Models of eddy viscosity for numerical simulation of horizontally inhomogeneous,neutral surface-layer flow

Modification of a turbulent flow due to a change from a smooth to a rough surface has been studied by means of a stream function-vorticity model. Results of four models of eddy viscosity (or turbulent exchange coefficient) K _mhave been compared. The models are: (1) K _m = l²S, where l is the mixing length and S is the deformation of mean flow; (2) K _m E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) K _m lE^1/2, the so called Prandtl-Kolmogoroff approach; and (4) K _m E²/, the E — closure, where is the dissipation of turbulent kinetic energy.It is found that net-production, i.e., the difference of production and dissipation of turbulent kinetic energy counteracts the influence of mean shear on turbulent shear stress and diminishes turbulent shear stress. The reduction of mixing-length, being predicted by Model 4 only, adds to this attenuation. As a consequence, in Models 2 and 4, loss of horizontal mean momentum is concentrated close to the ground, which results in an inflexion point in the logarithmic, vertical profile of horizontal mean velocity. By contrast, in Models 1 and 3, modification of turbulent shear stress reaches larger heights causing deeper internal boundary layers. Concerning the existence of an inflexion point in U(lnz), the depth of the internal boundary layer for mean velocity, and the modification of bottom shear stress, Model 4 comes closest to experimental data.A remarkable difference of Models 1, 2, 3 and Model 4 is that only Model 4 predicts a very slow relaxation of eddy viscosity which can be attributed to the reduction of mixing-length.     

Heat transport coefficients for constant energy flux models of broad leaves

Experimental determinations of the local heat transfer by forced convection from model leaves heated by a constant energy flux were made in the laboratory under laminar and turbulent flow conditions.The results are expressed in a logarithmic dimensionless plot of the local Nusselt number, Nu _d , against the local Reynolds number, Re _d . For the laminar case, Nu _d was only a linear function of Re _d ^1/2 downwind from the leading edge regions, although this relationship departed from that predicted theoretically due to the finite size and thickness of the model. For the turbulent case, a simple relationship between Nu _d and Re _d was found over a wide range of Reynolds numbers. The enhancement of heat transfer in the turbulent case depends primarily on the scale of turbulence rather than on the turbulent intensity.Past workers have discussed their results in relation to a factor , defined as the ratio between the heat transfer predicted by the Polhausen equation, and that measured. The results suggest that is not a unique parameter and may not be useful in describing the overall turbulent transfer process.     

Rapid vertical sampling in stably stratified turbulent shear flows

A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Re_λ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Ri_g=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (E_k) grows. In case 2, Ri_g=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Ri_g=0.25 and E_k decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, L_O=(ε/N³)^1/2 and the overturn scale, L_t=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.     

Penetrative convection in rapidly rotating flows: preliminary results from numerical simulation

Turbulent convection forced by a surface heat flux into a stably stratified region is a feature of both the atmospheric and oceanic planetary boundary layers. Of particular interest is the interface between the convective layer and the stable stratification, where the entrainment of fluid into the convective layer by penetrating plumes may lead to a reverse buoyancy flux, and an enhancement of the stable stratification. Whereas in the atmosphere the influence of rotation on this penetrative convection is negligible, oceanic convection may be subjected to lower Rossby numbers and hence greater rotational influence. To isolate the effects of rotation, we present three numerical solutions for turbulent penetrative convection, characterised by different rotation rates, with all other parameters being held constant. Our results indicate that at lower Rossby numbers the lateral scale of the plumes is reduced, whereas the vertical vorticity of the plumes is much enhanced. Vertical transports of buoyancy and kinetic energy across the convective layer are reduced, leading to less efficient penetration at the interface with the stratified layer, and hence less reverse buoyancy flux in this region.     

Vertical transport of turbulent kinetic energy in the surface layer over a paddy field

Turbulent kinetic energy and its vertical flux were measured at two heights over a paddy field. The vertical transport of turbulent kinetic energy was always downward right above the paddy field and was frequently downward at higher levels within a few metres above the crop. Contributions to the downward transport arise mainly from the turbulent kinetic energy of horizontal wind velocity components. It is shown from the analysis of probability distributions that appreciable transport takes place intermittently in a few large downward bursts and that these downdrafts are efficient for downward energy transport.In the budget of turbulent kinetic energy, the flux divergence term and the energy dissipation term are the main loss terms under unstable conditions. These terms increase in magnitude with increasing instability. Buoyant production is insufficient to balance these losses. The imbalance term involving the pressure-work term is probably one of the main energy sources in unstable conditions.     

Evaluation of the Turbulent Kinetic Energy Dissipation Rate Inside Canopies by Zero- and Level-Crossing Density Methods

Inferring the vertical variation of the mean turbulent kinetic energy dissipation rate (ε) inside dense canopies remains a basic research problem to be confronted. Using detailed laser Doppler anemometry (LDA) measurements collected within a densely arrayed rod canopy, traditional and newly proposed methods to infer ε profiles are compared. The traditional methods for estimating ε at a given layer include isotropic relationships applied to the viscous dissipation scales that are resolved by LDA measurements, higher order structure function methods, and residuals of the turbulent kinetic energy budget in which production and transport terms are all independently inferred. The newly proposed method extends earlier approaches based on zero-crossing statistics, which were shown to be promising in a number of laboratory flows. The extension to account for an arbitrary threshold (hereafter referred to as the level-crossing method) instead of zero-crossing minimizes the effects of instrument noise on the inferred ε. While none of the ε methods employed here can be titled as ‘measured’, these methods differ in their underlying assumptions and simplifications. Above the canopy, where a balance between production and dissipation rate of turbulent kinetic energy is expected, the agreement among all the methods is reasonably good. In the lower-to-middle layers of the canopy, all the methods agree except for those based on a structure-function inference of ε. This departure can be attributed to the lack of a well-defined inertial subrange in these layers. In the upper canopy layers, the disagreements between the methods are largest. Even the higher order structure-function methods disagree with each other when ε is inferred from third- and fifth-order moments. However, for all layers within the canopy, the proposed zero- and threshold-crossing methods agree well with estimates of ε derived from the isotropic relationship applied to the viscous dissipation range. Finally, the advantages of introducing thresholds to minimize two types of instrument noises, additive and multiplicative, are briefly discussed.     

On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer

Velocity and temperature derivatives were obtained at a height of 4 m in the atmospheric surface layer above land. With the assumption of local isotropy, these measurements are used to obtain some statistics of the turbulent energy and scalar dissipation fields. These statistics include the variances of the logarithms of the scalar and velocity dissipation fields and the correlation between these logarithms. When used in conjunction with the hypotheses for fluctuations in turbulent dissipation rates of Obukhov and Kolmogorov, the statistics suggest that the dependence of the flatness factor of temperature derivative on the turbulent Rynolds number R is not as large as that which had been previously reported in the literature. The experimental data indicate a R ^0.5 dependence for the kurtosis of the temperature derivative and a R ^0.15 variation for the strain rate-scalar dissipation correlation.     

Molecular dissipation of turbulent fluctuations in the convective mixed layer part I: Height variations of dissipation rates

During the Limagne and Beauce experiments, the INAG-IGN Aerocommander FL 280 aircraft made extensive ‘in situ’ measurements of turbulent fluctuations in diurnally evolving convective boundary layers. In this paper, these measurements were used to investigate characteristics of the molecular dissipation of turbulent fluctuations through the mixed layer and well into the overlying stable layer. The dimensionless dissipation rates of turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance (ψ, ψ_θ, ψ _qand ψ _θq) were computed and their height variations analysed. The behaviour of the dissipation rate ψ was found to differ significantly from those observed for the other rates. In the lowest region of the mixed layer, ψ does not obey the local free convection prediction. Instead, it follows practically a relationship similar to the one established in the surface layer by Wyngaard et al. (1971). The dissipation rate ψ remains fairly constant in the bulk of the mixed layer (0.3 ≤ z/Z _i≤ 0.8) and shows a very rapid decrease above the inversion. These results confirm those reported previously from the Minnesota and Ashchurch data by Kaimal et al. (1976), Caughey and Palmer (1979), etc. The height variations for the other dissipation rates were found to obey, as expected, the (z/Z _i)^-4/3 decrease predicted under the local free convection similarity hypothesis in the lowest region of the mixed layer. This region extends to the height z/Z _i- 0.4, 0.1, and 0.3, respectively, for ψ_θ, ψ_q, and ψ_θq. Above these levels, the dissipation rates ψ_θ and ψ_q show, on average, a slight increase to reach peak-values near the mixed-layer top, while the ‘dissipation’ rate ψ _θqchanges sign from positive to negative around the height z/Z _i, - 0.7. These characteristics confirm the fact that the structures of temperature and humidity fluctuations are considerably affected by their entrainment-induced fluctuations. Therefore, an attempt has been made to non-dimensionalize the dissipation rates near the mixed-layer top with the interfacial scaling factors.     

Airborne measurements of turbulent trace gas fluxes and analysis of eddy structure in the convective boundary layer over complex terrain

Using the new high-frequency measurement equipment of the research aircraft DO 128, which is described in detail, turbulent vertical fluxes of ozone and nitric oxide have been calculated from data sampled during the ESCOMPTE program in the south of France. Based on airborne turbulence measurements, radiosonde data and surface energy balance measurements, the convective boundary layer (CBL) is examined under two different aspects. The analysis covers boundary-layer convection with respect to (i) the control of CBL depth by surface heating and synoptic scale influences, and (ii) the structure of convective plumes and their vertical transport of ozone and nitric oxides. The orographic structure of the terrain causes significant differences between planetary boundary layer (PBL) heights, which are found to exceed those of terrain height variations on average. A comparison of boundary-layer flux profiles as well as mean quantities over flat and complex terrain and also under different pollution situations and weather conditions shows relationships between vertical gradients and corresponding turbulent fluxes. Generally, NO_x transports are directed upward independent of the terrain, since primary emission sources are located near the ground. For ozone, negative fluxes are common in the lower CBL in accordance with the deposition of O₃ at the surface.The detailed structure of thermals, which largely carry out vertical transports in the boundary layer, are examined with a conditional sampling technique. Updrafts mostly contain warm, moist and NO_x loaded air, while the ozone transport by thermals alternates with the background ozone gradient. Evidence for handover processes of trace gases to the free atmosphere can be found in the case of existing gradients across the boundary-layer top. An analysis of the size of eddies suggests the possibility of some influence of the heterogeneous terrain in mountainous area on the length scales of eddies.     

The drag coefficient as determined by the dissipation method and its relation to intermittent convection in the surface layer

The influence of intermittent convection on surface-layer stress estimates during the GARP Atlantic Tropical Experiment (GATE) is described. A negative correlation between the drag coefficient (C _D) and the wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]) is found when short averaging periods are used. Well-defined, discrete events produce this negative correlation, and these events are shown to correspond to the passage of convective plumes. Constraints on averaging times necessary to obtain reasonable stress estimates using the bulk method are discussed.Conditional sampling is used to produce average values of dissipation (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae% baaaa!37AB!\[\bar \varepsilon \]), wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]), and virtual temperature (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmivayaara% WaaSbaaSqaaiaaiw8aaeqaaaaa!385B!\[\bar T_\upsilon \]) for each high turbulent intensity event, and for the quiescent periods in between. Such statistics indicate that the highly turbulent states coincide with the presence of plumes and account for the negative correlation between C _D and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]. Some of these statistics are also stability dependent.The probability distributions of the dissipation rate are bimodally log-normal which suggests that turbulence generated at two different heights is being sampled. This, along with other results of this paper, support a picture of a boundary layer which is dominated by vertical exchange.Contribution Number 409, Department of Atmospheric Sciences, University of Washington.     

The effect of orchard crop structure on the integral length-scale of turbulence

The integral length-scalesL for the three orthogonal components of diffusivityK=L are derived from spectral analysis of velocity time series measurements. A 3-D sonic anemometer was used to make these velocity measurements at heights in the range 0.7–7.0 m in and above a 2 m orchard canopy with near-neutral atmospheric boundary-layer stability conditions. The integral length-scale is compared with another length-scale of diffusionL obtained by fitting an exponential model to the auto-correlation spectrumR _E (t) in the region 0.95<R _E (t)<0.5 for smallt. This length-scale is appropriate to a high frequency region of the energy spectrum where turbulent momentum transport becomes diffusion-like and the turbulent energy varies with the inverse square of frequence. This region has been shown by others to determine the magnitude of the dissipation rate of turbulent energy by the action of viscosity even though the dominant dynamics are inviscid. Within the crop, the ratio of the length-scalesL/L were found to be smaller than the values measured above the crop for vertical turbulence. This was attributed to the enhanced decay rate of turbulent energy due to the effect of the airflow interaction with the crop. It is unclear whether similar effects are present in the horizontal plane because of greater scatter in the data, resulting from the more variable nature of the wind direction in the horizontal plane.     

Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

The relation between the turbulence Reynolds numberR and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale and the Kolmogorov length scale .     

Estimation of the Monin-Obukhov similarity functions from a spectral model

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)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c 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     

On the Kinetic Energy Budget of the Unstable Atmospheric Surface Layer

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)^1/3 rather than the friction velocity, u_*. Here k is the von Kármán constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.     

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

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

Dissipation length in stable layers

An attempt is made, for an anticyclonic stable situation in the atmospheric boundary layer during November 1978, to estimate the dissipation length. The turbulent dissipation and the turbulent kinetic energy, as measured on a 100 m high mast, exhibit large variability, due to the sporadic turbulent structure of the stable layer, and associated variability of the Richardson number. A comparison with different parameterizations of the turbulent dissipation rate allows a validation of these parameterizations.     

Molecular dissipation of turbulent fluctuations in the convective mixed layer part II: Height variations of characteristic time scales and experimental test of molecular dissipation models

Extensive turbulence measurements from the Limagne and Beauce experiments were used to compute a characteristic time scale of the turbulence field (Τ = second moment/dissipation rate) for turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance. The height variations of these time scales were analysed. The characteristic half-time scale Τ/2 of the turbulent velocity field was found, as expected, to be of the same order of magnitude as the large-eddy time scale Τ _L = Z_i/w*, showing that the turbulence structure is controlled by large eddies in the bulk of the mixed layer. The increase of Τ/2 above z/Z _i ～- 0.7 implies, however, that this time scale is no longer relevant to destruction of turbulent kinetic energy in the statically stable region with negative heat fluxes. An effective time scale Τ_eff, introduced by Zeman (1975), has been computed and its behaviour discussed. The scales for θ′ ², q′², and θ′q′ were found to be much shorter than Τ. Furthermore, a significant difference in behaviour was also revealed between the characteristic time scales of temperature and humidity fields in the stable layer. By using these experimental estimates, we tested some of the models for molecular dissipations, which are currently in use in higher order closure atmospheric boundary-layer models. The parameterized dissipation rates for θ′ ², and q′ ² agree well qualitatively with experimental estimates in the bulk of the mixed layer. In the stable layer, however, the parameterized dissipation rate ε _θ tends to become larger than the experimental ones although the parameterized dissipation rate ε _q still agrees with the experimental ones. For the molecular dissipation of θ′q′, this current model becomes physically inconsistent in the middle part of the mixed layer, because this term may become a production term for temperature-humidity covariance.     

A “large‐eddy” approach to acoustic remote sensing of turbulent kinetic energy dissipation rate ϵ

Abstract

This paper suggests that a “large‐eddy” technique may be used to determine ?, the rate of dissipation of turbulent kinetic energy per unit mass, from measurements of the largest energy‐containing scales of the turbulent velocity field. The suggestion has been examined using vertical velocity data from a narrow‐beam acoustic Doppler profiler and also direct measurements of ? (using airfoil probes) from a microscale profiler. Initial results are encouraging, rasing the possibility of simultaneously measuring space/time continuous fields of “mean” velocity, turbulent velocity and ? with near‐standard acoustic Doppler techniques.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

Scaling Properties of Temperature Spectra and Heat-Flux Cospectra in the Surface Friction Layer Beneath an Unstable Outer Layer

Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive to the CBL depth, z _i. Neither the two-peak form at slight instability nor the dependence of peak position on z _i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies have sizes that scale on SFL depth, z _s. The z _s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling factor (z_sz)^1/3e_o^2/3{(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}} divided by the square of the surface temperature flux, where e_o{\varepsilon_{\rm o}} is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature spectra are collapsed with the mixed length scale (z _i z _s)^1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z _i z _s)^1/4 z ^1/2; (4) for z/z _s < 0.03, the peak in the cospectrum is replaced by another peak at a wavenumber about a magnitude larger. This peak’s position scales on z; (5) all these findings are consistent with the observations of Smedman et al.