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1.
In this study, we evaluate four different parameterizations of the turbulent Prandtl (Schmidt) number Prt = νt/Γt where νt is the eddy viscosity and Γt is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Prt are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. no extra transport equations are required) turbulence model for νt in a one-dimensional, turbulent channel flow is considered to evaluate the behavior of the different formulations of Prt. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems such as atmospheric boundary layer flows and tidally driven estuarine flows, to quantify the behavior of each of the four formulations of Prt. We perform model-to-model comparisons to highlight which of the models of Prt allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Prt given a model for νt in stably stratified flows.  相似文献   

2.
A case study of warm air advection over the Arctic marginalsea-ice zone is presented, based on aircraft observations with direct flux measurements carriedout in early spring, 1998. A shallow atmospheric boundary layer (ABL) was observed, which wasgradually cooling with distance downwind of the ice edge. This process was mainly connected with astrong stable stratification and downward turbulent heat fluxes of about 10–20 W m-2, but wasalso due to radiative cooling. Two mesoscale models, one hydrostatic and the other non-hydrostatic,having different turbulence closures, were applied. Despite these fundamental differences betweenthe models, the results of both agreed well with the observed data. Various closure assumptions had amore crucial influence on the results than the differences between the models.Such an assumption was, for example,the parameterization of the surface roughness for momentum (z0) and heat (zT). This stronglyaffected the wind and temperature fields not only close to the surface but also within and abovethe temperature inversion layer. The best results were achieved using a formulation for z0 that took intoaccount the form drag effect of sea-ice ridges together withzT = 0.1z0. The stability within theelevated inversion strongly depended on the minimum eddy diffusivity Kmin. A simple ad hocparameterization seems applicable, where Kmin is calculated as 0.005 timesthe neutral eddy diffusivity. Although the longwave radiative cooling was largest within the ABL, theapplication of a radiation scheme was less important there than above the ABL. This was related to theinteraction of the turbulent and radiative fluxes. To reproduce the strong inversion, it wasnecessary to use vertical and horizontal resolutions higher than those applied in most regional andlarge-scale atmospheric models.  相似文献   

3.
A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than the parameterizations used in the Mellor–Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter $E - \varepsilon - {\left\langle {\theta ^{2} } \right\rangle }$ model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.  相似文献   

4.
The empirical dependence of turbulence Prandtl number (Pr) on gradient Richardson number (Ri) is presented, derived so as to avoid the effects of self-correlation from common variables. Linear power relationships between the underlying variables that constitute both Pr and Ri are derived empirically from flux and profile observations. Pr and Ri are then reconstructed from these power laws, to indicate their interdependence whilst avoiding self-correlation. Data are selected according to the stability range prior to regression, and the process is iterated from neutral to higher stability until error analysis indicates the method is no longer valid. A Butterworth function is fitted to the resulting Pr −1(Ri) regression to give an empirical summary of the analysis. The form suggests that asymptotically Pr −1 decreases as Ri 3/2. Scatter in the data increases above Ri ~ 1, however, indicating additional constraints to Pr are not captured by Ri alone in this high stability regime. The Butterworth function is analytic for all Ri > 0, and may be included in suitable boundary-layer parameterisation schemes where the turbulent diffusivity for heat is derived from the turbulent diffusivity for momentum.  相似文献   

5.
Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin–Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a ‘critical value’ of about 0.20–0.25, the inertial subrange associated with the Richardson–Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson–Kolmogorov energy cascade weakens; therefore, the applicability of local Monin–Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri cr and Rf < Rf cr. However, it is found that Rf cr  =  0.20–0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin–Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson–Kolmogorov cascade) have been filtered out.  相似文献   

6.
We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri =  0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.  相似文献   

7.
利用兰州大学半干旱气候与环境观测站(Semi-Arid Climate and Environment Observatory of Lanzhou University,简称SACOL)2008年12月观测资料,研究了稳定边界层湍流特征.使用涡动相关资料研究湍流通量时,定义湍流的平均时间τ内的中尺度运动是造成湍流统计量变化范围大的主要原因,稳定情形? τ取几十秒至几分钟.对梯度理查森数大于0.3的强稳定情形的湍流尺度分解(MRD)谱分析表明,感热通量在112.4～449.9 s存在谱隙,尺度大于谱隙的中尺度运动造成了通量观测资料离散性大,甚至有支配性影响.动量通量的谱隙在112.4～224.9 s之间.弱风时,中尺度运动的影响更大,垂直风速标准差以0.1的比率随中尺度风速变化;垂直风速标准差同广义风速表现出很好的相关性,并随着广义风速消失而消失.三维风速标准差与摩擦速度呈很好的线性关系,垂直、水平、横风风速的无量纲标准差分别为1.35、2.54、2.21.对湍流动能的研究发现,在梯度理查森数大于0.3的条件下,仍然存在连续的湍流.以湍动能为依据,分析了湍流的平稳时间长度,其长度随稳定度变化而变化,2008年12月7～11日从133.5 s变化到856.2 s,湍流平稳时间长度反映了中尺度运动的发生频率.  相似文献   

8.
We have analyzed eddy covariance data collected within open canopy to investigate the influence of non-flat terrain and wind direction shear on the canopy turbulence. The study site is located on non-flat terrain with slopes in both south-north and east-west directions. The surface elevation change is smaller than the height of roughness element such as building and tree at this site. A variety of turbulent statistics were examined as a function of wind direction in near-neutral conditions. Heterogeneous surface characteristics results in significant differences in measured turbulent statistics. Upwind trees on the flat and up-sloping terrains yield typical features of canopy turbulence while upwind elevated surface with trees yields significant wind direction shear, reduced u and w skewness, and negligible correlation between u and w. The directional dependence of turbulence statistics is due that strong wind blows more horizontally rather than following terrain, and hence combination of slope related momentum flux and canopy eddy motion decreases the magnitude of Sk w and r uw for the downslope flow while it enhances them for the upslope flow. Significant v skewness to the west indicates intermittent downdraft of northerly wind, possibly due to lateral shear of wind in the presence of significant wind direction shear. The effects of wind direction shear on turbulent statistics were also examined. The results showed that correlation coefficient between lateral velocities and vertical velocity show significant dependence on wind direction shear through change of lateral wind shear. Quadrant analysis shows increased outward interaction and reduced role of sweep motion for longitudinal momentum flux for the downslope flow. Multi-resolution analysis indicates that uw correlation shows peak at larger averaging time for the upslope flow than for the downslope flow, indicating that large eddy plays an active role in momentum transfer for the upslope flow. On the other hand, downslope flow shows larger velocity variances than other flows despite similar wind speed. These results suggest that non-flatness of terrain significantly influences on canopy-atmosphere exchange.  相似文献   

9.
Thermal Stratification Effects on Flow Over a Generic Urban Canopy   总被引：1，自引：1，他引：0  
The influence of local surface heating and cooling on flow over urban-like roughness is investigated using large-eddy simulations. By adjusting the incoming or outgoing heat flux from the ground surface, various degrees of local thermal stratification, represented by a Richardson number \((Ri_\tau )\) , were attained. Drag and heat transfer coefficients, turbulence structure, integral length scales, and the strength of quadrant events that contribute to momentum and heat fluxes were obtained and are compared with locally stable, neutral and unstable flows. With increasing \(Ri_\tau \) , or equivalently as the flow characteristics change from local thermal instability to stability, a gradual decline in the drag and heat transfer coefficients is observed. These values are found to be fairly independent of the type of thermal boundary condition (constant heat flux or constant temperature) and domain size. The maps of anisotropy invariants showed that for the values of \(Ri_\tau \) considered, turbulence structures are almost the same in shape for neutral and unstable cases but differ slightly from those in the stable case. The degree of anisotropy is found to decrease as \(Ri_\tau \) increases from \(-2\) to 2.5. Compared to the neutral case, the integral length scales are shortened in the streamwise and vertical direction by ground cooling, but enhanced in the vertical direction with ground heating. Quadrant analysis showed that an increase in floor heating increases the strength of ejections above the canopy. However, the contributions of updrafts or downdrafts to the heat flux are found not to be significantly influenced by the type of local thermal stratification for the values of \(Ri_\tau \) considered. From the octant analysis, the transport mechanisms of momentum and heat above the canopy are found to be very similar in both locally unstable and stable flows.  相似文献   

10.
Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica   总被引：2，自引：2，他引：0  
Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An $E$ E – $l_{\mathrm{m}}$ l m single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.  相似文献   

11.
Similarity Scaling Over a Steep Alpine Slope   总被引：5，自引：5，他引：0  
In this study, we investigate the validity of similarity scaling over a steep mountain slope (30–41 $^\circ $ ). The results are based on eddy-covariance data collected during the Slope Experiment near La Fouly (SELF-2010); a field campaign conducted in a narrow valley of the Swiss Alps during summer 2010. The turbulent fluxes of heat and momentum are found to vary significantly with height in the first few metres above the inclined surface. These variations exceed by an order of magnitude the well-accepted maximum 10 % required for the applicability of Monin–Obukhov similarity theory in the surface layer. This could be due to a surface layer that is too thin to be detected or to the presence of advective fluxes. It is shown that local scaling can be a useful tool in these cases when surface-layer theory breaks down. Under convective conditions and after removing the effects of self-correlation, the normalized standard deviations of slope-normal wind velocity, temperature and humidity scale relatively well with $z/\varLambda $ , where $z$ is the measurement height and $\varLambda (z)$ the local Obukhov length. However, the horizontal velocity fluctuations are not correlated with $z/\varLambda $ under all stability regimes. The non-dimensional gradients of wind velocity and temperature are also investigated. For those, the local scaling appears inappropriate, particularly at night when shallow drainage flows prevail and lead to negative wind-speed gradients close to the surface.  相似文献   

12.
The parameterization of surface heat-flux variability in urban areas relies on adequate representation of surface characteristics. Given the horizontal resolutions (e.g. $\approx $ 0.1–1 km) currently used in numerical weather prediction (NWP) models, properties of the urban surface (e.g. vegetated/built surfaces, street-canyon geometries) often have large spatial variability. Here, a new approach based on Urban Zones to characterize Energy partitioning (UZE) is tested within a NWP model (Weather Research and Forecasting model; WRF v3.2.1) for Greater London. The urban land-surface scheme is the Noah/Single-Layer Urban Canopy Model (SLUCM). Detailed surface information (horizontal resolution 1 km) in central London shows that the UZE offers better characterization of surface properties and their variability compared to default WRF-SLUCM input parameters. In situ observations of the surface energy fluxes and near-surface meteorological variables are used to select the radiation and turbulence parameterization schemes and to evaluate the land-surface scheme and choice of surface parameters. For radiative fluxes, improved performance (e.g. $>$ 25 W m $^{-2}$ root-mean-square error reduction for the net radiation) is attained with UZE parameters compared to the WRF v3.2.1 default for all three methods from the simplest to the most detailed. The UZE-based spatial fluxes reproduce a priori expectations of greater energy storage and less evaporation in the dense city centre compared to the residential surroundings. Problems in Noah/SLUCM partitioning of energy between the daytime turbulent fluxes are identified with the overestimation of the turbulent sensible heat and underestimation of the turbulent latent heat fluxes.  相似文献   

13.
Scintillometer measurements of the turbulence inner-scale length $l_\mathrm{o }$ l o and refractive index structure function $C_n^2$ C n 2 allow for the retrieval of large-scale area-averaged turbulent fluxes in the atmospheric surface layer. This retrieval involves the solution of the non-linear set of equations defined by the Monin–Obukhov similarity hypothesis. A new method that uses an analytic solution to the set of equations is presented, which leads to a stable and efficient numerical method of computation that has the potential of eliminating computational error. Mathematical expressions are derived that map out the sensitivity of the turbulent flux measurements to uncertainties in source measurements such as $l_\mathrm{o }$ l o . These sensitivity functions differ from results in the previous literature; the reasons for the differences are explored.  相似文献   

14.
The local thermal effects in the wake of a single cube with a strong heated rear face, representing a large building in an urban area, are studied using large-eddy simulations (LES) for various degrees of heating, which are characterized by the local Richardson number, $Ri$ . New wall models are implemented for momentum and temperature and comparison of the flow and thermal fields with the wind-tunnel data of Richards et al. (J Wind Eng Ind Aerodyn 94, 621–636, 2006) shows fair agreement. Buoyancy effects are quite evident at low $Ri$ and a significant increase in the turbulence levels is observed for such flows. Apart from the comparisons with experiments, further analysis included the estimation of the thermal boundary-layer thickness and heat transfer coefficient for all $Ri$ . For sufficiently strong heating, the heat transfer coefficient at the leeward face is found to be higher than the roof surface. This suggests that, beyond a certain $Ri$ value, buoyancy forces from the former surface dominate the strong streamwise convection of the latter. Quadrant analysis along the shear layer behind the cube showed that the strength of sweeps that contribute to momentum flux is considerably enhanced by heating. The contribution of different quadrants to the heat flux is found to be very different to that of the momentum flux for lower $Ri$ .  相似文献   

15.
Doppler sodar derived values of the temperature structure parameter C infT sup2 , the vertical velocity variance ¯′w 2, and the rate of dissipation of turbulent energy ?, were measured during unstable conditions above the Lannemezan heterogeneous site. The vertical profiles of these turbulent parameters, normalized by the classical convective scales are compared with those obtained using the same acoustic sounder above an homogeneous site during convective conditions. The typical decrease of C infT sup2 as Z -4/3 is partially verified on the heterogeneous site: for the lower levels, C infT sup2 exhibits an increase with Z whereas for the intermediate levels C infT sup2 . decreases as Z -4/3. For the upper levels, C infT sup2 increases with Z due to a signal-to-noise ratio lower than 1. The vertical profiles of ¯′w 2 above the two sites are rather similar. However, near the base of the convective inversion Z i , the values measured on the heterogeneous site are more scattered. The same scattering is also observed with the ? values; moreover, for the lower levels (Z<0.17Z i ) the increase of ? as Z decreases is more important at the homogeneous site than at the heterogeneous one. It is suggested that these particular features observed at lower levels above the heterogeneous site are mainly related to a complex local boundary layer induced by the near environment of the sodar (vegetation and relief).  相似文献   

16.
We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.  相似文献   

17.
We examine the influence of a modern multi-megawatt wind turbine on wind and turbulence profiles three rotor diameters ( $D$ D ) downwind of the turbine. Light detection and ranging (lidar) wind-profile observations were collected during summer 2011 in an operating wind farm in central Iowa at 20-m vertical intervals from 40 to 220 m above the surface. After a calibration period during which two lidars were operated next to each other, one lidar was located approximately $2D$ 2 D directly south of a wind turbine; the other lidar was moved approximately $3D$ 3 D north of the same wind turbine. Data from the two lidars during southerly flow conditions enabled the simultaneous capture of inflow and wake conditions. The inflow wind and turbulence profiles exhibit strong variability with atmospheric stability: daytime profiles are well-mixed with little shear and strong turbulence, while nighttime profiles exhibit minimal turbulence and considerable shear across the rotor disk region and above. Consistent with the observations available from other studies and with wind-tunnel and large-eddy simulation studies, measurable reductions in wake wind-speeds occur at heights spanning the wind turbine rotor (43–117 m), and turbulent quantities increase in the wake. In generalizing these results as a function of inflow wind speed, we find the wind-speed deficit in the wake is largest at hub height or just above, and the maximum deficit occurs when wind speeds are below the rated speed for the turbine. Similarly, the maximum enhancement of turbulence kinetic energy and turbulence intensity occurs at hub height, although observations at the top of the rotor disk do not allow assessment of turbulence in that region. The wind shear below turbine hub height (quantified here with the power-law coefficient) is found to be a useful parameter to identify whether a downwind lidar observes turbine wake or free-flow conditions. These field observations provide data for validating turbine-wake models and wind-tunnel observations, and for guiding assessments of the impacts of wakes on surface turbulent fluxes or surface temperatures downwind of turbines.  相似文献   

18.
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.  相似文献   

19.
Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the $k-\varepsilon $ k - ε turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the $k-\varepsilon $ k - ε model.  相似文献   

20.
The three turbulent velocity components, water vapour (\(\text {H}_2\text {O}\)), carbon dioxide (\(\text {CO}_{2}\)), and methane (\(\text {CH}_{4}\)) concentration fluctuations are measured above a boreal peatland and analyzed using conditional sampling and quadrant analysis. The overarching question to be addressed is to what degree lower-order cumulant expansion methods describe transport efficiency and the relative importance of ejections and sweeps to momentum, \(\text {CH}_{4}\), \(\text {CO}_{2}\) and \(\text {H}_2\text {O}\) fluxes across a range of atmospheric flow regimes. The patchy peatland surface creates distinctly different source and sink distributions for the three scalars in space and time thereby adding to the uniqueness of the set-up. The measured and modelled fractional contributions to the momentum flux show that sweep events dominate over ejections in agreement with prior studies conducted in the roughness sublayer. For scalar fluxes, ejections dominate the turbulent fluxes over sweeps. While ejective motions persist longer for momentum transport, sweeping events persist longer for all three scalars. Third-order cumulant expansions describe many of the results detailed above, and the results are surprising given the highly non-Gaussian distribution of \(\text {CH}_{4}\) turbulent fluctuations. Connections between the asymmetric contributions of sweeps and ejections and the flux-transport term arising in scalar turbulent-flux-budget closure are derived and shown to agree reasonably well with measurements. The proposed model derived here is much simpler than prior structural models used to describe laboratory experiments. Implications of such asymmetric contributions on, (i) the usage of the now proliferating relaxed-eddy-accumulation method in turbulent flux measurements, (ii) the constant-flux assumption, and (iii) gradient-diffusion closure models are presented.  相似文献   

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