Wind-generated Surface Gravity Waves Research Articles

Continuous Peak Period Estimates from Discrete Surface-Wave Spectra

Abstract Peak periods estimated from finite-resolution frequency spectra are necessarily discrete. For wind-generated surface gravity waves, conflicting considerations of robust (quasi)-stationary statistics, and high spectral resolution, combined with the inverse relation between frequency and period, this typically implies that swell periods (above 10 s) are resolved at best at s intervals. Here, we consider a method to improve peak period estimates for finite-resolution spectra. Specifically, we propose to define the peak period based on continuous spectra derived from a spline-based interpolation of the discretely sampled monotone cumulative distribution function. The method may directly be applied to existing discrete spectra—the original time-domain data (which may not be available) are not required. We compare reconstructed spectra and derived peak periods to parametric shapes and field data. Peak estimates are markedly improved, allowing for better tracking of, e.g., swells. The proposed method also marginally improves spectral levels and shape for a given discretely sampled estimate.

The Impacts of Climate Change on Surfing Resources: Supplemental Online Materials

For the purposes of this review, we only discuss and consider impacts to wind-generated surface gravity waves on the ocean breaking in nearshore waters. The following non-technical summary of these processes is drawn from several sources, including (Garrison 2001, Hutt et al. 2001, Mead and Black 2001a, 2001b, Cool 2003, Scarfe et al. 2003, Butt et al. 2004, Espejo et al. 2014, Meldahl 2019). We divide the overview to focus separately on swell generation and wave breaking and also briefly summarize a variety of other factors relevant to breaking wave quality for surfing.

CMIP5 model performance of significant wave heights over the Indian Ocean using COWCLIP datasets

Wind-generated surface gravity waves forms an integral part in modulating the air-sea exchange processes. Information of wave parameters is also very essential in planning marine- and coastal-related activities. It is now well recognized that wind-wave activity shows changing trends over the global ocean basins. Numerous studies have addressed the projected changes in significant wave height for the Indian Ocean (IO) region, and there is a need to conduct thorough performance evaluation of global climate models (GCMs) over this region for futuristic planning. With this motivation, the present study examined the performance of historical dynamical wave climate simulations generated under the Coordinated Ocean Wave Climate Projections (COWCLIP) experiment. The simulations utilized near-surface wind speed datasets from 8 CMIP5 (Fifth phase of Coupled Model Intercomparison Project) GCMs to force a spectral wave model. The skill level of individual GCM forced wave simulations and multi-model mean (MMM) in reproducing the significant wave height (SWH) over four different sub-domains in the IO was evaluated with reference to the ECMWF Reanalysis 5th Generation (ERA5) datasets. Several performance metrics such as the Taylor Skill, M-Score, Model Climate Performance Index (MCPI), and Model Variability Index (MVI) are employed to establish the skill level of model simulations. The study deciphers that model performance is highly reliant on the region and its characteristics. Representation of the historical wave climate over the Arabian Sea (AS) and the Bay of Bengal (BoB) regions is remarkable in the COWCLIP datasets. However, there are discrepancies noticed in SWH distribution over the South Indian Ocean (SIO) attributed to model limitations in adequately reproducing swell wave fields over that region. The MMM constructed using the best-performing models (MRI-CGCM3, ACCESS1.0, INMCM4, HadGEM2-ES, and BCC-CSM1.1) is found consistent at all the sub-domains. The study signifies that the performance evaluation of GCM forced wave simulations is crucial before employing them for practical applications. Best-performing models listed from this study can be used to establish futuristic scenarios of SWH in a changing climate for the IO region.

The Tidal Stream Energy Resource of the Fromveur Strait—A Review

Refined assessments of the available tidal stream energy resource are required to optimize turbines design and guarantee successful implementations and operations of devices in the marine environment. Investigations primary focused on identifying areas with maximum current speeds. However, further information may be reached by exhibiting (i) resource temporal variability, (ii) superimposed effects of meteo-oceanographic conditions (including especially wind-generated surface-gravity waves), and (iii) potential environmental impacts of operating turbines at the regional (e.g., changes in sediment transport and surrounding seabed features, effects on marine water quality, etc.) and local (wake-wake interactions and energy output) scales. These aspects are here investigated by reviewing a series of research studies dedicated to the Fromveur Strait off western Brittany, a region with strong potential for tidal array development along the coast of France. Particular attention is dedicated to the exploitation of combined in-situ and remote-sensing observations and numerical simulations. Beyond a site specific characterization of the tidal stream energy resource, this review promotes a series of original approaches and analysis methods for turbines optimization, thus complementing technical specifications to secure the key steps of a tidal energy project and promote the growth of a reliable tidal stream energy exploitation.

US Navy Global and Regional Wave Modeling

Abstract : This article reviews the prediction of wind-generated surface gravity waves over the world ocean by the US Navy. The numerical wave model WAVEWATCH III? is used operationally for this purpose at the two primary Navy operational centers, the Fleet Numerical Meteorology and Oceanography Center and the Naval Oceanographic Office. This model is briefly described, and an overview is given of the current operational and near-operational features of global- and regional scale wave models at the two centers. Planned features are summarized.

Sea Surface Gravity Wave-wind Interaction in the Marine Atmospheric Boundary Layer

In this study, we investigate the turbulence structure over idealized wind-generated surface gravity waves with varying wave age using a wave-modified one-dimensional boundary layer model. To prescribe the shape of the water wave and the associated orbital velocities, we employ an empirical expression for the wave energy spectrum without assigning a prognostic equation for modelling wave evolution under the action of wind. The key element in this model is the the work done by the wave-induced momentum flux on the atmosphere in the presence of waves. This is incorporated into the airflow using an exponential decay function. Finally, we conduct a series of numerical experiments to identify wave effects on the airflow over a wavy moving interface as a function of wave age, and to check the skill of the present model in capturing wave-induced processes in the marine atmospheric boundary layer (MABL). The results obtained confirm again the significant role of wave-induced processes in influencing the MABL, for example, in modifying the wind profile. Meanwhile, it is shown that the modified one-dimensional model is sensitive to wave parameterizations and the wave energy spectrum. However, a number of uncertainties remain for further investigation, such as the choice of wave energy spectrum, wave forcing parametrization, and surface boundary conditions for momentum and energy.

Frequency width in predictions of windsea spectra and the role of the nonlinear solver

In this paper, the accuracy of predictions of the narrowness in frequency space of elevation spectra for wind-generated surface gravity waves is evaluated with the specific objective of determining the impact of the method for computing quadruplet interactions, Snl4. Alternate metrics are presented for concise quantification of this narrowness and applied to a case study: a 10-day duration hindcast for Lake Michigan during 2002 conducted using the Discrete Interaction Approximation (DIA) for Snl4. Under-prediction of frequency narrowness relative to observational data is clearly identifiable using non-concise methods. Two of four concise methods for quantifying spectral narrowness are found to adequately register this bias. By comparing with a hindcast that uses an expensive, exact solution for four-wave nonlinear interactions, it is determined that much of the bias can be attributed to the approximation used for the solution of these interactions in the first hindcast, which corresponds to the DIA, which is the solution method used today in nearly all routine, phase-averaged wave modeling.

Modeling the Tide-Induced Modulation of Wave Height in the Outer Seine Estuary

GUILLOU, N. and CHAPALAIN, G., 2012. Modeling the tide-induced modulation of wave height in the outer Seine estuary. During the last decades, numerous models have been implemented to investigate the effects of tide on wind-generated surface-gravity waves. The present study analyzes the influences of the tide-induced time-varying water depths and currents on the wave height in the outer Seine estuary (France, English Channel). Two modeling systems based on the coupling of circulation and wave propagation modules are applied at the scales of (i) the English Channel and the North Sea and (ii) the Bay of Seine and the harbor of Le Havre, respectively. Numerical results are compared with field data collected with two current meters and two wave buoys in the access channel to Port 2000 (Le Havre). Predictions exhibit a local increase of 30% of the wave height induced by current refraction at slack tide. On the basis of this local comparison of numerical results with measurements, three mappings of the wave height modified by the (i) tide, (ii) water levels alone, and (iii) currents alone are established at the scale of the outer Seine estuary. The currents have a major influence on the wave height modulating at a tidal frequency the direction of incident waves through refraction. This effect is exhibited along the southern breakwater of the harbor of Le Havre and the vicinity of coastal topographic features of the outer Seine estuary.

Erratum to: A note on stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea

Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.

Theoretical interpretation of fetch limited wind-drivensea observations

Abstract. We show that the results of major fetch limited field studies of wind-generated surface gravity waves on deep water can be explained in the framework of simple analytical model. The spectra measured in these experiments are described by self-similar solutions of ``conservative" Hasselmann equation that includes only advective and nonlinear interaction terms. Interaction with the wind and dissipation due to the wave breaking indirectly defines parameters of the self-similar solutions.

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.

Teaching time-series analysis. II. Wave height and water surface elevation probability distributions

This paper describes the second of a two-part series of pedagogical exercises to introduce students to methods of time-series analysis. While these exercises are focused on the analysis of wind generated surface gravity waves, they are cross-disciplinary in nature and can be applied to other fields dealing with random signal analysis. Two computer laboratory exercises are presented which enable students to understand many of the facets of random signal analysis with less difficulty and more understanding than standard classroom instruction alone. The first pedagogical exercise, described in the previous article, uses mathematical software on which the students execute the manual arithmetic operations of a finite Fourier analysis on a complex wave record. The results are then compared to those obtained by a fast Fourier transform. This article, the second of this two-part pedagogical series, addresses analysis of a complex sea using observed and theoretical wave height and water surface elevation probability distributions and wave spectra. These results are compared to a fast Fourier transform analysis, thus providing a link back to the first exercise.

Teaching time-series analysis. I. Finite Fourier analysis of ocean waves

The introduction of students to methods of time-series analysis is a pedagogical challenge, since the availability of easily manipulated computer software presents an attractive alternative to an understanding of the computations, as well as their assumptions and limitations. A two-part pedagogical tutorial exercise is offered as a hands-on laboratory to complement classroom discussions or as a reference for students involved in independent research projects. The exercises are focused on the analysis of ocean waves, specifically wind-generated surface gravity waves. The exercises are cross-disciplinary in nature and can be extended to any other field dealing with random signal analysis. The first exercise introduces the manual arithmetic steps of a finite Fourier analysis of a wave record, develops a spectrum, and compares these results to the results obtained using a fast Fourier transform (FFT). The second part of the exercise, described in the subsequent article, takes a longer wave record and addresses the theoretical and observed wave probability distributions of wave heights and sea surface elevations. These results are then compared to a FFT, thus linking the two pedagogical laboratory exercise parts for a more complete understanding of both exercises.

Nonlinear wave interactions and high‐frequency seafloor pressure

Linear wave theory predicts that pressure fluctuations induced by windgenerated surface gravity waves are maximum at the ocean surface and strongly attenuated at depths exceeding a horizontal wavelength. Although pressure fluctuations observed at the seafloor in deep water are indeed relatively weak at wind‐wave frequencies, the energy at double wind‐wave frequencies is frequently much higher than predicted by applying linear wave theory to near‐surface measurements. These double‐frequency waves can in theory be excited by nonlinear interactions between two surface wave components of about equal frequency, traveling in nearly opposing directions. Observations from a large aperture, 24‐element array of pressure sensors deployed in 13‐m depth are presented that quantitatively support this generation mechanism. As in previous studies, dramatic increases in the spectral levels of seafloor pressure at double wind‐wave frequencies (0.3–0.7 Hz) frequently occurred after a sudden veering in wind direction resulted in waves propagating obliquely to preexisting seas. The observed spectral levels and vector wavenumbers of these double‐frequency pressure fluctuations agree well with predictions obtained by applying second‐order nonlinear, finite depth wave theory (Hasselmann, 1962) to the observed directionally bimodal seas. High‐frequency seafloor pressure spectral levels also increased in response to directionally narrower but more energetic seas generated by strong, steady or slowly rotating winds. Bispectral analysis suggests that these pressure fluctuations are generated by nonlinear mechanisms similar to the veering wind cases.

Multi-wave interaction theory for wind-generated surface gravity waves

Consistently employing the assumption of localness of wave-wave interactions in the wavenumber space, the Kolmogorov treatment of the energy cascade is applied to the case of wind-generated surface gravity waves. The effective number v of resonantly interacting wave harmonics is not limited to four but is found as a solution of a coupled system of equations expressing: (i) the dependence of the spectrum shape on the degree of the wave nonlinearity, and (ii) the continuity of the wave action flux through the spectrum given a continuous positive input from wind. The latter is specified in a Miles-type fashion, and a simple scaling relationship based on the concept of the turnover time is derived in place of the kinetic equation. The mathematical problem is reduced to an ordinary differential equation of first order. The exponent in the 'power law' for the spectral density of the wave potential energy and the effective number of resonantly interacting wave harmonics are found as functions of the wave frequency and of external factors of wind-wave interaction. The solution is close to the Zakharov-Filonenko spectrum at low frequencies and low wind input while approaching the Phillips spectrum at high frequencies and sufficiently high wind.

Wind-Wave Nonlinearity Observed at the Sea Floor. Part II: Wavenumbers and Third-Order Statistics

This is Part 2 of a study of nonlinear effects on natural wind-generated surface gravity waves in 13-m depth, 30 km offshore of Virginia. At the sea floor in this depth, free surface gravity waves are only weakly attenuated at sea and swell frequencies (0.05–0.30 Hz) but are very strongly attenuated at frequencies higher than about 0.35 Hz. Hence, above 0.35 Hz, relatively long wavelength forced waves, excited by nonlinear interactions between directionally opposing free wind waves, are exposed at the sea floor. An array of pressure transducers at middepth was used to estimate the frequency-directional spectrum of (free) primary sea and swell waves, and the associated (forced) secondary pressure fluctuations were measured with an array on the sea floor. In Part 1, it was shown that forced-wave energy levels at the sea floor increase sharply in response to directionally opposing wind waves, in agreement with weakly nonlinear theory. In Part 2, wavelengths, propagation directions, and non-Gaussian phase coupling between free and forced waves are examined on three occasions with relatively high forced-wave energy levels. A root-mean-square wavenumber magnitude and a vector-averaged mean wave propagation direction (both functions of frequency) can be expressed accurately in terms of the pressure array cross-spectra. The wavenumber estimates at the sea floor show the theoretically expected sharp transition between a 0.05–0.30 HZ frequency range dominated by free sea and swell waves and a 0.35–0.60 Hz range dominated by forced waves with wavelengths that are long relative to free waves of the same frequency. In the “free-wave frequency range,” wavenumber estimates are usually well within 10% of the linear dispersion relation and wave direction estimates are in excellent agreement with the directional spectra extracted from the middepth array. In the “forced-wave frequency range,” wavenumber and direction estimates agree with nonlinear theory predictions, confirming that the observed forced waves have the sum vector wavenumber of the interacting directionally opposing wind waves. Phase coupling between free and forced waves is examined through third-order statistics of the sea floor pressure data. Consistent with theory, the normalized bispectrum has small imaginary parts scattered approximately randomly about zero and relatively large negative real parts at frequencies that correspond to directionally opposing seas and swell. Estimates of the bispectrum integrated for constant sum frequency confirm that nearly all the energy at double sea frequencies is nonlinearly coupled to directionally opposing wind waves. In qualitative agreement with nonlinear theory predictions, bispectral levels are sometimes significantly reduced by directional spreading of the interacting free waves.

The steepness and shape of wind waves

Variations are found in the shape and the steepness of wind-generated surface gravity waves between very young waves, such as seen in a laboratory tank, and larger waves of various wave ages encountered at sea as the result of wind stress over larger fetches. These differences in the characteristic shape of wind waves are presented as a function of the wave age. The wave steepness is also expressed as a function of wave age, the measurement of which is consistent with the 3/2-power law connecting wave height and characteristic period, normalized by the air friction velocity.

Modelling wind-generated surface gravity waves using similarity in a coupled discrete wave model

In deep water, there is a growing observational consensus that supports an ƒ4 variation for the Kitaigorodskii subrange of the high-frequency energy spectra. We therefore re-examine and extend the TMA (Texel Marsen Arsloe) similarity and concepts for shallow water waves, which were originally derived for an ƒ5 Phillips subrange. The similarity for an ƒ4 a subrange is found to closely resemble that of the ƒ5 subrange. The former exists when nonlinear transfer due to wave-wave interactions dominates over other source terms, such as wind input, in the energy balance. Starting with a standard second generation deep water coupled discrete spectral wave model, we implement the TMA similarity. To evaluate our modifications, we perform the real and synthetic shallow water tests of the recent SWIM study. Thus we intercompare our model with HYPAS, an analogously modified deep water coupled hybrid model, and with other wave models which were not based on the TMA similarity. Our model and HYPAS are found to behave quite similarly in the sloping and flat-bottom SWIM tests, compared to the other wave models of the SWIM intercomparison. The more difficult and complex North Sea SWIM hindcast extends this property, in some regards.

Spectral evolution of wind-generated surface gravity waves in a dispersed ice field

The Marginal Ice Zone includes wide areas covered by dispersed ice floes in which wave conditions are significantly affected by the ice. When the wind blows from the solid ice pack, towards the open sea, growing waves are scattered by the floes, and their spectral characteristics modified. To further understand this problem, a model for the evolution of wind waves in a sparse field of ice floes has been developed. The sea state is described by a two-dimensional discrete spectrum. Time-limited wave growth is obtained by numerical integration of the energy balance equation using the exact nonlinear transfer integral. Wave scattering by a single floe is represented in terms of far-field expressions of the diffracted and forced potentials obtained numerically by the Green function method. The combined effect of a homogeneous field of floes on the wave spectrum is expressed in terms of the Foldy–Twersky integral equations under the assumption of single scattering. The results show a strong dependence of the spectrum amplitude and directional properties on the ratio of the ice floe diameter to the wavelength. For a certain range of this parameter, the ice cover appears to be very effective in dispersing the energy; the wave spectrum rapidly tends to isotropy, a tendency which prevents the normal growth of wave energy and the decrease in peak frequency. Therefore, in the Marginal Ice Zone, the ability of an offshore wind to generate a significant wave field is severely limited.