Air Flow Structure Over Short-gravity Breaking Water Waves

Despite its importance for momentum and mass transfer across the air–sea interface, the dynamics of airflow over breaking waves is largely unknown. To fill this gap, velocity and vorticity distributions above short-gravity breaking waves have been measured in a wind-wave tank. A Digital Particle Image velocimetry technique (DPIV) was developed to accomplish these measurements above single breaking waves, propagating in mechanically-generated wave groups and forced by the wind. By varying the wind speed and initial characteristics of the groups, the airflow structure was captured over waves at different stages of the breaking process, and breaking with various intensities. The instantaneous airflow that separates from a sharp breaking crest is very similar to that occurring over a backward facing step. The separation bubble is however strongly unsteady: the steeper the wave crest and the larger the Reynolds number based on the crest-height, the higher the separated layer and the farther downwind the reattachment point. Instantaneous flow topology displays specific features of three-dimensional separation patterns. The tangential stress above the wave profile does not exhibit spikes at reattachment but grows progressively downwind from zero at reattachment to a value at the next crest approximately that found at the upwind breaking crest. Static pressure measurements revealed that large pressure falls are generated by vortices in the separated layer, as found in separated flows over solids. This study may provide useful data for theoretical and numerical modelling of the flow and associated phenomena.     

Ultra-wideband radar studies of steep crested waves with scanning laser measurements of wave slope profiles

We report results of ultra wide-band radar sea spike experiments using steep and weakly breaking non-linear water surface features in a wave tank. To generate these features we used a 1 s paddle wave and wind waves for a sequence of wind speeds. A scanning laser was used to measure synchronously the surface slope profile across 12 cm along the wave propagation direction once per radar pulse. A time domain reflectometer (TDR) radar transmitted short horizontally polarized pulses at X-band, several hundred picoseconds long, to give a range resolution of 10 cm. A radar range of 36 cm was digitally sampled so that surface feature echoes could be tracked through the area continuously with 5 ms temporal resolution with each instrument. We report results considering the wave slope component in the propagation direction and the corresponding curvature component. For the conditions studied, two types of features which produce sea spike radar echoes were generated–a non-linear feature near the crest front of the wind wave, caused by extreme steepening as a result of the passage of the paddle wave, and a steepened blocked wind wave in the trough of the paddle wave, caused by the local orbital current of the 1 s wave being nearly equal to and opposite the phase velocity of the wind wave.     

Phase-Averaged Flow Properties Beneath Microscale Breaking Waves

The phase-averaged characteristics of the turbulent velocity fields beneath steep short wind waves are investigated. A scheme was developed to compute the phase of individual wind waves using spatial surface displacement data. This information was used to analyze the two-dimensional velocity data acquired using particle image velocimetry (PIV) in a wind-wave tank. The experiments were conducted at a fetch of 5.5m and at wind speeds that ranged from 4 to 10ms⁻¹. Under these conditions previous studies have shown that a significant percentage of the waves are microscale breaking waves. An analysis of the phase-averaged results suggests under these conditions (short fetches and moderate wind speeds) a wind-driven water surface can be divided into three regions based on the intensity of the turbulence. These are the crests of microscale breaking waves, the crests of non-breaking waves and the troughs of all waves. The turbulence is most intense beneath the crests of microscale breaking waves. In the crest region of microscale breaking waves coherent structures were observed that were stronger and occurred more frequently than beneath the crests of non-breaking waves. Beneath the crests of non-breaking waves the turbulence is a factor of two to three times weaker and beneath the wave troughs it is a factor of six weaker. These findings provide additional support for the hypothesis that approximately two-thirds of the gas and heat fluxes occur across the turbulent wakes produced by microscale breaking waves.     

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.     

Estimation of the influence of surface waves on the sea surface radiative balance

The sea roughness effect on insolation and sun rays reflection for different sun heights above the horizon and unclouded sky is considered. Numerical assessments for albedo, insolation, and absorbed radiation are received for Stokes waves. Normal ray falling at the wave crest is suggested. The ray trace approach is used that allowed to take into account such effects as the dependence of albedo on the wave tilt, double light reflection from neighboring wave crests and the trough shading by the crest. It is concluded that the main roughness effect on the radiative balance is the insolation increasing and albedo diminishing at large wave steepness when the sun height above the horizon is less than 40°.     

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.     

Structure of air flow separation over wind wave crests

Air flow over wind waves generated in a wind-wave tunnel was visualized by numerous tiny suspended particles (zinc stearate), and instantaneous air flow fields over about one wavelength of wind waves were obtained. Air flow separation was detected over the wave crest in about a half of the samples. In such cases, the separation started near the crest about half of the time, with a vortex trapped over the convergence point of the surface flow which appeared at the leeward face of the crest. This structure was much different from a previously imagined picture in which the separation started at the convergence point. The high frequency of its occurrence suggested the stability of this structure. However, even when this structure was clearly seen, the structure behind the vortex to the next wave crest had various patterns. This variety seems to be related to an instability of the high-shear layer accompanied by separation. Other varieties were also seen, such as the occurrence of separation without the above mentioned structure, as well as the existence of non-separated air flow structures. These varieties seem to be related to the variability of individual wind wave crests. An analysis of correlation between the wave form and the air flow structure over it shows that there is a critical value of local gradient of wave form, above which the air flow always separates. This fact suggests a strong coupling between the air and the water, i.e., the local stress exerted on the water surface changes the nature of a wave crest, especially its form, and as a result, the air flow structure over it changes drastically.Decreased 21 November, 1981. Final draft of the paper prepared by Professor Yoshiaki Toba, Geophysical Institute, Tohoku University.     

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.     

Integrated modeling of the dynamic meteorological and sea surface conditions during the passage of Typhoon Morakot

In August 2009, Typhoon Morakot caused massive flooding and devastating mudslides in the southern Taiwan triggered by extremely heavy rainfall (2777 mm in 4 days) which occurred during its passage. It was one of the deadliest typhoons that have ever attacked Taiwan in recent years. In this study, numerical simulations are performed for the storm surge and ocean surface waves, together with dynamic meteorological fields such as wind, pressure and precipitation induced by Typhoon Morakot, using an atmosphere–waves–ocean integrated modelling system. The wave-induced dissipation stress from breaking waves, whitecapping and depth-induced wave breaking, is parameterized and included in the wave–current interaction process, in addition to its influence on the storm surge level in shallow water along the coast of Taiwan. The simulated wind and pressure field captures the characteristics of the observed meteorological field. The spatial distribution of the accumulated rainfall within 4 days, from 00:00 UTC 6 August to 00:00 UTC 10 August 2009, shows similar patterns as the observed values. The 4-day accumulated rainfall of 2777 mm at the A-Li Shan mountain weather station for the same period depicted a high correlation with the observed value of 2780 mm/4 days. The effects of wave-induced dissipation stress in the wave–current interaction resulted in increased surge heights on the relatively shallow western coast of Taiwan, where the bottom slope of the bathymetry ranges from mild to moderate. The results also show that wave-breaking has to be considered for accurate storm surge prediction along the east coast of Taiwan over the narrow bank of surf zone with a high horizontal resolution of the model domain.     

Transition of two‐layer stratified flow from the slope of bottom topography to a horizontal channel

Abstract

An experimental study was conducted to investigate the transition of two‐layer stratified flow from the slope of bottom topography to a horizontal channel. Three experiments, with a reduced gravity of g’ = 1.64, 6.47 and 18.0 cm s^?2, were performed. Particle image velocimetry and planar laser‐induced fluorescence were used to obtain the measurements of velocity and concentration fields. The flow rate, obtained from the measured velocity field, increases significantly toward the toe of the topography by almost 40% from that at the sill crest due to the interfacial wave activities. In the horizontal channel, however, the flow rate only increases marginally. Estimates of the composite Froude number indicate that the supercritical flow on the slope of the topography goes through the transition to the subcritical flow in the horizontal channel. The transition is mainly due to the increase in the lower‐layer thickness because of increasing interfacial friction caused by the breaking of interfacial waves, and no internal hydraulic jumps are observed. The measured mean concentration field showed the formation of an intermediate layer of medium density, which increased its thickness with g’ and helped to suppress turbulence. Spectral analysis of the density interfacial fluctuations indicated that the interfacial waves that developed on the slope of the topography broke up downstream of the toe into smaller amplitude waves at larger frequencies. The waves at several channel cross‐sections were also examined.     

Experimental study of nonlinear wave—wave interaction and white-cap dissipation of wind-generated waves

An experimental scheme was designed to obtain laboratory-scale verification of Hasselmann's nonlinear wave—wave interaction and white-cap dissipation theories. Water wave height and fluctuating air pressure were measured simultaneously in a fixed reference frame as a function of fetch in the Stanford Wind, Water-Wave Research Facility under the conditions of a steady wind and a stationary wave spectrum. All the data were obtained 5 mm above the highest point of the wind waves for five stations (3 m apart on average) and at three wind speeds (7.1, 8.0 and 8.9 m/sec). The wave height and fluctuating pressure were measured by a capacitance wave-height gauge and a crystal pressure transducer, respectively.Based on the experimental results, Hasselmann's nonlinear wave—wave interaction theory appears to be valid. Barnett's approximate parametric equation for calculating the energy transfer of nonlinear wave—wave interaction and Hasselmann's white-capping dissipation model were also verified and appeared to be applicable in the relatively low and intermediate frequency region of a wave spectrum for a normalized fetch range of 100–500. Based on the results of an overall energy balance in a gravity wind-wave spectrum, the nonlinear wave—wave interaction mechanism is shown to play a dominant role in the energy transfer processes after the wave spectrum is generated.     

An extended Miles' theory for wave generation by wind

Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model.The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input ß from wind to waves travelling in the same direction, e.g., the increase is 2gk ² for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.     

Radar measurement of the effect of boundary-layer saturation on mountain-wave amplitude

Meso-Strato-Troposphere and weather radars are used to show the effect of saturated air near the ground on mountain waves in the troposphere and lower stratosphere, at 52.4°N, 4.0°W. Mountain waves are observed above scattered precipitation; however, long-term observations confirm here that wave amplitude is reduced above extensive precipitation, as predicted from numerical models. Ceilometer measurements of average cloud base near the mountain tops suggest that saturated air could be reducing the generation of mountain waves, in addition to trapping or absorbing waves.     

Semi‐diurnal internal wave diffraction caused by Dixon Entrance,British Columbia

Abstract

To develop an understanding of the complex internal tidal phenomena observed near and inside Dixon Entrance, an idealized numerical model was developed for the area, which explores the influence of various topographic features on the scattering of internal tides. The model uses a non‐linear, two‐layered, frictionless finite difference formulation of the shallow water equations and is forced by a barotropic wave over simplified topography. It was found that the main bathymetric features responsible for the generation of semi‐diurnal internal tides are the steep continental slope together with the orientation of Dixon Entrance. The prevalent baroclinic wave pattern, which is similar to the one found by Buchwald (1971), suggests that the western end of Dixon Entrance can be considered as an internal tide generation region for the open ocean. Use of the simple model allows easy identification of the generated waves. When the model is run with a non‐flat channel it reproduces features observed inside Dixon Entrance.     

Vertical mixing of passive scalars owing to breaking gravity waves

In this paper, some aspects of dispersion of air pollutants as emitted from aircraft in the lower stratosphere have been investigated. As this part of the atmosphere is always stably stratified, mixing as a result of small-scale turbulence is very slow. Instead, effective vertical mixing can be provided by breaking gravity waves. We have examined the mixing properties of those events by means of a numerical model, which simulates the wave development as well as the dispersion of passive trace substances. From these simulations, an effective diffusion coefficient for the entire event of a breaking gravity wave of about 0.7 m² s⁻¹ was calculated.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

Diurnal momentum budget analysis of thermally induced slope winds

Summary  Data measured during the TRACT field campaign at various stations along a 7.5° steep and west-northwest facing slope of the Black Forest mountain range (Germany) are used to analyze the thermal structure and the momentum budget associated with thermally induced slope winds. Acceleration of the air close to the ground is found to be directed nearly vertically downward during the night and nearly vertically upward during the day, rather than parallel to the slope. This means that during the night the airflow is deflected by the slope surface in the down-slope direction, whereas during daytime stable stratification above the heated slope layer is required to establish up-slope flow parallel to the slope. The diurnal cycle of the momentum budget of the along-slope wind component near the surface is analyzed in detail with respect to the driving forces (buoyancy and pressure gradient force) and friction. It is found that a small imbalance between forcing and friction is responsible for the diurnal change in slope flow intensity. The along-slope components of the horizontal pressure gradient force and the buoyancy force are shown to have the same order of magnitude. This means that for small to moderate slope angles the pressure gradient force cannot be neglected as is done in some analytical slope wind models. The reaction time of the slope flow to changes in forcing is estimated to be in the range of 30 to 120 seconds, which confirms the empirically known fact that slope winds react very quickly. Received December 1, 1999 Revised June 13, 2000     

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.     

MODULATION OF WIND RIPPLES BY LONG SURFACE WAVES VIA THE AIR FLOW: A FEEDBACK MECHANISM

The evolution of a short-wave (SW) spectrum along a long wave (LW) isstudied. The evolution of the SW spectrum variation is treated in therelaxation time approximation. The variation of the SW spectrum is caused bythe LW orbital velocities and by the variation of the wind stress along thesurface of a LW. The latter is due to the distortion of the flow by a LW, andto the variation of the roughness induced by the modulated short waves. Thisintroduces a feedback mechanism: more SWs give rise to a larger roughness,which by increasing the local stress stimulates the growth of more SWs. It isshown that this aerodynamic feedback effect dominates the modulation of theSW spectrum for moderate and strong winds. The feedback mechanism is mosteffective for SWs in the gravity-capillary range, increasing its dominancewith increasing windspeed and decreasing frequency of a LW. The maximum ofthe SW amplitude modulation is situated at the crest of a LW. The results arein agreement with laboratory and field measurements of the short-wavemodulation.