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1.
The second of two experimental studies of the TKE budget conducted on sites of different roughness is described, and results are compared. The first took place within a shallow layer above a small field of mostly bare, cultivated soil; the second was carried out above a roughness sublayer of significant depth on an extensive plain of tall dry grass. Budget terms observed in the second study were scaled with a modified u which compensated for effects of an unusually large stress gradient and ensured that the m functions would be collinear. By showing that the modification becomes negligible in smaller gradients, it is demonstrated that in normal conditions, budgets observed above significant roughness sublayers should be normalized by scaling in terms of the unreduced Reynolds stress at the sublayer's upper surface. This procedure is shown to be consistent with the expectation that TKE budgets in layers near the surface all scale in fundamentally the same way.Other findings include: (1) the fact that most m functions previously reported are not quite collinear is attributed to a type of overspeeding known to affect three-cup anemometers; (2) revised m functions, collinear and largely free of the effects of overspeeding, are determined from a well-established characteristic of the linear m relation for the stable case; (3) data that define collinear m functions can also be represented with single hyperbolic curves; (4) dissipation is found to be 10 to 15% too small to balance total TKE production in unstable and neutral conditions and to decrease with increasing z/L in thestable regime; and (5) new relations for based on the observed behaviour of the dissipation deficit provide an improved closure for the set of equations that express the budget terms as functions of m and z/L.  相似文献   

2.
A numerical model of airflow above changes in surface roughness and thermal conditions is extended to include cases with stable thermal stratification within the internal boundary-layer. The model uses a mixing-length approach with empirical forms for M and H.Results are presented for some basic cases and an attempt is then made to compare results given by the model with the experimental results of Rider, Philip and Bradley. Tolerable agreement is achieved. The importance of roughness change and thermal stability effects in the diffusion of heat and moisture near a leading edge is emphasised.Notation A Refers to Taylor (1970) - B Businger-Dyer constant (= 16.0) in forms for M and H - C Constant in form for in stable case - c p Specific heat at constant pressure - E Scaled absolute humidity - g Acceleration due to gravity - H Upward vertical heat flux - H 0, H 1 Surface heat fluxes for x <0, x0 - H E Upward latent heat flux - k Von Kármán's constant (= 0.4) - K H K W Eddy transfer coefficients for heat and water vapour - L Monin-Obukhov length - L H Latent heat of evaporation for water - m Ratio of roughness lengths ( = z 1/z 0) - RPB Refers to Rider et al. (1964) - RL* Non-dimensional parameter (see Equations (9), (20a), (22a), (24a)) - R* Net radiation less ground heat flux (see Equations (15), (16)) - T Scaled temperature - T 1 Downstream scaled surface temperature - u 0 u 1(x) Surface friction velocities for x <0, x0 - U, W Horizontal and vertical mean velocities - x, z Horizontal and vertical co-ordinates - Z i Local roughness length - z 0, z i Roughness lengths for x < 0, x 0 - Temperature - 0, 1 Surface temperatures for x<0, x0 - E Non-dimensional absolute humidity gradient - H Non-dimensional temperature gradient of heat flux - M Non-dimensional wind shear - = M = H = E an assumption used in stable conditions - Air density - Absolute humidity - w Density of water - Kinematic shear stress - Logarithmic height scale (= ln(z+z 1)/z 1)  相似文献   

3.
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4.
Turbulence measurements performed in a stable boundary layer over the sloping ice surface of the Vatnajökull in Iceland are described. The boundary layer, in which katabatic forces are stronger than the large-scale forces, has a structure that closely resembles that of a stable boundary layer overlying a flat land surface, although there are some important differences. In order to compare the two situations the set-up of the instruments on an ice cap in Iceland was reproduced on a flat grass surface at Cabauw, the Netherlands. Wind speed and temperature gradients were calculated and combined with flux measurements made with a sonic anemometer in order to obtain the local stability functions m and h as a function of the local stability parameter z/L. Unlike the situation at Cabauw, where m was linear as a function of z/L, in the katabatically forced boundary layer, the dependence of m on stability was found to be non-linear and related to the height of the wind maximum. Thermal stratification and the depth of the stable boundary layer however seem to be rather similar under these two different forcing conditions.Furthermore, measurements on the ice were used to construct the energy balance. These showed good agreement between observed melt and components contributing to the energy balance: net radiation (supplying 55% of the energy), sensible heat flux (30%) and latent heat flux (15%).Local sources and sinks in the turbulent kinetic energy budget are summed and indicate a reasonable balance in near-neutral conditions but not in more stable situations. The standard deviation of the velocity fluctuations u, v, and w, can be scaled satisfactorily with the local friction velocity u* and the standard deviation of the temperature fluctuation with the local temperature scale *.  相似文献   

5.
Turbulence mechanisms at an agricultural site   总被引：8，自引：0，他引：8  
An extensive set of turbulence data from the 3- and 12-m heights taken over an agricultural site (Marsta, Sweden) are analyzed and compared with data from ideal sites.In unstable air, Monin-Obukhov similarity is found to be valid for the non-dimensional gradients of wind, m , temperature, h , and humidity, e , for (only a few data), for T /|T *|,/ E /|E *| and for the non-dimensionalized inertial subrange spectra of temperature and humidity. Where comparison is possible, the unstable data also agree with those found in the Kansas study, with one remarkable exception, the inertial subrange constant of the temperature spectrum, 1, being only 0.39, compared to the value 0.80 found at the Kansas site.On the stable side, most similarity predictions break down, with most of the data differing systematically from the corresponding Kansas results, the only exception being . The inertial subrange constants for temperature, 1, and for humidity, 1 are found to have the same values, 0.39 and 0.30, respectively, as they do on the unstable side. Remarkable similarity is found for the shape of the stable u- and - and e-spectra. In addition, this shape is found to be identical with that found in Kansas. The peak wavelength of the stable u-, and -spectra is found to be about four times larger than it is for the corresponding Kansas spectra. This is interpreted to be a result of the increased macro-roughness at the Marsta site as compared with that at the Kansas site. A possible explanation for the low 1-value is discussed, suggesting that 1 is not a universal constant, but instead dependent on the turbulent structure.  相似文献   

6.
From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - Ci constants i=u, v, w, (see Equation (5) - kme,kmT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - kmi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - ksb, kc characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - m nondimensional mean shear - H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - D nondimensional divergence of vertical transports of turbulent linetic energy  相似文献   

7.
Summary Interannual modes are described in terms of three-month running mean anomaly winds (u,v), outgoing longwave radiation (OLR), and sea surface temperature (T * ). Normal atmospheric monsoon circulations are defined by long-term average winds (u n,v n) computed every month from January to December. Daily winds are grouped into three frequency bands, i.e., 30–60 day filtered winds (u L,v L); 7–20 day filtered winds (u M,v M); and 2–6 day filtered winds (u S,v S). Three-month running mean anomaly kinetic energy (signified asK L , K M , andK S , respectively) is then introduced as a measure of interannual variation of equatorial disturbance activity. Interestingly, all of theseK L , K M , andK S perturbations propagate slowly eastward with same phase speed (0.3 ms–1) as ENSO modes. Associated with this eastward propagation is a positive (negative) correlation between interannual disturbance activity (K L , K M , K S ) and interannualu (OLR) modes. Namely, (K L , K M , K S ) becomes more pronounced than usual nearly simultaneously with the arrival of westerlyu and negativeOLR (above normal convection) perturbutions. In these disturbed areas with (K L , K M , K S >0), upper ocean mixing tends to increase, resulting in decreased sea surface temperature, i.e.T * 0. Thus, groups (not individual) of equatorial disturbances appear to play an important role in determiningT * variations on interannual time scales. HighestT * occurs about 3 months prior to the lowestOLR (convection) due primarily to radiational effects. This favors the eastward propagation of ENSO modes. The interannualT * variations are also controlled by the prevailing monsoonal zonal windsu n, as well as the zonal advection of sea surface temperature on interannual time scales. Over the central Pacific, all of the above mentioned physical processes contribute to the intensification of eastward propagating ENSO modes. Over the Indian Ocean, on the other hand, some of the physical processes become insignificant, or even compensated for by other processes. This results in less pronounced ENSO modes over the Indian Ocean.With 10 FiguresContribution No. 89-6, Department of Meteorology, University of Hawaii, Honolulu, Hawaii.  相似文献   

8.
Surface-Layer Fluxes in Stable Conditions   总被引：2，自引：2，他引：0  
Micrometeorological tower data from the Microfronts experiment are analyzed. Scale-dependencies of the flux and flux sampling error are combined to automatically determine Reynolds turbulence cut-off time scales for computing fluxes from time series. The computed downward heat flux at the 3 m height averaged over nine nights with 7.3 hours each night is 20% greater than the downward heat flux computed at the 10 m height. In contrast, there is only a 1.2% difference between 3 m and 10 m heat fluxes averaged over daytime periods, and there is less than a 2% difference between 3 m and 10 m momentum fluxes whether averaged over nighttime or daytime periods.Stability functions, M(z/L) and H(z/L) are extended to z/L up to 10, where z is the observational height and L is the Obukhov length. For 0.01 < z/L < 1 the estimated functions generally agree with Businger-Dyer formulations, though the H estimates include more scatter compared to the M estimates. For 1 < z/L < 10, the flux intermittency increases, the flux Richardson number exceeds 0.2, and the number of flux samples decreases. Nonetheless the estimates of the stability function M based on 3-m fluxes are closer to the formula proposed by Beljaars and Holtslag in 1991 while the M functions based on 10-m fluxes appears to be closer to the formula proposed by Businger et al. in 1971. The stability function H levels off at z/L = 0.5.  相似文献   

9.
Analytical solutions for the Ekman layer   总被引：1，自引：0，他引：1  
The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U *z (0.4,U *=friction velocity,z=elevation) to the geostrophic asymptoteK GU *d forzd is solved through an expansion in fd/U *1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU *d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U *d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U * (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U * and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U *d[1–exp(–z/d)] are developed in appendices.  相似文献   

10.
E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c 2 /e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c 2 = 1.92, = 1.3, e = 1). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and e to 1.1 and 1.6, respectively, giving, with c 2 = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.  相似文献   

11.
Effect of finite sampling on atmospheric spectra   总被引：2，自引：0，他引：2  
The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1 – sinc2f T), valid for variances, is a reasonable approximation for power spectra only when T 10 m , where f is the cyclic frequency, and m is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to m , indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f > 1/T) than predicted by (1 – sinc2f T). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f 1/T.  相似文献   

12.
The extension of Lagrangian similarity theory of diffusion to stratified flow is examined, to improve its prediction of the vertical spread of a passive substance. In the basic equation, where is the average height of a cluster of particles,u * is the friction velocity andL is Monin-Obukhov length. It is shown theoretically, under the assumption of an equivalence between the diffusivities of heat and matter, that the unspecified function is the reciprocal of a more familiar meteorological parameter n , the dimensionless temperature gradient. The universal constantb is found to be approximately equal to von Karman's constant for various stability conditions. The predicted effect of stability on vertical spread shows excellent agreement with that of the published data from the O'Neill experiments.  相似文献   

13.
Summary The effect of the Alpine orography on prototype cold fronts approaching from the west is investigated by three-dimensional numerical model simulations. The numerical experiments cover a range of parameter constellations which govern the prefrontal environment of the front. Especially, the appearance and intensity of prefrontal northern Alpine foehn varies from case to case.The behaviour of a cold front north of the Alps depends much on the prefrontal condition it encounters. It is found that prefrontal foehn can either accelerate or retard the approaching front.An important feature is the pressure depression along the northern Alpine rim that results from the southerly foehn flow. In cases where this depression compensates the eastward directed pressure gradient associated with the largescale flow, the front tends to accelerate and the foehn breaks down as soon as the front passes. In contrast, the foehn prevents the front from a rapid eastward propagation if it is connected with a strong southerly wind component.No-foehn experiments are performed for comparison, where either the mountains are removed, or the static stability is set to neutral. Also shown are effects of different crossfrontal temperature contrasts.List of Symbols c F propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - z vertical grid spacing (cartesian system) - cross-frontal potential temperature difference - i potential temperature step at an inversion - E turbulent kinetic energy - f Coriolis parameter - FGP frontogenesis parameter (see section 2.2) - g gravity acceleration (g=9.81 m s–2) - vertical gradient of potential temperature - h terrain elevation (above MSL) - h i height of an inversion (h i =1000 m MSL) - H height of model lid (H=9000 m MSL) - K M exchange coefficient of momentum - K H exchange coefficient of heat and moisture - longitude - N Brunt-Väisäla-frequency - p pressure - Exner function (=T/) - latitude - q v specific humidity - R d gas constant of dry air (R d =287.06 J kg–1 K–1) - density of dry air - t time - T temperature - potential temperature - TFP thermal front parameter (see section 2.2) - u, v, w cartesian wind components - u g ,v g geostrophic wind components - horizontal wind vector - x, y, z cartesian coordinates Abbreviations GND (above) ground level - MSL (above) mean sea level - UTC universal time coordinated With 20 Figures  相似文献   

14.
Summary The integral aerosol optical depths (k ) at the hour of 08:20 Local Standard Time (LST), are compared with those calculated previously at 11:20 and 14:20 LST, for clear days during summer in Athens over the period 1962–1988. The mean values at 08:20 LST were consistently lower than the values at 11:20 and 14:20 LST. The influence of the vertical wind profile on the values ofk was also investigated. A comparison was made of the wind profiles at 02:00 and 14:00 LST, for days in which the 11:20 and 14:20 LST values ofk were 0.200 andk 0.350, respectively. The corresponding bulk wind shear s was also found for the period 1980–1988. The most significant results occurred with the first category of days. The resultant wind velocities from the surface to the 900 hPa level, in each hour were higher by 2–4 m·s–1 with respect to the corresponding values for the second category. At 02:00 LST the bulk wind shear showed a considerable difference (1.8) between the two categories of days in the surface to 700 hPa layer at 02:00 LST. Finally, the associated weather conditions that appear to initiate a period of low values ofk (k 0.200) at 11:20 and 14:20 LST were examined for the period 1980–1988. Fifteen such cases were identified and it was found that they all occurred after the passage of weak cold fronts.With 6 Figures  相似文献   

15.
Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely m = 1+ 5.8 and h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.  相似文献   

16.
This paper considers the near-field dispersion of an ensemble of tracer particles released instantaneously from an elevated source into an adiabatic surface layer. By modelling the Lagrangian vertical velocity as a Markov process which obeys the Langevin equation, we show analytically that the mean vertical drift velocity w(t) is w()=bu *(1–e –(1+)), where is time since release (nondimensionalized with the Lagrangian time scale at the source), b Batchelor's constant, and u *, the friction velocity. Hence, the mean height and mean depth of the ensemble are calculated. Although the derivation is formally valid only when 1, the predictions for w, mean height and mean depth are consistent in the downstream limit ( 1) with surface-layer Lagrangian similarity theory and with the diffusion equation. By comparing the analytical predictions with numerical, randomflight solutions of the Langevin equation, the analytical predictions are shown to be good approximations at all times, both near-field and far-field.  相似文献   

17.
The effect of changes in zonal and meridional atmospheric moisture transports on Atlantic overturning is investigated. Zonal transports are considered in terms of net moisture export from the Atlantic sector. Meridional transports are related to the vigour of the global hydrological cycle. The equilibrium thermohaline circulation (THC) simulated with an efficient climate model is strongly dependent on two key parameters that control these transports: an anomaly in the specified Atlantic–Pacific moisture flux (Fa) and atmospheric moisture diffusivity (Kq). In a large ensemble of spinup experiments, the values of Fa and Kq are varied by small increments across wide ranges, to identify sharp transitions of equilibrium THC strength in a 2-parameter space (between Conveyor On and Off states). Final states from this ensemble of simulations are then used as the initial states for further such ensembles. Large differences in THC strength between ensembles, for identical combinations of Fa and Kq, reveal the co-existence of two stable THC states (Conveyor On and Off)—i.e. a bistable regime. In further sensitivity experiments, the model is forced with small, temporary freshwater perturbations to the mid-latitude North Atlantic, to establish the minimum perturbation necessary for irreversible THC collapse in this bistable regime. A threshold is identified in terms of the forcing duration required. The model THC, in a Conveyor On state, irreversibly collapses to a Conveyor Off state under additional freshwater forcing of just 0.1 Sv applied for around 100 years. The irreversible collapse is primarily due to a positive feedback associated with suppressed convection and reduced surface heat loss in the sinking region. Increased atmosphere-to-ocean freshwater flux, under a collapsed Conveyor, plays a secondary role.  相似文献   

18.
Summary The influence of agricultural management on the CO2 budget of a typical subalpine grassland was investigated at the Swiss CARBOMONT site at Rigi-Seebodenalp (1025m a.s.l.) in Central Switzerland. Eddy covariance flux measurements obtained during the first growing season from the mid of spring until the first snow fall (17 Mai to 25 September 2002) are reported. With respect to the 10-year average 1992–2001, we found that this growing season had started 10 days earlier than normal, but was close to average temperature with above-normal precipitation (100–255% depending on month). Using a footprint model we found that a simple approach using wind direction sectors was adequate to classify our CO2 fluxes as being controlled by either meadow or pasture. Two significantly different light response curves could be determined: one for periods with external interventions (grass cutting, cattle grazing) and the other for periods without external interventions. Other than this, meadow and pasture were similar, with a net carbon gain of –128±17g Cm–2 on the undisturbed meadow, and a net carbon loss of 79±17g Cm–2 on the managed meadow, and 270±24g Cm–2 on the pasture during 131 days of the growing season, respectively. The grass cut in June reduced the gross CO2 uptake of the meadow by 50±2% until regrowth of the vegetation. Cattle grazing reduced gross uptake over the whole vegetation period (37±2%), but left respiration at a similar level as observed in the meadow.  相似文献   

19.
A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u 2 and w 2 increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.  相似文献   

20.
A Random Displacement Model (RDM) and a Langevin Equation Model (LEM) are used to simulate point releases in a complex flow around a building. The flow field is generated by a three-dimensional finite element model that uses the standardk- model to parameterize the turbulence. The RDM- and LEM-calculated concentration fields are compared, with particular emphasis on the structure in regions with high turbulence and/or recirculation. RDM and LEM results are similar qualitatively, but RDM tends to predict lower concentration levels. In part this is due to the higher early-time diffusion. However, the expected convergence at later times is prevented by the interaction of the diffusion with the strongly inhomogeneous mean flow.Notation a i coefficient in the Langevin equation - b ij coefficient in the Langevin equation - C 0 the universal constant associated with the Lagrangian structure function - H building height (22.5 m) - K eddy viscosity - K k eddy viscosity used in the definition of the off-diagonal Reynolds stresses - k turbulent kinetic energy - LEM Langevin Equation Model - p 1 local unit vector in thexy-plane, orthogonal tos - p 2 local unit vector, orthogonal to boths andp 1 - RDM Random Displacement Model - s local unit vector in the streamline direction - T local decorrelation time (Lagrangian time scale) - U magnitude of the local Eulerian mean wind velocity - u s total velocity in the streamline direction - u 1 velocity component in thexy-plane, orthogonal to the streamline direction - u 2 velocity component orthogonal to bothu s andu 1 - i mean Eulerian wind velocity - W i stochastic vector-valued Wiener process - x unit vector inx-direction - y unit vector iny-direction - z unit vector inz-direction - angle between thexy-plane and the mean wind streamline - angle between the projection in thexy-plane of the streamline and thex-axis - ij the Kronecker delta function - rate of turbulence dissipation - i/ga the part ofa i that contains mean wind and turbulence gradients - ij inverse of a Reynolds stress tensor component - ij shorthand for a quantity that defines a part of i/ga - i shorthand for a quantity that defines a part of i/ga - ij Reynolds stress tensor component  相似文献   

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