW3 source term packages, the older parameterization ST2 is basically the least accurate because of its systematic underestimation of high waves. The remaining three packages (ST3/4/6) are performed well under Ivan. However, we also find that they tend to overestimate energy of waves traveling in the oblique and opposing winds. It is shown that enhancing the strength of negative wind input properly can effectively improve model skills in such situations. Limited by the uncertainty in the wind forcing, we could not determine the most accurate package among ST3/4/6 unambiguously.

Evidence of Sea-State Dependence of Aerosol Concentration in the Marine Atmospheric Boundary Layer

AbstractSea spray aerosols represent a large fraction of the aerosols present in the maritime environment. Despite evidence of the importance of surface wave– and wave breaking–related processes in coupling the ocean with the atmosphere, sea spray source generation functions are traditionally parameterized by the 10-m wind speed U10 alone. It is clear that unless the wind and wave field are fully developed, the source function will be a function of both wind and wave parameters. This study reports primarily on the aerosol component of an air–sea interaction experiment, the phased-resolved High-Resolution Air–Sea Interaction Experiment (HIRES), conducted off the coast of northern California in June 2010. Detailed measurements of aerosol number concentration in the marine atmospheric boundary layer (MABL) at altitudes ranging from as low as 30 m up to 800 m above mean sea level (MSL) over a broad range of environmental conditions (significant wave height Hs of 2 to 4.5 m and U10 from 10 to 18 m s−1) collected from an instrumented research aircraft are presented. Aerosol number densities and volume are computed over a range of particle diameters from 0.1 to 200 μm, while the sea surface conditions, including Hs, moments of the breaker length distribution Λ(c), and wave breaking dissipation, were measured by a suite of electro-optical sensors that included the NASA Airborne Topographic Mapper (ATM). The sea-state dependence of the aerosol concentration in the MABL is evident, stressing the need to incorporate wave parameters in the spray source generation functions that are traditionally parameterized by surface winds alone.

Surface gravity wave transformation across a platform coral reef in the Red Sea

AbstractThe transformation of surface gravity waves across a platform reef in the Red Sea is examined using 18 months of observations and a wave transformation model developed for beaches. The platform reef is 200 m across, 700 m long, and the water depth varies from 0.3 to 1.2 m. Assuming changes in wave energy flux are due to wave breaking and bottom drag dissipation, the wave transformation model with optimal parameters characterizing the wave breaking (γm = 0.25) and bottom drag (hydrodynamic roughness zo = 0.08 m) accounts for 75%–90% of the observed wave‐height variance at four sites. The observations and model indicate that wave breaking dominates the dissipation in a 20–30 m wide surf zone while bottom drag dominates the dissipation over the rest of the reef. Friction factors (drag coefficients) estimated from the observed wave energy balance range from fw = 0.5 to fw = 5 and increase as wave‐orbital displacements decrease. The observed dependence on wave‐orbital displacement is roughly consistent with extrapolation of an empirical relationship based on numerous laboratory studies of oscillatory flow. As a consequence of the dependence on wave‐orbital displacement, wave friction factors vary temporally due to changes in water depth and incident wave heights, and spatially across the reef as the waves decay.

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

Abstract. An analytical weakly nonlinear model of the Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly varying steady current. In contrast to the models based on versions of the cubic Schrödinger equation, the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. The spatial scale of the current variation is assumed to have the same order as the spatial scale of the Benjamin–Feir (BF) instability. The model includes wave action conservation law and nonlinear dispersion relation for each of the wave's triad. The effect of nonuniform current, apart from linear transformation, is in the detuning of the resonant interactions, which strongly affects the nonlinear evolution of the system. The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, resulting in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the waves accompanied by energy income from sufficiently strong opposing current. We employ the model for the estimation of the maximum amplification of wave amplitudes as a function of opposing current value and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Evaluation of WAVEWATCH III performance with wind input and dissipation source terms using wave buoy measurements for October 2006 along the east Korean coast in the East Sea

In the winter, in the East Sea (ES), storm waves due to moving developed lows are frequently reported and cause extensive coastal disasters. During October 2006, there were extensive damages along the east Korean coast due to high storm waves induced by winter storms passing over the ES. This paper investigates the performance of a wave model, WAVEWATCH III, for the rough sea conditions in October 2006 with respect to the wind input and dissipation terms because the wave-breaking dissipation is the least known source term, which acts as a tuning knob for the closure of the action balance equation. Three package-like wind input-dissipation parameterizations, the WAM3 type (WAM-equiv), Tolman and Chalikov terms (TC96), and WAM4 type and its variant (WAM4+), are used experimentally for their performances under the same wind forcing obtained from atmospheric modelling with WRF. Overall, all experiments illustrate good accordance with observed wave characteristics. Among them, the WAM4+ results exhibit the best performance based on the Taylor diagram and index of agreement. In terms of dissipation behaviour, the TC96 results depict high energy losses at high frequency over 0.25Hz, whereas the WAM-equiv runs display less dissipation at the same frequency. The WAM4+ results lie between those of the WAM-equiv and TC96.

Radar Remote Sensing Estimates of Waves and Wave Forcing at a Tidal Inlet

AbstractThe time and space variability of wave transformation through a tidal inlet is investigated with radar remote sensing. The frequency of wave breaking and the net wave breaking dissipation at high spatial resolution is estimated using image sequences acquired with a land-based X-band marine radar. Using the radar intensity data, transformed to normalized radar cross section σ0, the temporal and spatial distributions of wave breaking are identified using a threshold developed via the data probability density function. In addition, the inlet bathymetry is determined via depth inversion of the radar-derived frequencies and wavenumbers of the surface waves using a preexisting algorithm (cBathy). Wave height transformation is calculated through the 1D cross-shore energy flux equation incorporating the radar-estimated breaking distribution and bathymetry. The accuracy of the methodology is tested by comparison with in situ wave height observations over a 9-day period, obtaining correlation values R = 0.68 to 0.96, and root-mean-square errors from 0.05 to 0.19 m. Predicted wave forcing, computed as the along-inlet gradient of the cross-shore radiation stress was onshore during high-wave conditions, in good agreement (R = 0.95) with observations.

On the nonlinear behaviour of Boussinesq type models: Amplitude-velocity vs amplitude-flux forms

In this paper we consider the modelling of nonlinear wave transformation by means of weakly nonlinear Boussinesq models. For a given couple linear dispersion relation-linear shoaling parameter, we show how to derive two systems of nonlinear PDEs differing in the form of the linear dispersive operators. In particular, within the same asymptotic accuracy, these operators can either be formulated by means of derivatives of the velocity, or in terms of derivatives of the flux. In the first case we speak of amplitude-velocity form of the model, in the second of amplitude-flux form. We show examples of these couples for several linear relations, including a new amplitude-flux variant of the model of Nwogu (J. Waterway, Port, Coast. Ocean Eng. 119, 1993). We then show, both analytically and by numerical nonlinear shoaling tests, that while for small amplitude waves the accuracy of the dispersion and shoaling relations is fundamental, when approaching breaking conditions it is only the amplitude-velocity or amplitude-flux form of the equations which determines the behaviour of the model, and in particular the shape and the height of the waves. In this regime we thus find only two types of behaviours, whatever the form of the linear dispersion relation and shoaling coefficient. This knowledge has tremendous importance when considering the use of these models in conjunction with some wave breaking detection and dissipation mechanism.

Scaling depth-induced wave-breaking in two-dimensional spectral wave models

Wave breaking in shallow water is still poorly understood and needs to be better parameterized in 2D spectral wave models. Significant wave heights over horizontal bathymetries are typically under-predicted in locally generated wave conditions and over-predicted in non-locally generated conditions. A joint scaling dependent on both local bottom slope and normalized wave number is presented and is shown to resolve these issues. Compared to the 12 wave breaking parameterizations considered in this study, this joint scaling demonstrates significant improvements, up to ∼50% error reduction, over 1D horizontal bathymetries for both locally and non-locally generated waves. In order to account for the inherent differences between uni-directional (1D) and directionally spread (2D) wave conditions, an extension of the wave breaking dissipation models is presented. By including the effects of wave directionality, rms-errors for the significant wave height are reduced for the best performing parameterizations in conditions with strong directional spreading. With this extension, our joint scaling improves modeling skill for significant wave heights over a verification data set of 11 different 1D laboratory bathymetries, 3 shallow lakes and 4 coastal sites. The corresponding averaged normalized rms-error for significant wave height in the 2D cases varied between 8% and 27%. In comparison, using the default setting with a constant scaling, as used in most presently operating 2D spectral wave models, gave equivalent errors between 15% and 38%.

Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline

The pycnocline in a closed domain is tilted by external wind forcing and tends to restore to a level position when the wind falls. An internal seiche oscillation exhibits if the forcing is weak, otherwise internal surge and internal solitary waves emerge, which serve as a link to cascade energy to small-scale processes. A two-dimensional non-hydrostatic code with a turbulence closure model is constructed to extend previous laboratory studies. The model could reproduce all the key phenomena observed in the corresponding laboratory experiments. The model results further serve as a comprehensive and reliable data set for an in-depth understanding of the related dynamical process. The comparative analyses indicate that nonlinear term favors the generation of internal surge and subsequent internal solitary waves, and the linear model predicts the general trend reasonably well. The vertical boundary can approximately reflect all the incoming waves, while the slope boundary serves as an area for small-scale internal wave breaking and energy dissipation. The temporal evolutions of domain integrated kinetic and potential energy are also analyzed, and the results indicate that about 20% of the initial available potential energy is lost during the first internal wave breaking process. Some numerical tactics such as grid topology and model initialization are also briefly discussed.

Hydrodynamic response of a fringing coral reef to a rise in mean sea level

Ningaloo Reef, located along the northwest coast of Australia, is one of the longest fringing coral reefs in the world extending ~300 km. Similar to other fringing reefs, it consists of a barrier reef ~1–6 km offshore with occasional gaps, backed by a shallow lagoon. Wave breaking on the reef generates radiation stress gradients that produces wave setup across the reef and lagoon and mean currents across the reef. A section of Ningaloo Reef at Sandy Bay was chosen as the focus of an intense 6-week field experiment and numerical simulation using the wave model SWAN coupled to the three-dimensional circulation model ROMS. The physics of nearshore processes such as wave breaking, wave setup and mean flow across the reef was investigated in detail by examining the various momentum balances established in the system. The magnitude of the terms and the distance of their peaks from reef edge in the momentum balance were sensitive to the changes in mean sea level, e.g. the wave forces decreased as the mean water depth increased (and hence, wave breaking dissipation was reduced). This led to an increase in the wave power at the shoreline, a slight shift of the surf zone to the lee side of the reef and changes in the intensity of the circulation. The predicted hydrodynamic fields were input into a Lagrangian particle tracking model to estimate the transport time scale of the reef-lagoon system. Flushing time of the lagoon with the open ocean was computed using two definitions in renewal of semi-enclosed water basins and revealed the sensitivity of such a transport time scale to methods. An increase in the lagoon exchange rate at smaller mean sea-level rise and the decrease at higher mean sea-level rise was predicted through flushing time computed using both methods.

Experimental and numerical studies on wave breaking characteristics over a fringing reef under monochromatic wave conditions.

Fringing reefs play an important role in protecting the coastal area by inducing wave breaking and wave energy dissipation. However, modeling of wave transformation and energy dissipation on this topography is still difficult due to the unique structure. In the present study, two-dimensional laboratory experiments were conducted to investigate the cross-shore variations of wave transformation, setup, and breaking phenomena over an idealized fringing reef with the 1/40 reef slope and to verify the Boussinesq model under monochromatic wave conditions. One-layer and two-layer model configurations of the Boussinesq model were used to figure out the model capability. Both models predicted well (r 2 > 0.8) the cross-shore variation of the wave heights, crests, troughs, and setups when the nonlinearity is not too high (A 0/h 0 < 0.07 in this study). However, as the wave nonlinearity and steepness increase, the one-layer model showed problems in prediction and stability due to the error on the vertical profile of fluid velocity. The results in this study revealed that one-layer model is not suitable in the highly nonlinear wave condition over a fringing reef bathymetry. This data set can contribute to the numerical model verification.

Waves and the equilibrium range at Ocean Weather Station P

[1] Wave and wind measurements at Ocean Weather Station P (OWS-P, 50°N 145°W) are used to evaluate the equilibrium range of surface wave energy spectra. Observations are consistent with a local balance between wind input and breaking dissipation, as described by Philips (1985). The measurements include direct covariance wind stress estimates and wave breaking dissipation rate estimates during a 3 week research cruise to OWS-P. The analysis is extended to a wider range of conditions using observations of wave energy spectra and wind speed during a 2 year mooring deployment at OWS-P. At moderate wind speeds (5–15 m/s), mooring wave spectra are in agreement, within 5% uncertainty, with the forcing implied by standard drag laws and mooring wind measurements. At high wind speeds (>15 m/s), mooring wave spectra are biased low, by 13%, relative to the forcing implied by standard drag laws and mooring wind measurements. Deviations from equilibrium are associated with directionality and variations at the swell frequencies. A spectral wave hindcast accurately reproduces the mooring observations, and is used to examine the wind input.

Wave Breaking Dissipation Observed with “SWIFT” Drifters

Abstract Energy dissipation rates during ocean wave breaking are estimated from high-resolution profiles of turbulent velocities collected within 1 m of the surface. The velocity profiles are obtained from a pulse-coherent acoustic Doppler sonar on a wave-following platform, termed a Surface Wave Instrument Float with Tracking (SWIFT), and the dissipation rates are estimated from the structure function of the velocity profiles. The purpose of the SWIFT is to maintain a constant range to the time-varying surface and thereby observe the turbulence in breaking crests (i.e., above the mean still water level). The Lagrangian quality is also useful to prefilter wave orbital motions and mean currents from the velocity measurements, which are limited in magnitude by phase wrapping in the coherent Doppler processing. Field testing and examples from both offshore whitecaps and nearshore surf breaking are presented. Dissipation rates are elevated (up to 10−3 m2 s−3) during strong breaking conditions, which are confirmed using surface videos recorded on board SWIFT. Although some velocity contamination is present from platform tilting and heaving, the structure of the velocity profiles is dominated by a turbulent cascade of eddies (i.e., the inertial subrange). The noise, or uncertainty, in the dissipation estimates is shown to be normally distributed and uncorrelated with platform motion. Aggregated SWIFT measurements are shown to be useful in mapping wave-breaking dissipation in space and time.

NUMERICAL ANALYSIS OF TSUNAMI PROPAGATION ON WIDE REEF PLATFORM

During the 2009 Samoan Islands Tsunami, the wide coral reef platform in front of the islands affected the approaching tsunami behavior. This research aims to understand the characteristics of a tsunami propagating over a reef platform by using a turbulence model. A Large Eddy Simulation (LES) model was used to simulate wave breaking and energy dissipation. The results of numerical simulations by using LES model were shown to reproduce well the results of the field survey in the 2009 Samoan Islands Tsunami. The present method may also apply to other countries which have coral reefs and contribute to regional tsunami mitigation strategies. It is important to understand what is the phenomenon that people in coastal areas actually experience as well as the height and arrival time of a tsunami.

Numerical simulation of wave transformation across the surf zone over a steep bottom

The combined effect of wave shoaling, breaking and energy dissipation on a steep sloping bottom was developed. Based on the conservation principle of wave motion, a combined shoaling and bottom slope coefficient is included in the mild-slope equation (MSE), which is derived as a function of the bottom slope perturbed to the third-order. The model incorporates the nonlinear shoaling coefficient and energy dissipation factor due to wave breaking to improve the accuracy of the numerical simulation prior to wave breaking and in the surf zone over a steep bottom. The model validity is verified by comparison with laboratory experiments for waves traveling over two steep sloping beaches and a bar/step-type beach profile.

A hydrodynamic model of nearshore waves and wave-induced currents

In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.

A hydrodynamic model of nearshore waves and wave-induced currents

In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.

Optical and Microwave Detection of Wave Breaking in the Surf Zone

Synchronous and colocated optical and microwave signals from waves in the surf zone are presented and analyzed. The field data were collected using a high-resolution video system and a calibrated horizontally polarized marine radar during the decaying phase of a storm. The resulting changes in the received signals from varying environmental conditions were analyzed. The analysis of the optical signal histograms showed functional shapes that were in accordance with the expected imaging mechanisms from the breaking and nonbreaking waves. For the microwave returns, the histogram shape showed a little dependence on the environmental parameters and exhibited an inflexion point at high returned power that is attributed to a change in the scattering mechanism. The high intensity signals were clearly associated with active wave breaking. However, with either sensor, it can be difficult to effectively isolate the wave breaking signature from other sources, such as a remnant foam or the highly steepened nonbreaking waves. A combined method was developed using the joint histograms from both sensors, and it is shown to effectively discriminate between active breaking, remnant foam, and steepened waves. The new separation method allows a further analysis of the microwave scattering from the breaking waves and a better quantification of the length scales of the breaking wave roller and the spatial/temporal distribution of wave breaking and wave dissipation in the surf zone.

Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

Abstract New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but, overall, the parameterizations probably yield the most accurate estimates of wave parameters to date. Perspectives for further improvement are also given.

On internal wave breaking and tidal dissipation near the centre of a solar-type star

We study the fate of internal gravity waves, which are excited by tidal forcing by a short-period planet at the interface of convection and radiation zones, approaching the centre of a solar-type star. We study at what amplitude these wave are subject to instabilities. These instabilities lead to wave breaking whenever the amplitude exceeds a critical value. Below this value, the wave reflects perfectly from the centre of the star. Wave breaking results in spinning up the central regions of the star, and the formation of a critical layer, which acts as an absorbing barrier for ingoing waves. As these waves are absorbed, the star is spun up from the inside out. This results in an important amplitude dependence of the tidal quality factor Q'. If the tidal forcing amplitude exceeds the value required for wave breaking, efficient dissipation results over a continuous range of tidal frequencies, leading to Q' \approx 10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of 5 throughout the range of G and K type main sequence stars, for a given orbit. We predict fewer giant planets with orbital periods of less than about 2 days around such stars, if they cause breaking at the centre, due to the efficiency of this process. This mechanism would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.