Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

Fine structure of laboratory wind-wave surfaces studied using an optical method

The fine structure of laboratory wind-wave surfaces was investigated using an optical method. Several characteristic structures, closely associated with wind speed and the stage of development of the waves, are described. A parallel light, incident on the wind-wave surface, was backscattered by specular facets perpendicular to the incident angle. These specular facets, which represented the fine structures, were photographed and quantitatively analyzed by image processing techniques.For wind speeds ranging from 3.6 to 13.6 m s^–1, different types of small-scale undulations appeared: a three-dimensional rhombic structure; a train of capillary waves on the forward face with wavelengths gradually decreasing with distance from the crest, and a streaky structure on the backward face in the direction of the wind; and random and wide-spreading irregularities covering the whole wind-wave surface. The spatial scales and temporal variation of the undulations are described.     

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.     

On the analysis of wind wave-induced disturbances in the atmospheric turbulent surface layer

Simultaneous measurements of wind velocity, air humidity and sea surface wave-elevation fluctuations obtained on a platform in the open Caspian Sea are analyzed.It is shown that wave noises exist in the spectra and cospectra of the lower part of the atmospheric boundary layer, not only for the frequency of the main energy transporting component of the sea waves, but also in other parts of the spectra, at both lower and higher frequencies. The high frequencies are noncoherent with the sea waves and could be considered as measurement errors due to the existence of the waves. A method of elimination of the coherent wave noises from the spectra and cospectra is suggested and the effectiveness of its application is demonstrated.The essential difference between cases of developing and decaying wind waves is demonstrated.     

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).     

Wind-Direction Effects on Urban-Type Flows

Practically all extant work on flows over obstacle arrays, whether laboratory experiments or numerical modelling, is for cases where the oncoming wind is normal to salient faces of the obstacles. In the field, however, this is rarely the case. Here, simulations of flows at various directions over arrays of cubes representing typical urban canopy regions are presented and discussed. The computations are of both direct numerical simulation and large-eddy simulation type. Attention is concentrated on the differences in the mean flow within the canopy region arising from the different wind directions and the consequent effects on global properties such as the total surface drag, which can change very significantly—by up to a factor of three in some circumstances. It is shown that for a given Reynolds number the typical viscous forces are generally a rather larger fraction of the pressure forces (principally the drag) for non-normal than for normal wind directions and that, dependent on the surface morphology, the average flow direction deep within the canopy can be largely independent of the oncoming wind direction. Even for regular arrays of regular obstacles, a wind direction not normal to the obstacle faces can in general generate a lateral lift force (in the direction normal to the oncoming flow). The results demonstrate this and it is shown how computations in a finite domain with the oncoming flow generated by an appropriate forcing term (e.g. a pressure gradient) then lead inevitably to an oncoming wind direction aloft that is not aligned with the forcing term vector.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Models of the wave boundary layer

A general approach to model the structure of the wave boundary layer, based on the nonlinear Reynolds equations in a curvilinear system of coordinates, is described. Both spectral and numerical grid models are used. The energetic interactions between wind and wave in terms of Miles' parameter are studied. For waves outrunning or running against the wind, the range of the inverse flux of energy is found. For waves running slower than the wind, quadratic growth of is established. Vertical profiles of the wave momentum flux for different fetches are given. Following P. Janssen, a one-dimensional analytical model of the wave boundary layer is suggested. The effect of waves on the drag coefficient is analyzed.     

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.     

On Internal Gravity Waves Associated with the Stable Boundary Layer

The stable planetary boundary layer at the baseof the residual layer supports internalwaves that are unambiguously boundary layer incharacter. Some of these wavesare instabilities and some are neutrally stable modes, but they all have critical levelsin the residual layer. These waves exist for a broad range of conditions and should bea major component of any ducted disturbance that propagates within ninety degreesof the wind direction. The wave properties can be computed without the numericaldifficulties usually associated with critical-level systems.     

The KABEG’97 field experiment: An aircraft-based study of katabatic wind dynamics over the Greenland ice sheet

The aircraft-based experiment KABEG97 (Katabatic wind and boundary-layer front experiment around Greenland) was performed in April/May 1997. During the experiment, surface stations were installed at five positions on the ice sheet and in the tundra near Kangerlussuaq, West Greenland. A total of nine katabatic wind flights were performed during quite different synoptic situations and surface conditions, and low-level jets with wind speeds up to 25m s^-1 were measured under strong synoptic forcing of the katabatic wind system. The KABEG data represent a unique data set for the investigation of katabatic winds. For the first time, high-resolution and accurate aircraft measurements can be used to investigate the three-dimensional structure of the katabatic wind system for a variety of synoptic situations.Surface station data show that a pronounced daily cycle of the near-surface wind is present for almost all days due to the nighttime development of the katabatic wind. In a detailed case study the stably-stratified boundary layer over the ice and the complex boundary-layer structure in the transition zone ice/tundra are investigated. The katabatic wind system is found to extend about 10 km over the tundra area and is associated with strong wind convergence and gravity waves. The investigation of the boundary-layer dynamics using the concept of a two-layer katabatic wind model yields the results that the katabatic flow is always a shooting flow and that the pure katabatic force is the main driving mechanism for the flow regime, although a considerable influence of the large-scale synoptic forcing is found as well.     

Richardson number profiles through shear instability wave regions observed in the lower planetary boundary layer

Remote sensing of the lower planetary boundary layer in the vicinity of a meteorological tower on many occasions reveals the existence of shear instability (Kelvin-Helmholtz) waves. In general, such waves are found within shallow strata which are marked by strong thermal stability and large vertical wind shear. The independent and concurrent measurements of the vector wind and temperature, made on a 152-m high tower, allow the construction of wind and temperature profiles. From such measurements, the Richardson number profile is constructed as well as the instability regime according to Drazin's criterion. The results show that regions of shear-instability waves as depicted by the remote sensor (an acoustic sounder) agree well with Drazin's instability regime, and that within such regions the Richardson number is indeed 0.25.     

A three-dimensional numerical sensitivity study of mesoscale circulations induced by circular lakes

Summary A three-dimensional mesoscale planetary boundary layer model with theE- turbulence closure is used to simulate airflow over a lake of circular shape. A series of model sensitivity studies are performed to examine the effects of lake-land temperature difference, ambient wind magnitude and direction, lake size, surface roughness, the Coriolis force and baroclinic ambient wind conditions on mesoscale lake circulations.The lake-land temperature difference is essentially the basic energy source driving the mesoscale circulations over the lake on synoptically undisturbed days. A lake-breeze convergence zone is predicted by the model due to the differential heating between the land and the water. It is found that spatial and temporal variations of this convergence zone and associated convection are strongly controlled by the direction and the magnitude of the ambient wind. Under southeasterly and southwesterly ambient winds, the lake-breeze convergence zone and the associated convection occur primarily along up wind and lateral sides of the lake with reference to the general direction of the ambient flow. In contrast to the southeasterly and southwesterly ambient winds, the lake-breeze convergence zone and the convection are predicted all around the coastline of the lake under calm wind.The model also predicts a cloudless region over the lake in all the case studies due to divergent nature of the lake-breeze circulation. The lake size is found to have a significant effect in intensifying convection. Surface roughness over the land surface is found to be important in determining the intensity of the convection. The combined effect of the Coriolis force and the differential surface roughness between land and water appear to be the responsible mechanism for producing the asymmetric shape of the lake-breeze convergence zone around the symmetric circular lake. Finally, it was found that an initial baroclinic flow has different mesoscale lake-breeze circulation patterns as compared to an initial barotropic flow.With 16 Figures     

Field Experiments and Numerical Modeling of Wind Speed and Surface Waves in Medium-size Inland Reservoirs

An attempt is made to apply the modern methods of surface wave simulation developed for oceanic conditions to the modeling of waves in medium-size inland reservoirs (10–100 km). The results of field measurements of wind speed and waves are described, and on their basis the parameterization C _D (U ₁₀) is proposed. WAVEWATCH III spectral wave model was adapted to the conditions of a medium-size inl and reservoir. The simulated data are compared with the field data. The use of the new parameterization C _D (U ₁₀) allowed reducing the values of the wind wave growth rate that improved consistency in data from the field experiment and numerical modeling concerning the height of significant waves. Further steps towards improving the quality of prediction of the adapted WAVEWATCH III model are discussed.     

On the Role of Wind Direction in ERS SAR Signatures of Internal Waves on the Iberian Shelf

The relationship between internal wave (IW) signatures in Synthetic Aperture Radar (SAR) images and wind velocity is investigated. The effect of the wind velocity relative to the IW propagation direction on the IW signature is studied by means of a defined signature mode parameter ( S m ). S m is the parameter that quantifies the signature of the IW intensity profile in relation to the mean backscatter of the image background.

A wind contrast model based on a simple first-order Bragg scattering theory is combined with hydrodynamic modulation theory to explain the modulation of IW signatures. It takes into account the modulation of short-scale surface waves by the effect of the relative variations of wind velocity and the surface currents generated by the IWs.

It is shown that the signature mode parameter increases with the angle between the wind velocity and the IW propagation direction so that IWs propagating against the wind direction are imaged mostly as positive sign signatures, while those propagating in the wind direction are mostly negative sign signatures.     

Sea surface winds derived from cloud motion vectors over the tropical Atlantic

The relationship between satellite-derived low-level cloud motion, surface wind and geostrophic wind vectors is examined using GATE data. In the trades, surface wind speeds can be derived from cloud motion vectors by the linear relation: V = 0.62 V _s + 1.9 m s^–1 with a mean scatter of ±1.3 m s^–1. The correlation coefficient between surface and satellite wind speed is 0.25. Considering baroclinicity, i.e., the influence of the thermal wind, the correlation coefficient does not increase, because of the uncertainty of the thermal wind vectors. The ratios of surface to geostrophic wind speed and surface to satellite wind speed are 0.7 and 0.8, respectively, with a statistical uncertainty of ±0.3. Calculations of the ratio of surface to geostrophic wind speed on the basis of the resistance law yield V/V _g = 0.8 ± 0.2, in agreement with experimental results. The mean angle difference between the surface and the satellite wind vectors amounts to - 18 °, taking into account baroclinicity. This value is in good agreement with the mean ageostrophic angle - 25 °.     

Mesoscale observations of surface fronts and low pressure centres in Canadian East Coast winter storms

The movements of surface cold and warm fronts and low pressure centres have been observed in several Atlantic Canada winter storms. Statistical aspects of the well-defined surface fronts (7 warm and 6 cold) are presented. Surface wind direction change was considered as the best indicator of the boundaries of the front; frontal zone widths ranged from 23 to 144 km. Average values of wind shifts were 107° for the cold fronts and 85° for warm fronts. Several case studies are presented, based primarily on surface MesoNet data (near Halifax, Nova Scotia and on Sable Island). In two of the cold fronts, there was a two-stage surface structure and rapid evolution as the front passed over the MesoNet. In some cases, both warm and cold, the wind shift and temperature change were coincident while in others they were not. In particular we observed that wind shifts often started 20–30 min ahead of the start of a temperature decrease in these cold frontal passages. A possible mechanism for this is discussed. We found little or no evidence of along-front structure in our data although other investigators have found considerable along-front variation on scales of 0(10 km). Observations of the passage of one low pressure centre are presented. In a second case, surface temperature changes indicated an apparent low pressure centre passage through the Sable Island MesoNet but closer inspection provides an alternative interpretation.     

Temporal Evolution of Low-Level Winds Induced by Two-dimensional Mesoscale Surface Heat-Flux Heterogeneity

Using large-eddy simulation (LES), the effects of mesoscale local surface heterogeneity on the temporal evolution of low-level flows in the convective boundary layer driven by two-dimensional surface heat-flux variations are investigated at a height of about 100 m over flat terrain. The surface variations are prescribed with sinusoids of wavelength 32 km and varying amplitudes of 0, 50, 100, and 200 W m $^{-2}$ . The Weather Research and Forecasting numerical model is used as a mesoscale-domain LES model that has a grid spacing fine enough to explicitly resolve energy-containing turbulent eddies and a model domain large enough to include mesoscale circulations. Mesoscale circulations induced by the two-dimensional surface heterogeneity may undergo a flow transition and an associated spectral energy cascade, which has been found previously but only with one-dimensional surface heat-flux variations. Over a strongly heterogeneous surface prescribed with a two-dimensional sinusoid of amplitude 200 W m $^{-2}$ , the domain-averaged variance of the horizontal wind component initially grows rapidly, then undergoes a flow transition and subsequently rapidly decays. With a background wind, the induced mesoscale circulations are inhibited in the streamwise direction. However in the spanwise direction, somewhat stronger mesoscale circulations are induced, compared with those with no background wind. The background wind attenuates the significant reduction of the low-level temperature gradient by the fully-developed mesoscale horizontal flow. Spectral decomposition reveals that this rapid transition also exists in the mesoscale horizontal flows induced by the intermediate surface heterogeneity prescribed with a sinusoid of amplitude 100 W m $^{-2}$ . However the transition is masked by continuously growing turbulence.     

Atmospheric dispersion in the arctic: Winter-time boundary-layer measurements

The winter-time arctic atmospheric boundary layer was investigated with micrometeorological and SF₆ tracer measurements collected in Prudhoe Bay, Alaska. The flat, snow-covered tundra surface at this site generates a very small (0.03 cm) surface roughness. The relatively warm maritime air mass originating over the nearby, partially frozen Beaufort Sea is cooled at the tundra surface resulting in strong (4 to 30 °C · (100 m)^-1) temperature inversions with light winds and a persistent weak (1 to 2 °C · (100 m)^-1) surface inversion with wind speeds up to 17 m s^-1. The absence of any diurnal atmospheric stability pattern during the study was due to the very limited solar insolation. Vertical profiles were measured with a multi-level mast from 1 to 17 m and with a Doppler acoustic sounder from 60 to 450 m. With high wind speeds, stable layers below 17 m and above 300 m were typically separated by a layer of neutral stability. Turbulence statistics and spectra calculated at a height of 33 m are similar to measurements reported for non-arctic, open terrain sites and indicate that the production of turbulence is primarily due to wind shear. The distribution of wind direction recorded at 1 Hz was frequently non-Gaussian for 1-hr periods but was always Gaussian for 5-min periods. We also observed non-Gaussian hourly averaged crosswind concentration profiles and assume that they can be modeled by calculating sequential short-term concentrations, using the 5-min standard deviation of horizontal wind direction fluctuations () to estimate a horizontal dispersion coefficient ( _y ), and constructing hourly concentrations by averaging the short-term results. Non-Gaussian hourly crosswind distributions are not unique to the arctic and can be observed at most field sites. A weak correlation between horizontal ( _v ) and vertical ( _w ) turbulence observed for both 1-hr and 5-min periods indicates that a single stability classification method is not sufficient to determine both vertical and horizontal dispersion at this site. An estimate of the vertical dispersion coefficient, _z , could be based on or a stability classification parameter which includes vertical thermal and wind shear effects (e.g., Monin-Obukhov length, L).     

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

A recently-developed large-eddy simulation framework is validated and used to investigate turbulent flow within and above wind farms under neutral conditions. Two different layouts are considered, consisting of thirty wind turbines occupying the same total area and arranged in aligned and staggered configurations, respectively. The subgrid-scale (SGS) turbulent stress is parametrized using a tuning-free Lagrangian scale-dependent dynamic SGS model. The turbine-induced forces are modelled using two types of actuator-disk models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force based on one-dimensional momentum theory and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses blade-element momentum theory to calculate the lift and drag forces (that produce both thrust and rotation), and distributes them over the rotor disk based on the local blade and flow characteristics. Validation is performed by comparing simulation results with turbulence measurements collected with hot-wire anemometry inside and above an aligned model wind farm placed in a boundary-layer wind tunnel. In general, the ADM-R model yields improved predictions compared with the ADM-NR in the wakes of all the wind turbines, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces in the ADM-R appear to be important. Another advantage of the ADM-R model is that, unlike the ADM-NR, it does not require a priori specification of the thrust coefficient (which varies within a wind farm). Finally, comparison of simulations of flow through both aligned and staggered wind farms shows important effects of farm layout on the flow structure and wind-turbine performance. For the limited-size wind farms considered in this study, the lateral interaction between cumulated wakes is stronger in the staggered case, which results in a farm wake that is more homogeneous in the spanwise direction, thus resembling more an internal boundary layer. Inside the staggered farm, the relatively longer separation between consecutive downwind turbines allows the wakes to recover more, exposing the turbines to higher local wind speeds (leading to higher turbine efficiency) and lower turbulence intensity levels (leading to lower fatigue loads), compared with the aligned farm. Above the wind farms, the area-averaged velocity profile is found to be logarithmic, with an effective wind-farm aerodynamic roughness that is larger for the staggered case.