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.     

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.     

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.     

Visualization of airflow separation over wind-wave crests under moderate wind

An intermittently-smoking smoke-wire was devised to visualize the airflow structure over individual crests of actual wind waves. The device was used under a moderate wind 6 m s^-1 (maximum speed in the vertical cross-section) at a fetch 3.8 m in a wind-wave tunnel. Airflow patterns with separation were clearly visualized over wind-wave crests which were not accompanied by wave breaking characterized by air entrainment. A classification of 41 samples of airflow structures showed that two distinct patterns (with and without separation) exist, with significant frequency of occurrence for each.     

Boundary-layer effects on mountain waves: a new look at some historical studies

Early studies of mountain waves reported various results that have rarely been investigated since. These include: large-amplitude mountain waves above an unstable boundary layer much higher than the mountains; a repeated downwind drift and upwind jump of mountain waves; and larger vertical wind magnitude near sunrise and/or sunset. These are investigated using over 3,000 radiosondes and meso-strato-troposphere (MST) radar. Superadiabatic temperature gradients are found beneath mountain waves, explainable by convection which appears to raise the mountain-wave launching height. Movement of mountain-wave patterns is studied by a new method using height–time vertical wind data. A swaying motion of mountain waves, with period of a few minutes, appears to be equally upwind and downwind, rather than asymmetric at the heights measurable. Also, vertical wind shows no change in mean, variance or extreme values near sunrise and sunset, despite the expected diurnal changes of boundary-layer structure. An explanation for differences between MST radar and other measurements and models of mountain waves is suggested in terms of more than one variety of mountain wave. Type 1 has stable air near the ground; type 2 is above a convective/turbulent boundary layer of significant height as compared to the mountains.     

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.     

Measurements of Flows Over Isolated Valleys

Wind-tunnel measurements of the flow over an isolated valley both normal and at an angle (45°) to a simulated neutrally stable atmospheric boundary layer are presented. Attention is concentrated on the nature of the flow within the valley itself. The work formed part of a wider study that included detailed field measurements around an African desert valley and some limited comparisons with that work are included. A scale of about 1:1000 was used for the laboratory work, in which an appropriate combination of hot wire and particle image velocimetry was employed. For a valley normal to the upwind flow, it is shown that the upstream influence of the valley extends to a distance of at least one half of the axial valley width upstream of the leading edge, whereas differences in mean flow and turbulence could be identified well beyond two valley widths from the downwind edge. Non-normal wind angles lead to significant along-valley flows within the valley and, even at two valley heights above the valley ridge level, there remains a significant spanwise flow component. Downwind turbulence levels are somewhat lower in this case, but are still considerably higher than in the undisturbed boundary layer. At both flow angles, there are significant recirculation regions within the valleys, starting from mean separation just beyond the leading edge, but the strong spanwise flow in the 45° case reduces the axial extent of the separated zone. The flow is shown to be in some ways analogous to flow over an isolated hill. Our results usefully enhance the field data and could be used to improve modelling of saltation processes in the field.     

Deep and shallow south foehn in the region of Innsbruck: Typical features and semi-idelized numerical simulations

Summary ?Numerical simulations of the south foehn in the region of Innsbruck are presented. They are semi-idealized in the sense that realistic orography but idealized initial and boundary conditions are used. The focus of this study is on typical features of the fully developed foehn, the breakthrough phase of the foehn and the diurnal cycle of the foehn. In addition, the impact of the large-scale wind direction is examined, including conditions leading to shallow foehn. The simulated flow fields have been found to be in very good agreement with observations except for a few minor details. In the lower part of the Sill Valley (the valley going from the Brenner pass down to Innsbruck), the wind speed is significantly higher than in the upper part. The acceleration can be traced back to the three-dimensional propagation of gravity waves excited over the adjacent mountain ridges. The amplitude of the gravity waves over the various mountain ridges depends sensitively on the wind direction, large wave amplitudes occurring only when the angle between the wind direction and the ridge line is not too small. For southwesterly or south–southwesterly large-scale flow, wave amplitudes are significantly larger to the east of Innsbruck than to the west. Foehn breakthrough at Innsbruck is usually preceded by a moderate westerly (downvalley) wind that is restricted to a rather small area around Innsbruck. The simulations reveal that this so-called pre-foehn is mainly a consequence of the gravity wave asymmetry, producing an asymmetric pressure perturbation with lower pressure to the east of Innsbruck. Shallow foehn, defined as a foehn occurring when the large-scale flow at crest height (700 hPa) is approximately westerly, is associated with relatively weak wave activity along the Sill Valley. It is found that at least a weak southerly wind component below crest height is necessary to maintain a significant shallow foehn over a longer time. Received October 10, 2001; accepted June 20, 2002 Published online: February 20, 2003     

Observations of Boundary-Layer Wind-Tunnel Flow over Isolated Ridges of Varying Steepness and Roughness

Boundary-layer wind-tunnel flow is measured over isolated ridges of varyingsteepness and roughness. The steepness/roughness parameter space is chosento produce flows that range from fully attached to strongly separated. Measurementsshow that maximum speedup at the hill crest is significantly lower than predictedby linear theory and that recovery in the lee of the hill is much slower for stronglyseparated flow over steep terrain. The measurements also show that behaviour ofthe mean and turbulent components of the flow on the downwind side of the ridgeis fundamentally different between separated and non-separated flows. This suggeststhe dominance of much increased turbulence time and length scales in the lee of thehill in association with a production mechanism that scales with the hill length ratherthan the proximity to the surface as on the windward side of the hill crest.     

三层模式中风场对背风波的影响

为了研究风场对背风波的影响,针对边界层附近为弱稳定层结的背风波,建立了一个三维三层的理论模型和线性计算模式,分析了各层中风速和风向的变化对背风波特征的影响,揭示了气流过孤立山脉产生背风波的有利风场条件。结果表明：背风波的波长、振幅等特征对各层风速和风向的变化具有相当的敏感性,波长随着低、高层风速的增大而增大,随着中层风速的增大先减小后增大;振幅随着低、中层风速的增大先增大后减小,随着高层风速的增大而增大。此外,风速和上下层风向切变的增大均使背风波的形态逐渐由横波型转为辐散型,但是上下层风向的切变对背风波形态的影响比风速更为显著。     

Flow dynamics in a trough blowout

The dynamics and geomorphological development of a trough blowout located at Fiona Beach in the Myall Lakes National Park in NSW, Australia are examined. Wind velocities and flow structure were measured utilising an array of miniature Rimco cup anemometers, Gill bi-vane and UVW instruments, and wind vanes. Flow measurements indicate that when the wind approaches the trough blowout parallel to the throat orientation, jets occur both in the deflation basin and along the erosional walls, relative flow deceleration and expansion occur up the depositional lobe, jets are formed over the depositional lobe crest accompanied by downwind flow separation on the leeward side of the lobe, and flow separation and the formation of corkscrew vortices occur over the crests of the erosional walls. Maximum erosion and transport occur up the deflation basin and onto the depositional lobe. Trough blowout morphologies are explained as a function of these flow patterns.When the wind approaches the blowout obliquely, the flow is steered considerably within the blowout. The degree and complexity of topographic steering is dependent on the blowout topography. The flow is usually extremely turbulent and large corkscrew vortices are common. The local topography of a blowout can be very important in determining flow patterns, overall sand transport and blowout evolutionary conditions and paths.Estimates of potential sand transport within the blowout may be up to two orders of magnitude lower than actual rates if remote wind data are used.     

新疆克拉玛依强下坡风暴的机理研究

利用美国中尺度数值模式 WRF 对2013年3月7—8日克拉玛依强风进行了模拟,对下坡风发生、发展和结束3个阶段的三维结构特征进行了分析,并由此提出克拉玛依强下坡风的形成机制模型：上游地区出现中高层西南风、低层西北风并伴有强冷平流的配置,当风速不断增大时,气流能够翻越加依尔山在背风坡侧形成重力波,重力波相位向气流上游方向倾斜产生非线性效应,促进了波不稳定区域的形成并导致波破碎,形成湍流活跃层,不断把上层的能量向下传播;克拉玛依中低层形成三层夹心的大气层结稳定度分布,出现明显的过渡气流带从而导致强下坡风的形成;南北风分量在低层和中层符号相反,形成了临界层,不断吸收上层波能量并向地面传送,强下坡风暴不断维持发展。最后利用2006—2012年克拉玛依33个强下坡风过程中的探空观测资料对提出的形成机制进行了验证。     

The turbulent wind flow over an embankment

Under neutral conditions and with low winds, profiles of mean and turbulent wind components have been measured at various points across an embankment with aspect ratio 0.3. These measurements have been compared with and related to those of undisturbed flow in a horizontal homogeneous area on the windward side. The speed-up ratio, the turbulent and mean kinetic energy and the turbulent shear stress are examined. It is found that the flow stagnates on the windward side, accelerates above the crest, and separates behind the crest. The results show a remarkable dependence on the angle of attack. With an angle smaller than 90 °, the influence of the embankment on the mean wind field is reduced but is increased on the turbulent part, as lateral gustiness components are amplified. With the incoming flow normal to the embankment, maximum turbulence is found on the top of the ridge near the surface but at greater heights farther downwind. The same is true for the shear stress, but only for oblique flow, whereas for normal flow a minimum is found above the crest and a maximum on the windward side. Therefore, with varying angle of attack the embankment acts in different ways on mean wind, turbulent kinetic energy, and turbulent stress. Although the winds were low, all effects are clearly evident in the data.     

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.     

Numerical analysis of flux footprints for different landscapes

Summary A model for the canopy – planetary boundary layer flow and scalar transport based on E- closure was applied to estimate footprint for CO₂ fluxes over different inhomogeneous landscapes. Hypothetical heterogeneous vegetation patterns – forest with clear-cuts as well as hypothetical heterogeneous relief – a bell-shaped valley and a ridge covered by forest were considered. The distortions of airflow caused by these heterogeneities are shown – the upwind deceleration of the flow at the ridge foot and above valley, acceleration at the crest and the flow separation with the reversed flow pattern at lee slopes of ridge and valley. The disturbances induce changes in scalar flux fields within the atmospheric surface layer comparing to fluxes for homogeneous conditions: at a fixed height the fluxes vary as a function of distance to disturbance. Correspondingly, the flux footprint estimated from model data depends on the location of the point of interest (flux measurement point) and may significantly deviate from that for a flat terrain. It is shown that proposed method could be used for the choice of optimal sensor position for flux measurements over complex terrain as well as for the interpretation of data for existing measurement sites. To illustrate the latter the method was applied for experimental site in Solling, Germany, taking into account the complex topography and vegetation heterogeneities. Results show that in certain situations (summer, neutral stratification, south or north wind) and for a certain sensor location the assumptions of idealized air flow structure could be used for measurement interpretation at this site, though in general, extreme caution should be applied when analytical footprint models are used in the interpretation of flux measurements over complex sites.     

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.     

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.     

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.     

Note on the Growth Rate of Water Waves Propagating at an Arbitrary Angle to the Wind

The dependence of the turbulent airflow over water waves on the angle,, between mean wind and wavedirections is investigated. To this end,an existing semi-analytical model is extended. In this model, the main simplification of the problem is obtained by using the well-established divisionof the wave boundary layer into inner and outer regions for modelling turbulence. The effect of waves on turbulence is restricted to the thin inner region. Simulations show that the influence of the wind speed component transverse to the wave direction on the air flow, and hence on the growth rate of the waves, is small. This is confirmed by calculations with a numerical model that solves the full Reynolds equations using a second-order turbulence closure scheme. The growth rate of slowly moving waves (as compared to the wind speed) is then proportional to cos², whereas, for faster waves, it has a narrower angular distribution.