Impact of waves on air-sea exchange of sensible heat and momentum

The impact of sea waves on sensible heat and momentum fluxes is described. The approach is based on the conservation of heat and momentum in the marine atmospheric surface layer. The experimental fact that the drag coefficient above the sea increases considerably with increasing wind speed, while the exchange coefficient for sensible heat (Stanton number) remains virtually independent of wind speed, is explained by a different balance of the turbulent and the wave-induced parts in the total fluxes of momentum and sensible heat.Organised motions induced by waves support the wave-induced stress which dominates the surface momentum flux. These organised motions do not contribute to the vertical flux of heat. The heat flux above waves is determined, in part, by the influence of waves upon the turbulence diffusivity.The turbulence diffusivity is altered by waves in an indirect way. The wave-induced stress dominates the surface flux and decays rapidly with height. Therefore the turbulent stress above waves is no longer constant with height. That changes the balance of the turbulent kinetic energy and of the dissipation rate and, hence the diffusivity.The dependence of the exchange coefficient for heat on wind speed is usually parameterized in terms of a constant Stanton number. However, an increase of the exchange coefficient with wind speed is not ruled out by field measurements and could be parametrized in terms of a constant temperature roughness length. Because of the large scatter, field data do not allow us to establish the actual dependence. The exchange coefficient for sensible heat, calculated from the model, is virtually independent of wind speed in the range of 3–10 ms^-1. For wind speeds above 10 ms^-1 an increase of 10% is obtained, which is smaller than that following from the constant roughness length parameterization.The investigation was in part supported by the Netherlands Geosciences Foundation (GOA) with financial aid from the Netherlands Organization for Scientific Research (NWO).     

Effects of Sea-Surface Waves and Ocean Spray on Air-Sea Momentum Fluxes

The effects of sea-surface waves and ocean spray on the marine atmospheric boundary layer(MABL) at different wind speeds and wave ages were investigated. An MABL model was developed that introduces a wave-induced component and spray force to the total surface stress. The theoretical model solution was determined assuming the eddy viscosity coefficient varied linearly with height above the sea surface. The wave-induced component was evaluated using a directional wave spectrum and growth rate. Spray force was described using interactions between ocean-spray droplets and wind-velocity shear. Wind profiles and sea-surface drag coefficients were calculated for low to high wind speeds for wind-generated sea at different wave ages to examine surface-wave and ocean-spray effects on MABL momentum distribution. The theoretical solutions were compared with model solutions neglecting wave-induced stress and/or spray stress. Surface waves strongly affected near-surface wind profiles and sea-surface drag coefficients at low to moderate wind speeds. Drag coefficients and near-surface wind speeds were lower for young than for old waves. At high wind speeds, ocean-spray droplets produced by wind-tearing breaking-wave crests affected the MABL strongly in comparison with surface waves, implying that wave age affects the MABL only negligibly. Low drag coefficients at high wind caused by ocean-spray production increased turbulent stress in the sea-spray generation layer, accelerating near-sea-surface wind. Comparing the analytical drag coefficient values with laboratory measurements and field observations indicated that surface waves and ocean spray significantly affect the MABL at different wind speeds and wave ages.     

Aerodynamic roughness of the sea surface at high winds

The role of the surface roughness in the formation of the aerodynamic friction of the water surface at high wind speeds is investigated. The study is based on a wind-over-waves coupling theory. In this theory waves provide the surface friction velocity through the form drag, while the energy input from the wind to waves depends on the friction velocity and the wind speed. The wind-over-waves coupling model is extended to high wind speeds taking into account the effect of sheltering of the short wind waves by the air-flow separation from breaking crests of longer waves. It is suggested that the momentum and energy flux from the wind to short waves locally vanishes if they are trapped into the separation bubble of breaking longer waves. At short fetches, typical for laboratory conditions, and strong winds the steep dominant wind waves break frequently and provide the major part of the total form drag through the air-flow separation from breaking crests, and the effect of short waves on the sea drag is suppressed. In this case the dependence of the drag coefficient on the wind speed is much weaker than would be expected from the standard parameterization of the roughness parameter through the Charnock relation. At long fetches, typical for the field, waves in the spectral peak break rarely and their contribution to the air-flow separation is weak. In this case the surface form drag is determined predominantly by the air-flow separation from breaking of the equilibrium range waves. As found at high wind speeds up to 60 m s⁻¹ the modelled aerodynamic roughness is consistent with the Charnock relation, i.e. there is no saturation of the sea drag. Unlike the aerodynamic roughness, the geometrical surface roughness (height of short waves) could be saturated or even suppressed when the wind speed exceeds 30 m s⁻¹.     

The Impact Of Air-Flow Separation On The Drag Of The Sea Surface

An approach that allows assessment ofthe impact of air-flow separation (AFS) fromwave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumedthat the dynamics of the AFS from wave breaking crests is similar to thatfrom the backward facing step. The form drag supported by an individualbreaker is described by the action of the pressure drop distributed alongthe forward face of the breaking front. The total stress due to the AFS isobtained as a sum of contributions from breaking fronts of different scales.Outside the breaking fronts the drag of the sea surface is supported by theviscous surface stress and the wave-induced stress. To calculate the stressdue to the AFS and the wave-induced stress a physical model of the wind-wavespectrum is used. Together with the model of the air flow described in termsof surface stresses it forms a self-consistent dynamical system for the seasurface-atmosphere where the air flow and wind waves are strongly coupled.Model calculations of the drag coefficient agree with measurements. It is shownthat the dimensionless Charnock parameter (roughness length normalized onthe square of the friction velocity and the acceleration of gravity)increases with the increase of the wind speed in agreement with fieldmeasurements. The stress due to the AFS normalized on the square of thefriction velocity is proportional to the cube of wind speed. At low windsthe viscous surface stress dominates the drag. The role of the form drag,which is the sum of the stress due to the AFS and the wave-induced stress, isnegligible. At moderate and high winds the form drag dominates. At windspeeds higher than 10 m s^-1 the stress supported by the AFS becomescomparable to the wave-induced stress and supports up to 50% of the totalstress.     

One-dimensional theory of the wave boundary layer

Results obtained in a 2-D modeling of the statistical structure of the wave boundary layer (WBL) are used for elaboration of the general approach to 1-D modeling taking into account the spectral properties of wave drag for an arbitrary wave field. In the case of the wave field described by the JONSWAP spectrum, the momentum and energy spectral density exchange, vertical profiles of the wave-induced momentum flux and dependence of total roughness parameter and drag coefficient on peak frequency are given. The reasons that the total roughness parameter increases with decreasing fetch are explained. The role of wind waves as an active element of the ocean-atmosphere dynamic system is also discussed.     

New evidence for a relation between wind stress and wave age from measurements during ASGAMAGE

Data from the 1996 ASGAMAGE experiment, performed in the southern North Sea at research platform Meetpost Noordwijk (MPN), are analysed for the parameters affecting the momentum flux. The stress turns out to be quadratically related to the 10-m wind speed and linearly to the wind speed at a wavelength related level. The Charnock parameter (dimensionless roughness length) shows a pronounced correlation with wave age. This implies, due to a coupling between wave age and the steepness of the waves, a connection between the stress and the steepness. We find that our North Sea results are consistent withopen ocean observations. For a given wind speed the mean stress at MPN turns out to be higher because the wave age there is in general lower. We define and give an expression for a drag coefficient at a wavelength related level that can be calculated straightforwardly from the wave age and then reduced to a standard level.     

The roughness of wind waves

In this paper, a new dynamic roughness equation for airflow over wind waves is proposed, based on relationships of dimensionless parameters and the 1986 HEXMAX field data. The equation can be considered as a modification of the Charnock formula. The data are also compared with the parameterizations of Toba and Koga, and of Hsu, and the consequences of the new equation for aerodynamic drag are discussed. In the new equation, the drag coefficient is expressed as a function of both wind speed and wave age c _p/u_*. This testifies to the strong wave-age dependence of the drag, found in several experimental studies. It is also in good agreement with results of a theoretical model of the airflow-seawave interaction, proposed by Janssen (1989).Also: Dept. of Applied Physics, Techn. Univ. Delft, the Netherlands.     

A Note on Wind Speed and sea State Dependence of the Heat Exchange Coefficient

Both mean and wave-induced motions generate turbulence in the air flow above sea waves. Assuming a local balance between production of turbulent kinetic energy and its dissipation, an explicit relation for the heat exchange coefficient CH is obtained. It is shown that CH follows a square-root dependence on the drag coefficient CD. However, the proportionality coefficient appears to depend on the sea state, expressed in terms of the coupling parameter. Dependence on the sea state suppresses the CD1/2 wind-speed dependence, and results in a marginal increase of CH with increase in the wind speed.     

Turbulence intensities and bulk coefficients in the surface layer above the sea

The structure of the atmospheric surface layer above the sea is analysed from aircraft turbulence measurements. The data are issued from two experiments performed in 1990 above the Mediterranean sea: Crau and PYREX, and correspond to moderately unstable conditions and to wind velocities ranging from 6 to 20 m/s. Low-altitude straight and level runs were used to compute the variances of the wind components, as well as of the temperature and moisture. Their dependence on the stability index —z/L is analysed. The turbulent fluxes of momentum, sensible heat and latent heat, calculated by the eddy-correlation technique, are used to estimate the neutral bulk coefficients: drag coefficient, Stanton number and Dalton number. The neutral drag coefficient clearly exhibits a dependence on the windspeed, which could be well fitted by the Charnock relation, with a constant of 0.012.     

Turbulent Airflow and Wave-Induced Stress Over the Ocean

We examine the structure of turbulent airflow over ocean waves. Based on an analysis of wind and wave observations derived from a moored and floating Air–Sea Interaction Spar buoy during the Shoaling Waves Experiment field campaign, we show that the cospectra of momentum flux for wind–sea conditions follow established universal scaling laws. Under swell-dominant conditions, the wave boundary layer is extended and the universal cospectral scaling breaks down, as demonstrated previously. On the other hand, the use of peak wave frequency to reproduce the universal cospectra successfully explains the structure of the turbulent flow field. We quantify the wave-coherent component of the airflow and this clarifies how ocean waves affect momentum transfer through the wave boundary layer. In fact, the estimated wave-induced stresses for swell-dominant conditions explain the anomalous cospectral shapes observed near the peak wave frequency.     

Nonlinear Formulation of the Bulk Surface Stress over Breaking Waves: Feedback Mechanisms from Air-flow Separation

Historically, our understanding of the air-sea surface stress has been derived from engineering studies of turbulent flows over flat solid surfaces, and more recently, over rigid complex geometries. Over the ocean however, the presence of a free, deformable, moving surface gives rise to a more complicated drag formulation. In fact, within the constant-stress turbulent atmospheric boundary layer over the ocean, the total air-sea stress not only includes the traditional turbulent and viscous components but also incorporates surface-wave effects such as wave growth or decay, air-flow separation, and surface separation in the form of sea-spray droplets. Because each individual stress component depends on and alters the sea state, a simple linear addition of all stress components is too simplistic. In this paper we present a model of the air-sea surface stress that incorporates air-flow separation and its effects on the other stress components, such as a reduction of the surface viscous stress in the separated region as suggested by recent measurements. Naturally, the inclusion of these effects leads to a non-linear stress formulation. This model, which uses a variable normalized dissipation rate of breaking waves and normalized length of the separation bubble, reproduces the observed features of the drag coefficient from low to high wind speeds despite extrapolating empirical wave spectra and breaking wave statistics beyond known limits. The model shows the saturation of the drag coefficient at high wind speeds for both field and laboratory fetches, suggesting that air-flow separation over ocean waves and its accompanying effects may play a significant role in the physics of the air-sea stress, at least at high wind speeds.     

The KNMI HEXMAX stress data – a reanalysis

An earlier discussion of the wind stress measurements of the 1986 HEXMAX experiment off the Dutch coast left some uncertainty about the actual relationship between the stress and the wave field. In this paper we try to find a more definitive answer by looking at the consequences for gradients of wind speed, stress and phase speed of the waves if we assume the Charnock coefficient to be either a constant or to have an inverse wave age dependence. It turns out that both assumptions have a wind speed range where they produce coherent results, but that they break down when the wave length exceeds a value that is related to the water depth.     

Impact Of Dominant Waves On Sea Drag

The impact of air-flow separation from breaking dominant waves is analyzed.This impact results from the correlation of the pressure drop with theforward slope of breaking waves. The pressure drop is parameterized via thesquare of the reference mean velocity. The slope of breaking waves isrelated to the statistical properties of the wave breaking fronts describedin terms of the average total length of breaking fronts. Assuming that thedominant waves are narrow and that the length of breaking fronts is relatedto the length of the contour of the breaking zone it is shown that theseparation stress supported by dominant waves is proportional to thebreaking probability of dominant waves. The breaking probability of dominantwaves, in turn, is defined by the dominant wave steepness. With thedominant wave steepness increasing, the breaking probability is increasedand so does the separation stress. This mechanism explains wave age (youngerwaves being steeper) and finite depth (the spectrum is steeper in shallowwater) dependence of the sea drag. It is shown that dominant waves support asignificant fraction of total stress (sea drag) for young seas due to theair-flow separation that occurs when they break. A good comparison of themodel results for the sea drag with several data sets is reported.     

Numerical simulation of air flow over breaking waves

The air flow above breaking monochromatic Stokes waves is studied using a numerical nonlinear model of the turbulent air flow above waves of finite amplitude. The breaking event (spilling breaker) is parameterized by increasing the local roughness at the downwind slope of the wave, just beyond the crest. Both moderate slope waves and steep waves are considered. Above steep breaking waves, a large increase (typically 100%) in the total wind stress — averaged over the wave profile — is found compared to nonbreaking moderate slope waves. This is due to the drastic increase of the form drag, which arises from the asymmetrical surface pressure pattern above breaking waves. Both increase of wave slope (sharpening of the crest) and increase of local roughness in the spilling breaker area cause this asymmetrical surface pressure pattern. A comparison of the numerical results with the recent experimental measurements of Banner (1990) is carried out and a good agreement is found for the structure of the pressure pattern above breaking waves and for the magnitude of enhanced momentum transfer. Also: Dept. of Applied Physics, Techn. Univ. Delft, Netherlands.     

Signatures of Air–Wave Interactions Over a Large Lake

The air–water exchange of momentum and scalars (temperature and water vapour) is investigated using the Lake-Atmosphere Turbulent EXchange (LATEX) dataset. The wind waves and swell are found to affect the coupling between the water surface and the air differently. The surface-stress vector aligns with the wind velocity in the presence of wind waves, but a wide range of stress–wind misalignment angles is observed during swell. The momentum transport efficiency decreases when significant stress–wind misalignment is present, suggesting a strong influence of surface wave properties on surface drag. Based on this improved understanding of the role of wave–wind misalignment, a new relative wind speed for surface-layer similarity formulations is proposed and tested using the data. The new expression yields a value of the von Kármán constant (\(\kappa \)) of 0.38, compared to 0.36 when using the absolute wind speed, as well as reduced data fitting errors. Finally, the ratios of aerodynamic to scalar roughness lengths are computed and various existing models in the literature are tested using least-square fitting to the observed ratios. The tests are able to discriminate between the performance of various models; however, they also indicate that more investigations are required to understand the physics of scalar exchanges over waves.     

The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length.Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u _*/c>0.07), the effect of stratification on wave growth is weell described by Monin-Obukhov scaling of the friction velocity. For smaller values ofu _*/c, Monin-Obukhov scaling overpredicts.The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.     

Wave generation on the air-sea interface

The sea state and the air flow above the sea during active wave generation is discussed. From energy balance considerations, a relationship between the wind duration and the phase speed of the waves at the peak of the energy spectrum is derived and compared with previous experimental results. It is shown that fluid viscosity plays a negligible role in the transfer of momentum from the air to the sea. Consequently the drag coefficient for the air-sea interface is related only to the apparent roughness of the sea surface.     

Fetch Limited Drag Coefficients

Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Risø Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.