Wind-wave Generation Research Articles

The Earliest Stages of Wind Wave Generation in the Open Sea

Abstract We have explored the earliest stages of wind wave generation in the open sea, from the first initial wavelets appearing on an otherwise flat surface or low, smooth undulations until the practically fully developed conditions for the very low range of wind speeds we have considered. We suggest the minimal wind speed for the appearance of the first wavelets to be close to 1.8 m s−1. The peculiar conditions associated with the development of coastal sea breezes allow us to consider the local waves as generated under time-limited conditions. The 2D spectra measured during these very early stages provide the first evidence of an active Phillips process generation in the field. After appearing in these very early stages, wavelets quickly disappear as soon as the developing wind waves take a leading role. We suggest that this process is due to the strong spatial gradients in the surface orbital velocity, which impedes the instability mechanism at the base of their formation, while at a later stage of development, these gradients decrease and wavelets reappear. On a decadal perspective, the progressive decrease of the intensity of the sea breezes in the northern Adriatic Sea, where we have carried out our measurements, is associated with the steadily milder winters, and therefore not sufficiently cold local sea temperatures in early summer. Significance Statement We have explored for the first time the earliest stages of wind wave generation (millimeter scale) in the open sea. This was possible with the combination of the daily sea breeze development and the availability of an oceanographic tower 15 km offshore. The minimum wind speed for wave generation was 1.8 m s−1, lower than previously assumed. The data provide strong indications on the different stages of the generation process, offering measured and visual evidence, under these very light wind conditions, of the Phillips one. The presence of wind-related ripples, essential for remote sensing measurements, turns out to be dependent on the stage of generation.

Direct numerical evidence of the Phillips initial stage and its antecedent during wind-wave generation

How wind generates ocean surface waves is a classic fluid mechanics problem, and it is commonly believed that the resonance mechanism between wind and surface waves, first proposed by Phillips in 1957, is responsible for the early stages of wind-wave generation. However, there has not been any conclusive study to fully validate this theory. We present the results of a combined theoretical and computational study of the initial response of a calm water surface to turbulent wind and an analysis in terms of the Phillips theory on wind-wave generation. We address a nascent stage of wind-wave generation after the sudden impact of a turbulent wind on a calm water surface but before the initial stage described by Phillips. We show that in such nascent stage, the wave energy grows over time following a quartic law. We provide direct numerical evidence of the resonance mechanism during the initial stage and clarify its role in the formation of the heterogeneous wave energy distribution in the spectral space.

A combined VOF-RANS approach for studying the evolution of incipient two-dimensional wind-driven waves over a viscous liquid

Recent laboratory experiments have revealed that important insights into the physical processes involved in the wind-driven generation of surface waves may be obtained by varying the viscosity of the carrying liquid over several orders of magnitude. The present paper reports on the development of a companion approach aimed at studying similar phenomena through numerical simulation, a way expected to remove some of the experimental limitations, especially in the near-interface region, and to allow the relative influence of several physical processes to be assessed by disregarding or inactivating arbitrarily some of them. After reviewing available options, we select and approach based on the combination of a volume of fluid technique to track the evolution of the air–liquid interface, and a two-dimensional Reynolds-averaged version of the Navier–Stokes equations supplemented with a turbulence model to predict the velocity and pressure fields in both fluids. We examine the formal and physical frameworks in which such a time-dependent two-dimensional formulation is meaningful, and close the governing momentum equations with the one-equation Spalart–Allmaras model which directly solves a transport equation for the eddy viscosity. For this purpose, we assume the interface to behave as a rigid wall with respect to turbulent fluctuations in the air, and implement a versatile algorithm to compute the local distance to the interface whatever its shape. We first assess the performance of this model in unseparated and separated single-phase flows over a wavy rigid wall, which are of specific relevance with respect to wind-wave generation. Then, we discuss the initialization protocol used in two-phase simulations, which involves an impulse disturbance with a white noise distribution applied to the interface position. We finally present some examples of interface evolutions obtained at several wind speeds with liquids of various viscosities, and discuss the underlying physics revealed by the associated statistics of interface disturbances, streamline patterns and energy spectra.

Влияние гидрофобных частиц пыли на параметры ветровых волн в зоне генерации

The paper investigates the effect of a film of natural dust deposited from the air on the generation of gravitational-capillary wind waves with a length of 𝜆<0.06 m. It is shown that with an increase in the deposition time of hydrophobic dust particles on the water surface, the contact wetting angle between the water surface and the hydrophobic particle increases, which indicates an increase in the surface tension coefficient. At the same time, the time of convergence of hydrophobic particles increases. It was found that with increasing film concentration for a given wind speed, the length of the wind wave in the generation zone decreases, and the steepness increases, which is associated with an increase in roughness and coefficient of friction at the interface. Nonlinear plane waves with a steepness of 0.13 <ak<0.25 arise in the generation zone. A method for calculating the phase velocity of such waves has been obtained and verified. The critical value of the wind speed at which the generation of wind waves begins decreases with an increase in the concentration of the dust film, and the values lie in the range 2.3 < Umin < 3 m/s.

Effect of Impurities at Low Concentrations on the Generation of Wind Waves

Effect of Impurities at Low Concentrations on the Generation of Wind Waves

Fully Coupled Analysis of an Integrated Floating Wind-Wave Power Generation Platform in Operational Sea-States

The offshore wind power exploitation has experienced rapid development in recent years and has gradually moved into deeper waters with the floating wind turbine technology getting mature. Due to the strong concurrence of the wind and wave power in offshore sites, the idea of combined utilization of wind and wave power by one integrated device has attracted tremendous interests worldwide and a number of concepts and designs have been proposed. This article describes a novel integrated floating wind-wave generation platform (FWWP) consisting of a DeepCwind semi-submersible floating offshore wind turbine (FOWT) and a point absorber wave energy convertor (PAWEC). Three models including the single PAWEC, single FOWT, and FWWP are considered to investigate the feasibility of the FWWP and its advantages over the single device. Hydrodynamic analyses are first conducted using the potential flow code AQWA with the viscous correction to investigate the hydrodynamic interactions effect of the integrated model. Then, a fully coupled model for the FWWP is established by calling OpenFAST in AQWA using the F2A method. The accuracy of the established coupled model is firstly validated with OpenFAST for analysing the dynamics of the single FOWT. Finally, fully coupled analyses of the FWWP are carried out for both regular and irregular waves in the operational sea-states. The coupled dynamics and wind and wave power generation of the FWWP are compared with those of the single PAWEC and FOWT for both the regular and irregular waves.

The principal stage in wind-wave generation

The dynamics of wind-generated water waves in the principal stage of the Phillips theory (Phillips, J. Fluid Mech., vol. 2, 1957, pp. 417–445) is investigated by a combined numerical and analytical approach. We perform a number of high-resolution direct numerical simulation (DNS) of turbulent wind over initially calm water to capture the multistage generation of water waves. Detailed analyses are conducted to evaluate the Phillips theory in both physical space and wavenumber space. Numerical evidence is obtained for the existence of a principal stage when the surface elevation variance grows linearly with time. We further propose a random sweeping turbulence pressure–wave interaction model by introducing the random sweeping hypothesis of air pressure fluctuations to the Phillips theory, and obtain an asymptotic solution of the mean square of surface wave elevations over time. This asymptotic analysis captures the temporal oscillations of surface elevation variance in the principal stage, which is also confirmed by our DNS results. The wavenumber spectrum of surface wave elevations is analysed using a time-dependent norm to elucidate the role of the resonance mechanism on wave generation. In physical space, we use the random sweeping turbulence pressure–wave interaction model to obtain a quantitative prediction of the growth rate of surface elevation variance in the principal stage, which is found to agree with the DNS results better than the original Phillips model.

Generation of Gravity-Capillary Wind Waves by Instability of a Coupled Shear-Flow

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

Multiobjective Economic Optimal Dispatch for the Island Isolated Microgrid under Uncertainty Based on Interval Optimization

In order to analyse the impact of renewable generation and load uncertainties on the economic operation optimization of the island microgrid, a multiobjective economic optimal dispatch model under uncertainty based on interval optimization is proposed in this paper. The mathematical model of distributed generation and the prediction model of wind speed and wave generation are established. The uncertainties of renewable generation and load are described by the interval mathematical method. On this basis, the interval multiobjective optimal dispatch model is presented. For the “battery disgusting” users on the island, the battery cost is regarded as a separate optimization objective, and a multiobjective optimization objective function to minimize the economic cost, battery cost, and pollution emission of the island microgrid is discussed. An island microgrid, composed of wind turbine, photovoltaic, wave energy generation, diesel generator, and energy storage system, is chosen as a case study. The NSGA-II algorithm is applied to solve the multiobjective optimal problem. The results for deterministic forecast data and load are analysed, and the optimal operation scheme is obtained by the improved multiobjective grey target decision-making method. The influence of renewable generation fluctuations ±10%, ±20%, and ±30% and the load fluctuations ±10% and ±20% on island microgrid operation optimization is discussed in detail, respectively. The relevant research results can provide a reference for formulating the operating scheme of the island microgrid.

Effect of the wind acceleration magnitude during the first stages of the wind-wave generation process

A comprehensive analysis of the wavefield evolution under accelerated wind conditions provides an essential contribution to understanding the wind-wave generation process. A set of experiments was carried out in a large wind-wave facility where it is possible to reproduce high wind speed conditions to study the wind acceleration effect in the wind-wave development. The facility was equipped with high-frequency sampling devices that provide accurate air turbulence and water surface displacement measurements. From this deployment, it was possible to describe the evolution of the wave characteristics under different magnitudes of constant wind acceleration in detail. This study analyzes the wind acceleration effect in the early stages of wind-wave generation and evolution. The increase of spectrum energy saturation level and the downshift of the peak frequency are processes associated with the spectral shape evolution under low acceleration wind conditions. Under high wind acceleration conditions, the spectral shape did not vary with wind speed and fetch. Despite under low acceleration wind conditions, the wavefield is more developed than under high acceleration wind conditions; there was no direct relation between wind acceleration and the wavefield efficiency to grow. Besides, during these early instants, it was observed that a more developed wave field, associated with low acceleration wind conditions, could slow down the increase of drag coefficient with wind speed.

Effect of Water Vorticity on Wind-Generated Gravity Waves in Finite Depth

The generation of wind waves at the surface of an established underlying vertically sheared water flow, of constant vorticity, is considered. A particular attention is paid to the role of the vorticity in water on wind-wave generation in finite depth. The present theoretical results are compared with experimental data obtained by Young and Verhagen (Coast Eng 29:47–78, 1996), in the shallow Lake George (Australia), and the least squares fit of these data by Young (Coast Eng 32:181–195, 1997). It is shown that without vorticity in water, there is a deviation between theory and experimental data. However, a good agreement between the theory and the fit of experimental data is obtained when negative vorticity is taken into account. Furthermore, it is shown that the amplitude growth rate increases with vorticity and depth. A limit to the wave energy growth, corresponding to the vanishing of the growth rate, is obtained. The corresponding limiting wave age is derived in a closed form showing its explicit dependence on vorticity and depth. The limiting wave age is found to increase with both vorticity and depth.

The Kelvin–Helmholtz instability, a useful model for wind-wave generation?

The Kelvin–Helmholtz instability, one of the most classical instabilities in fluid mechanics, was initially introduced to describe the generation of waves by wind. This instability is relevant to several natural and engineering flow configurations, and has led to many experimental variants, in tilted channel with stratified fluids, in circular cells or quasi-2D Hele-Shaw cells. As many physicists, Yves Couder, who passed away in 2019, was fascinated by the problem of wind-wave generation, but also frustrated by the fact that, despite considerable studies over the years, it was still poorly understood. Yves was always eager for simple explanations about physics phenomena, with qualitative arguments rather than equations, and this problem was for him and his collaborators a recurrent source of inspiration. Sharing views about physics with him, making experiments, or even contemplating natural phenomena, was always highly stimulating. In the spirit of these discussions with Yves, we recall here the basics of the Kelvin–Helmholtz instability, and discuss to what extent it may be relevant to the problem of wind-wave generation — not in the air–water case but, rather surprisingly, for very viscous liquids.

Wind-induced changes to surface gravity wave shape in deep to intermediate water

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.

Miles Theory Revisited with Constant Vorticity in Water of Infinite Depth

The generation of wind waves at the surface of a pre-existing underlying vertically sheared water flow of constant vorticity is considered. Emphasis is put on the role of the vorticity in water on wind-wave generation. The amplitude growth rate increases with the vorticity except for quite old waves. A limit to the wave energy growth is found in the case of negative vorticity, corresponding to the vanishing of the growth rate.

Effects of Hydrocarbons on Wind Waves in a Mine Pit Lake

The extraction and upgrading of bitumen to crude oil from the Canadian oil sands has produced large quantities of byproducts such as fluid fine tailings (FFT) and oil sands process affected water (OSPW). One reclamation strategy for these byproducts is to backfill a mined-out pit with FFT and cap it with a mix of OSPW and non-process affected water to form a pit lake. We investigated the effects of hydrocarbons, residual bitumen, on the generation and growth of wind waves, both in the laboratory and in a pit lake. In the laboratory, we compared the wind wave characteristics in the presence and absence of a hydrocarbon film. We showed that the hydrocarbon film dampens high frequency waves, resulting in a slower growing wave field dominated by lower frequency waves. These results were consistent with our field observations. Thus, it appears that the presence of a hydrocarbon film on a pit lake leads to a wind wave field dominated by longer wavelength waves that take more time to develop and grow at a slower rate. This is important since wind wave-driven mixing, in tandem with biogeochemical processes, governs water quality in mine pit lakes. Thus, this work improves understanding of the physical processes that effect water quality in mine pit lakes and enhances the ability of mine managers to conduct pit lake reclamation.

Spatial and temporal variability of sea breezes and synoptic influences over the surface wind field of the Yucatán Peninsula

The balance between synoptic and sea breeze atmospheric phenomena can profoundly influence atmospheric circulation in coastal regions. In this paper, a comprehensive study to understand the quasi-permanent patterns of such variability over the surface wind field of the Yucatan Peninsula is described. We performed a Complex Empirical Orthogonal Function (CEOF) analysis on 10 years (May 2007-May 2017) of modeled surface winds from the North American Mesoscale Forecast System (hereafter, NAM). High-pass/low-pass filtering was applied to the time series obtained from the CEOF analysis, to study the high and low-frequency temporal behavior that can be associated with the modes. Results show that for the period from October to March, cold fronts dominate in two different patterns (first two modes), which damp the local winds that show higher amplitude during the nighttime (land breezes) than during the daytime (sea breezes). By the end of this season, the influence of tropical systems, although smaller, is noticeable (third mode). From April to September the peninsula is dominated by sea breezes accentuated at the western shelf (first mode) while land breezes exhibit lesser dominance than sea breezes (third mode). In this period cold fronts and tropical systems (mode 2) exert milder influence over local winds. A distinctive phenomenon seen in the high frequencies of the second mode during this period is the occurrence of peninsula-wide sea breeze. The results of this work have important implications for atmospheric pollutant dispersion, wind wave generation and coastal erosion, among others.

Generation of Wind Waves in Large Streams

Generation of Wind Waves in Large Streams

Effects of the Sea Surface Roughness and Sea Spray‐Induced Flux Parameterization on the Simulations of a Tropical Cyclone

AbstractA tropical cyclone (TC) interacts with the ocean through the interchange of surface fluxes of heat and momentum at the air‐sea interface. The sustainability and intensification of TCs are maintained by the enhancement in the latent heat flux in the high wind speed regime. An accurate calculation of heat fluxes is vital to understand the dynamics of the TC. The sea surface roughness is a crucial parameter that modulates the air‐sea fluxes. A coupled ocean‐atmosphere‐wave model is used to simulate TC Vardah over the Bay of Bengal during 10–15 December 2016. The study focuses on the influence of sea surface roughness on the heat fluxes, track, and intensity of TC Vardah. Four numerical experiments are performed with different parameterization schemes for surface roughness on the basis of (i) frictional velocity (Charnock), (ii) wave age, (iii) wave steepness, and (iv) a combination of wave steepness and wave age. A change in ocean surface roughness results in the modification of the cyclone track and heat fluxes. However, the effect of sea spray on the simulation of wind intensity of TC Vardah is only marginal. Out of the four experiments, the wave age‐based roughness parameterization was found to improve cyclone track, wind, and, hence, the generation of wind waves on the sea surface. In the case study of TC Vardah, the dynamic sea spray reduces surface wind speed up to 1.5 m/s which is within the uncertainty range of the model. An intercomparison of model experiments reveals the impact of surface heat fluxes on the TC Vardha characteristics.

Simulation-based study of wind—wave interactions under various sea conditions

Despite their importance in the ocean environment, the key physical processes in wind-wave interactions are poorly understood. Using a solver developed for undulatory boundaries, we perform numerical simulations of the wind-wave system under various sea conditions, including wind over monochromatic waves, early wind-wave generation, and wind over a broadband wave field. Our results show that the wave direction and wave age can significantly change the distribution of streamwise vorticity in the wind field. Different wave patterns are observed in the process of wind-wave generation. In a broadband wave field, the wave growth rate due to wind input is found to depend on the wave steepness.