Wind Wave Growth Research Articles

Evolution of water wave packets by wind in shallow water

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Changing wind-generated waves in the Red Sea during 64 years

This study analyzes the wind-generated wave climate conditions in the Red Sea. A 64-year (1959–2022) wave hindcast is developed using the spectral wave model WAVEWATCH III forced with ERA5 wind fields. The study addresses the climatologies of the significant wave height (Hs), mean period (Tm), and wave power (P) parameters, as well as the wind-sea and swell distributions throughout the basin. Special interest has been paid on assessing the extreme climate conditions. Additionally, the climate variability at seasonal and inter-annual scales, and the long-term trends are analyzed. The relationship between the Red Sea wave climate and the large-scale teleconnection climate patterns is investigated. The model is calibrated for wind-wave growth and validated against buoy and altimeter measurements revealing higher performance than previous datasets. The root mean square errors of Hs and Tm are reduced by 25% and 37%, respectively. Results show that wind-seas dominate in the northern and southernmost Red Sea regions. We also detect that the 100-year return period of Hs reaches ∼5 m in the central basin. Furthermore, regional annual and seasonal variations of the wave climate show strong correlations with the circulation patterns described by the North Atlantic Oscillation at the northern Red Sea and both the Dipole Mode Index and El-Niño Southern Oscillation at the southern Red Sea. Finally, contrasting behaviours of negative and positive trends occur at the southern and northern regions, respectively, for Hs, and P with a contrary behavior for Tm. Trends under both mean and extreme conditions are mild, reaching 3 cm/decade, 0.016 s/decade, and 0.3 kW/m/decade for Hs, Tm, and P, respectively, in the northern basin in winter.

Wind-wave growth over a viscous liquid

Wind-wave growth over a viscous liquid

Wind Wave Growth and Dissipation in a Narrow, Fetch-Limited Estuary: Long Island Sound

The geometry of the Long Island Sound (LIS) renders the wave field fetch-limited and leads to marked differences between western and eastern areas. The mechanisms that contribute to the formation and dissipation of waves in the LIS are not well understood. We evaluated the ability of the wave module of a wave-coupled hydrodynamic model to simulate different wind–wave scenarios. We were unable to capture wave statistics correctly using existing meteorological model results for wind forcing due to the low resolution of the models and their inability to resolve the LIS coastline sufficiently. To solve this problem, we modified the wind fields using in situ wind observations from buoys. We optimized both the Komen and Jansen parameterizations for the LIS to better present the peak winds during storms. Waves in the LIS develop more quickly than simple theory predicts due to quadruplet nonlinear wave–wave interaction effects. Removing quadruplet nonlinear wave–wave interaction increases the time to full saturation by 50%. The spatial distribution of wave energy density input reveals the complex interaction between wind and waves in the LIS, with the area of greatest exposure receiving higher wave energy density. The interaction of nonlinear wave–wave interaction and whitecapping dissipation defines the shape of the directional spectrum along the LIS. Dissipation due to whitecapping and shoaling are the main parameters modulating a fully developed wave field.

Effect of Wave Directions on Orientation and Magnitude of Surface Wind Stress under Typhoon Megi (2010)

Abstract The relationship between the wind-wave spectrum and surface wind stress τ in tropical cyclones, especially for the misalignment |ϕ| between the wind and τ, was investigated using data from three Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats deployed in Super Typhoon Megi (2010). The floats measured τ by integrating downward momentum flux in the ocean and, in a recent development, directional spectra of surface waves. The wind was captured by aircraft surveys. At wind speeds from 25 to 40 m s−1, the |ϕ| increased with the increasing angle between the wind and dominant waves. The |ϕ| was small near the eyewall, where wave energy concentrated in a narrow frequency band. At the location far away from the eyewall, where most spectra were bimodal in directions with similar frequencies, the stress direction might be similar to the high-frequency waves. The misalignment between the wind and propagating swell might affect the growth and directional spreading of wind waves under tropical cyclones. The resulting wave breaking might then release wave momentum into the ocean as most stress clockwise from the wind direction. C‖, the downwind drag coefficient, increased with increasing inverse wave age of dominant waves. |C⊥|, the magnitude of the crosswind drag coefficient, was significant when low-frequency waves deviated from the wind by more than 90°. The wave directions are used in the inverse wave age for scaling drag coefficients. The new parameterization based on wave dynamics can be useful for improving the prediction of wind stress curl under storms. Significance Statement Tropical cyclones can impact the maximum sea surface temperature cooling through the curl of surface wind stress τ, which causes divergence under the storm eye. To investigate the effect of surface waves on τ, measurements of downward momentum flux and surface waves from three EM-APEX floats deployed under Typhoon Megi in 2010 are used. The inverse wave age involving wind forcing on the wave directions of dominant waves and swells can significantly influence the momentum transfer efficiency in the downwind and crosswind directions, respectively. That is, the propagating swell under storms should play a crucial role in the downward momentum flux during its interaction with high-frequency waves and wind. Incorporating wave directions to parameterize the magnitude and orientation of τ will improve future models’ ability to predict wind stress curl and thereby the heat fluxes to storm intensification.

Effects of surface tension reduction on wind-wave growth and air–water scalar transfer

Effects of surface tension reduction on wind-wave growth are investigated using direct numerical simulations of air–water two-phase turbulent flows. The incompressible Navier–Stokes equations for air and water sides are solved using an arbitrary Lagrangian–Eulerian method with boundary-fitted moving grids. The wave growth of finite-amplitude and non-breaking gravity–capillary waves, whose wavelength is less than 0.07 m, is simulated for two cases of different surface tensions under a low-wind-speed condition of several metres per second. The results show that significant wave height for the smaller surface tension case increases faster than that for the larger surface tension case. Energy fluxes for gravity and capillary wave scales reveal that when the surface tension is reduced, the energy transfer from the significant gravity waves to capillary waves decreases, and the significant waves accumulate more energy supplied by wind. This results in faster wave growth for the smaller surface tension case. The effect on the scalar transfer across the air–water interface is also investigated. The results show that the scalar transfer coefficient on the water side decreases due to the surface tension reduction. The decrease is caused by suppression of turbulence in the water side. In order to support the conjecture, the surface tension effect is compared with laboratory experiments in a small wind-wave tank.

Revisiting wind wave growth with fully coupled direct numerical simulations

We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed$c$to the wind friction velocity$u_*$from$c/u_*= 2$to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness$ak$from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. The wall friction Reynolds number is 720. The novel fully coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent surface elevation is in quantitative agreement with that computed from the surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. Intermittent and localised airflow separation is observed for steep waves with small wave age, but its effect on setting the phase-averaged pressure distribution is not drastically different from that of non-separated sheltering. We find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. In addition, the history of wind wave coupling can affect the wave form drag, due to the wave crest shape and other complex coupling effects. The normalised wave growth rate we obtain agrees with previous studies. We make an effort to clarify various commonly adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical and experimental results, as we revisit this longstanding problem with new numerical evidence.

Experimental study on the growth and conversion of duration- and fetch-limited wind waves in water of finite depth

This paper presents laboratory experiment results on the initial growth of wind waves in water of finite depth. Under the action of a steady wind flow, mixtures of duration- and fetch-limited waves were generated over a constant water depth. Variations of dimensionless growth rate data against finite-depth wave age and dimensionless depth for both scenarios are found to be highly depth-dependent; however, the growth rates of duration-limited waves are larger than those for fetch-limited waves. Our experiment showed that when wave age increases up to the so-called critical wave age, wind-induced wave growth reaches a limit due to the depth effect. The critical age values determined in our flume agree well with the theoretical ones. Dimensionless power-law predictions are presented for significant wave height and spectral peak period in each wave regime, based on which a set of time-space conversion relationships is obtained. However, our results suggest different conversion equations for wave height and wave period. Even if our data are obtained in a laboratory environment, the widely-used hyperbolic model fitted over our measurements could forecast available field data with a Scatter Index of 0.06 for wave height and 0.17 for wave period.

Growth of surface wind-waves in water of finite depth: A laboratory experiment

This paper reports on laboratory experiment results on wind-driven surface waves in finite depth and their comparison with theoretical predictions and experimental in-situ studies. We introduce the Miles theory’s extension to the case of finite depth, as well as the rules transforming theoretical expressions to formulae commonly used in experimental routines, in particular the important rules transforming theoretical growth rates to experimental ones. Wind waves depend strongly on boundary marine layer parameters, namely, the aerodynamic roughness length, the Charnock constant, as well as the drag coefficient. Consequently, this work gives detailed measurements of these parameters in finite depths. Experiments conducted in the IRPHÉ/Pythéas wind-wave tank (Marseille, France), reveal that for a given wind speed, these values are higher in finite depth than in deep water. In the limit case of fully developed surface, due to depth, theoretical and empirical formulas relating the critical values of wave age to the non-dimensional depth have been experimentally verified. Plots of non-dimensional peak frequency, non-dimensional energy, and the inverse of wave age, against non-dimensional depth are presented. The plots clearly show that these quantities admit a limit due to the depth influence. All data obey the range of empirical values established in field experiments. Experimental data, obtained in the facility, agree with the theoretical family of depth-dependent wave growth rate as a function of wave age in finite depth. The non-dimensional growth-rate data obtained in our laboratory, as a function of the inverse of wave age, are consistent with the theoretical predictions of Miles theory in finite depth (Montalvo et al., 2013a,b, Latifi et al.. 2017), as well as measurements from other laboratories. • Wind-wave tank experiment on wave growth by the wind in finite depth environment. • Low-water depth have effects on transfers, drag, roughness and Charnock parameters. • For certain conditions of water depth and other parameters, the wave growth rate tend to zero. • Good comparison between Montalvo et al 2013 theory and experimental data. • All our experimental data are within the Young 1997 asymptotic depth limits.

Evidence of the critical layer mechanism in growing wind waves

Highly resolved laboratory measurements of the airflow over wind-generated waves are examined using a novel wave growth diagnostic that quantifies the presence of Miles’ critical layer mechanism of wind-wave growth. The wave growth diagnostic is formulated based on a linear stability analysis, and results in growth rates that agree well with those found by a pressure reconstruction method as well as other, less direct, methods. This finding, combined with a close agreement between the airflow measurements and the predictions of linear stability (critical layer) theory, demonstrate that the Miles’ critical layer mechanism can cause significant wave growth in young (wave age $c/u_* = 6.3$ , where $c$ is the wave phase speed, and $u_*$ the friction velocity) wind-forced waves.

Unified Wind-Wave Growth and Spectrum Functions for All Water Depths: Field Observations and Model Results

Abstract Wind-wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity functions, the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interpreted as the wave energy evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave-age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind-wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measured and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake. Significance Statement This paper presents a growth function and spectrum model to describe wind-wave development in all water depths. Their applicability covers a wide range of wind forcing conditions including steady, accelerating, decelerating, and tropical cyclone events. Support for the unified spectrum model and growth function is presented with field observations and numerical computations.

Influence of Following, Regular, and Irregular Long Waves on Wind-Wave Growth with Fetch: An Experimental Study

AbstractA series of experiments were conducted in a wind-wave tank facility in Marseilles (France) to study the effects of preexisting swell conditions (represented by long mechanically generated waves) on wind-wave growth with fetch. Both monochromatic and irregular (JONSWAP-type) long-wave conditions with different values of wave steepness have been generated in the presence of a constant wind forcing, for several wind velocities. A spectral analysis of temporal wave signals combined with airflow measurements allowed for the study of the evolution of both wave systems with the aim of identifying the interaction mechanisms transportable to prototype scale. In particular, a specific method is used to separate the two wave systems in the measured bimodal spectra. In fetch-limited conditions, pure wind-wave growth is in accordance with anterior experiments, but differs from the prototype scale in terms of energy and frequency variations with fetch. Monochromatic long waves are shown to reduce the energy of the wind-waves significantly, as it was observed in anterior laboratory experiments. The addition of JONSWAP-type long waves instead results in a downshift of the wind-wave peak frequency but no significant energy reduction. Overall, it is observed that the presence of long waves affects the wind-wave energy and frequency variations with fetch. Finally, in the presence of JONSWAP-type long waves, variations of wind-wave energy and peak frequency with fetch appear in close agreement with the wind-wave growth observed at prototype scale both in terms of variations and nondimensional magnitude.

The Dynamical Coupling of Wind-Waves and Atmospheric Turbulence: A Review of Theoretical and Phenomenological Models

When wind blows over the ocean, short wind-waves (of wavelength smaller than 10 m) are generated, rapidly reaching an equilibrium with the overlying turbulence (at heights lower than 10 m). Understanding this equilibrium is key to many applications since it determines (i) air–sea fluxes of heat, momentum and gas, essential for numerical models; (ii) energy loss from wind to waves, which regulates how swell is generated and how energy is transferred to the ocean mixed layer and; (iii) the ocean surface roughness, visible from remote sensing measurements. Here we review phenomenological models describing this equilibrium: these models couple a turbulence kinetic energy and wave action budget through several wave-growth processes, including airflow separation events induced by breaking waves. Even though the models aim at reproducing measurements of air–sea fluxes and wave growth, some of the observed variability is still unexplained. Hence, after reviewing several state-of-the-art phenomenological models, we discuss recent numerical experiments in order to provide hints about future improvements. We suggest three main directions, which should be addressed both through dedicated experiments and theory: (i) a better quantification of the variability wind-wave growth and of the role played by the modulation of short and breaking wind-waves by long wind-waves; (ii) an improved understanding of the imprint of wind-waves on turbulent coherent structures and; (iii) a quantification of the interscale interactions for a realistic wind-wave sea, where wind-and-wave coupling processes coexist at multiple time and space scales.

Wind wave growth in the viscous regime

How water surface waves grow under wind forcing has long been an interesting and challenging question. For short gravity-capillary waves, the viscous effects are important but have not been well studied. In this paper, we simulate the wind-wave growth by directly solving the two-phase Navier-Stokes equations. The numerical method features a momentum conserving scheme, interface reconstruction using Volume of Fluid, and adaptive mesh refinement (AMR). As a result, we observe concurrent growth of the irrotational traveling wave and the rotational drift layer (current). The growth rate of the wave and the evolution of the drift layer under different forcing parameters are discussed respectively.

Evaluating essential processes and forecast requirements for meteotsunami-induced coastal flooding

Meteotsunamis pose a unique threat to coastal communities and often lead to damage of coastal infrastructure, deluge of nearby property, and loss of life and injury. The Great Lakes are a known hot-spot of meteotsunami activity and serve as an important region for investigation of essential hydrodynamic processes and model forecast requirements in meteotsunami-induced coastal flooding. For this work, we developed an advanced hydrodynamic model and evaluate key model attributes and dynamic processes, including: (1) coastal model grid resolution and wetting and drying process in low-lying zones, (2) coastal infrastructure, including breakwaters and associated submerging and overtopping processes, (3) annual/seasonal (ambient) water level change, and (4) wind wave-current coupling. Numerical experiments are designed to evaluate the importance of these attributes to meteotsunami modeling, including a “representative storm” scenario in the context of regional climate change in which a meteotsunami wave is generated under high ambient lake-level conditions with a preferable wind direction and speed for wind-wave growth. Results demonstrate that accurate representation of coastal topography and fully resolving associated hydrodynamic processes are critical to forecasting the realistic hazards associated with meteotsunami events. As most of existing coastal forecast systems generally do not resolve many of these features due to insufficient model grid resolution or lack of essential model attributes, this work shows that calibrating or assessing existing forecast models against coastal water level gauges alone may result in underestimating the meteotsunami hazard, particularly when gauging stations are sparse and located behind harbor breakwaters or inside estuaries, which represent dampened or otherwise unrepresentative pictures of meteotsunami intensity. This work is the first hydrodynamic modeling of meteotsunami-induced coastal flooding for the Great Lakes, and serves as a template to guide where resources may be most beneficial in forecast system development and implementation.

A global wave parameter database for geophysical applications. Part 3: Improved forcing and spectral resolution

Numerical wave models are used for a wide range of applications, from the global ocean to coastal scales. Here we report on significant improvements compared to the previous hindcast detailed in Part 2 of the present study by Rascle and Ardhuin (2013). This result was obtained by updating forcing fields, adjusting the spectral discretization and retuning wind wave growth and swell dissipation parameters. Most of the model calibration and performance analysis is done using significant wave heights (Hs) from the recent re-calibrated and denoised satellite altimeter data set provided by the European Space Agency Climate Change Initiative (ESA-CCI), with additional verification using spectral buoy data. We find that, for the year 2011, using wind fields from the recent ERA5 reanalysis provides lower scatter against satellite Hs data compared to historical ECMWF operational analyses, but still yields a low bias on wave heights that can be mitigated by re-scaling wind speeds larger than 20 m/s. Alternative blended wind products can provide more accurate forcing in some regions, but were not retained because of larger errors elsewhere. We use the shape of the probability density function of Hs around 2 m to fine tune the swell dissipation parameterization. The updated model hindcast appears to be generally more accurate than the previous version, and can be more accurate than the ERA5 Hs estimates, in particular in strong current regions and for Hs>7 m.

2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time

AbstractA fully consistent 2D parametric model of wave development under spatially and/or time varying winds is developed. Derived coupled equations are written in their characteristic form to provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are developing and distributed under varying wind forcing conditions. For young waves, nonlinear interactions drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are governing the wave energy evolution. With a prescribed wind wave growth rate, proportional to (u*/c) squared, wave breaking dissipation must follow a power‐function of the dominant wave slope. For uniform wind conditions, this choice for the growth rate imposes solutions to follow fetch laws, with exponents q = −1/4, p = 3/4 correspondingly. This set of exponents recovers the Toba's laws, and imposes the wave breaking exponent equal to 3. A varying wind direction can then drive spectral peak direction changes, leading to the occurrence of focusing/defocusing wave groups over localized areas where wave‐rays merge and cross. Significant (but finite) local variations of the energy are then expected under varying wind forcing. Propagating away from a stormy area, wave rays generally diverge, leading to dispersive swell systems. Examples of practical applications of this model are provided in (Kudryavtsev et al., 2021, companion paper).

Spatial evolution of young wind waves: numerical modelling verified by experiments

Abstract

A Theoretical Model of Wind-Wave Growth Over an Ice-Covered Sea

A wind-wave generation model over an ice-covered sea is proposed. The wind velocity over the ice upper surface is decomposed into the mean velocity profile of the boundary-layer flow and small perturbations, while the ice cover is modelled as a viscoelastic layer, with the water part modelled as an inviscid fluid. The present model is based on two-dimensional linear flow-instability theory, with no-slip boundary conditions at the air–ice interface, and both normal and shear stress boundary conditions matched on the air–ice interface. It is shown that the model converges to the field and experimental data for open-water cases. The ice elasticity is found to be the critical factor for generating wind waves, and the generation of flexural-gravity waves and elastic waves in ice is analyzed.

On fetch- and duration-limited wind wave growth: Data and parametric model

Self-similarity power-laws of wind-wave growth describe idealized cases of fetch-limited and duration-limited conditions. In this paper, a generalized view on wave growth in these two cases is discussed. A parametric model describing uniformly fetch- and duration-limited development of wind waves is suggested. The key assumption of the model is the universality of the self-similar shape of wave spectra for both fetch- and duration-limited conditions. The model justifies the conversion of the data collected at fetch-limited conditions to the data corresponding to duration-limited growth and determines the power-law constants of duration-limited growth from the fetch-limited constants. This general view on wave growth is validated against the experimental data reported previously and wave-gauge data obtained at the Black Sea research platform. As demonstrated, the model tuned through fetch-limited data is also consistent with the field data that correspond to the duration-limited conditions. Possible applications of the suggested parametric model are briefly highlighted.