Turbulence Characteristics of the Stable Boundary Layer Over a Mid-Latitude Glacier. Part I: A Combination of Katabatic and Large-Scale Forcing

Profile and eddy-correlation (heights of 4 and 10 m) measurements performed on the Pasterze glacier (Austria) are used to study the characteristics of the stable boundary layer under conditions of katabatic and large-scale forcing. We consider cases where large-scale forcing results in a downslope (or following) ambient wind. The analysis of averaged spectra and cospectra reveals low frequency perturbations that have a large influence on the variances of temperature and horizontal wind components and also alter the cospectra of momentum and sensible heat flux. Only the spectrum of the vertical wind speed is comparable to universal spectra. The low frequency perturbations occur as brief intermittent events and result in downward entrainment of ambient air thereby producing enhanced downward sensible heat fluxes and downward as well as upward momentum fluxes with various magnitudes and timescales. After the variances were high pass filtered, the normalised standard deviations of wind speed and temperature compare favourably to findings in the literature within the range 0>z/L>0.5. For larger z/L they deviate as a result of an increased influence from low frequency perturbations and thus non-stationarity. In line with this, the turbulent kinetic energy budget (at 4 m height) indicates that production (shear) is in balance with destruction (buoyancy and dissipation) within the range 0>z/L>0.3. Non-dimensional gradients of wind speed within the range 0>z/L>0.3 have a slope of about 3.5. The scatter for the dimensionless temperature gradient is quite large, and the slope is comparable to that for wind speed gradients. For z/L>0.3 the imbalance in the turbulent kinetic energy budget grows and non-dimensional gradients for wind speed and temperature deviate considerably from accepted values as a result of increased non-stationarity. Average roughness lengths for momentum and sensible heat flux derived from wind speed and temperature profiles are respectively 1 × 10^-3 m and 6 × 10^-5 m, consistent with the literature. The ratio (z_0h/z_0m) compares to those predicted by surface renewal models. A variation of this ratio with the roughness Reynolds number is not indicated by our data.     

Numerical Studies with a Regional Atmospheric Climate Model Based on Changes in the Roughness Length for Momentum and Heat Over Antarctica

A regional atmospheric climate model is used toexamine the effect of changes in the roughnesslengths of momentum (_z0m) and heat (_z0h)on the structure of the lower atmosphere and on thesurface energy fluxes over Antarctica. Fourexperiments were carried out in which _z0mand/or _z0h were altered with respect to acontrol experiment. The changes consisted of (1) alowering of _z0m from a field aggregated froma vegetation map with an orographic correction basedon the European Centre for Medium-Range WeatherForecasts _z0m field, to a constant value of10^-3 m; and (2) a lowering of _z0h from a valueequal to _z0m to a constant value of 10^-3 mor a value dependent on the wind speed via a surfacerenewal model. A reduction of _z0m results in theexpected increase in near-surface wind speed. It alsoresults in an increase in the depth of the layer in whichsouth-easterly near-surface winds prevail, and in adecrease in the strength of the large-scale flow overthe continent, in particular in summer. In theescarpment region a decrease of _z0m is foundto result in too high wind speeds. Surface temperatureson average decrease while atmospheric temperaturesincrease, resulting in an increase of near-surfacestatic stability. Changes in roughness lengths donot significantly change the temperature profiles.The surface fluxes, on average found reduced, aremodelled best by using the _z0h based on thesurface renewal method.     

Atmospheric turbulence within and above a Douglas-fir stand. Part I: Statistical properties of the velocity field

This is the first of two papers reporting the results of a study of the turbulence regimes and exchange processes within and above an extensive Douglas-fir stand. The experiment was conducted on Vancouver Island during a two-week rainless period in July and August 1990. The experimental site was located on a 5^o slope. The stand, which was planted in 1962, and thinned and pruned uniformly in 1988, had a (projected) leaf area index of 5.4 and a heighth=16.7 m. Two eddy correlation units were operated in the daytime to measure the fluctuations in the three velocity components, air temperature and water vapour density, with one mounted permanently at a height of 23.0m (z/h=1.38) and the other at various heights in the stand with two to three 8-hour periods of measurement at each level. Humidity and radiation regimes both above and beneath the overstory and profiles of wind speed and air temperature were also measured. The most important findings are:

1. A marked secondary maximum in the wind speed profile occurred in the middle of the trunk space (aroundz/h=0.12). The turbulence intensities for the longitudinal and lateral velocity components increased with decreasing height, but the intensity for the vertical velocity component had a maximum atz/h=0.60 (middle of the canopy layer). Magnitudes of the higher order moments (skewness and kurtosis) for the three velocity components were higher in the canopy layer than in the trunk space and above the stand.
2. There was a 20% reduction in Reynolds stress fromz/h=1.00 to 1.38. Negative Reynolds stress or upward momentum flux perisistently occurred atz/h=0.12 and 0.42 (base of the canopy), and was correlated with negative wind speed gradients at the two heights. The longitudinal pressure gradient due to the land-sea/upslope-downslope circulations was believed to be the main factor responsible for the negative Reynolds stress.
3. Momentum transfer was highly intermittent. Sweep and ejection events dominated the transfer atz/h=0.60, 1.00 and 1.38, with sweeps playing the more important role of the two atz/h=0.60 and 1.00 and the less important role atz/h=1.38. But interaction events were of greater magnitude than sweep and ejection events atz/h=0.12 and 0.42.

     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

Momentum and scalar transfer coefficients over aerodynamically smooth antarctic surfaces

Vertical profiles of wind speed, temperature and humidity were used to estimate the roughness lengths for momentum (z ₀), heat (z _H ) and moisture (z _Q) over smooth ice and snow surfaces. The profile-measurements were performed in the vicinity of a blue ice field in Queen Maud Land, East Antarctica. The values ofz ₀ over ice (3·10^–6 m) seem to be the smallest ever obtained over permanent, natural surfaces. The settling of snow on the ice and the loss of momentum at saltating snow particles serve as momentum dissipating processes during snow-drift events, expressed as a strong dependence ofz ₀ on u_#.The scalar roughness lengths and surface temperature can be evaluated from the temperature and humidity profile measurements if the ratioz _H /z _Q is specified. This new method circumvents the difficult measurement of surface temperature. The scalar roughness lengths seem to be approximately equal toz0 for a large range of low roughness Reynolds numbers, despite the frequent occurrence of drifting snow. Possible reasons for this agreement with theory of non-saltating flow are discussed.     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.     

On the role of roughness lengths in flux parameterizations of boundary-layer models

Flux-profile relationships based on surface-layer similarity theory are used to derive relationships between the Monin-Obukhov stability parameter = z/L and the bulk Richardson number Ri _b . In contrast to previous studies, the roughness length for heat, z _0h ,is assumed unequal to the roughness length for momentum, z _0m .For the stable case, an analytic expression of in terms of Ri _b can be derived and in the unstable case, the solution is obtained through a simple iterative process.Errors introduced from the simplification of z _0h = z _0m are evaluated and are shown to be very significant in most cases. Thus, this error in many practical applications may invalidate the intended solution.     

Computational Fluid Dynamics Modelling of the Diurnal Variation of Flow in a Street Canyon

Urban surface and radiation processes are incorporated into a computational fluid dynamics (CFD) model to investigate the diurnal variation of flow in a street canyon with an aspect ratio of 1. The developed CFD model predicts surface and substrate temperatures of the roof, walls, and road. One-day simulations are performed with various ambient wind speeds of 2, 3, 4, 5, and 6 ms⁻¹, with the ambient wind perpendicular to the north–south oriented canyon. During the day, the largest maximum surface temperature for all surfaces is found at the road surface for an ambient wind speed of 3 ms⁻¹ (56.0°C). Two flow regimes are identified by the vortex configuration in the street canyon. Flow regime I is characterized by a primary vortex. Flow regime II is characterized by two counter-rotating vortices, which appears in the presence of strong downwind building-wall heating. Air temperature is relatively low near the downwind building wall in flow regime I and inside the upper vortex in flow regime II. In flow regime II, the upper vortex expands with increasing ambient wind speed, thus enlarging the extent of cool air within the canyon. The canyon wind speed in flow regime II is proportional to the ambient wind speed, but that in flow regime I is not. For weak ambient winds, the dependency of surface sensible heat flux on the ambient wind speed is found to play an essential role in determining the relationship between canyon wind speed and ambient wind speed.     

Turbulent exchange above a pine forest,I: Fluxes and gradients

Measurements of gradients of wind, temperature and humidity and of the corresponding turbulent fluxes have been carried out over a sparse pine forest at Jädra»s in Sweden. In order to ascertain that correct gradient estimates were obtained, two independent measuring systems were employed: one system with sensors at 10 fixed levels on a 51 m tower and another with reversing sensors for temperature and humidity, covering the height interval 23 to 32 m. Turbulent fluxes were measured at three levels simultaneously. Data from three field campaigns: in June 1985, June 1987 and September 1987 have been analyzed. The momentum flux is found on the average to be virtually constant from tree top level, at 20 to 50 m. The average fluxes of sensible and latent heat are not so well behaved. The ratio of the non-dimensional gradients of wind and temperature to their corresponding values under ideal conditions (low vegetation) are both found to be small immediately above the canopy (about 0.3 for temperature and 0.4 for wind). With increasing height, the ratios increase, but the values vary substantially with wind direction. The ratios are not found to vary systematically with stability (unstable stratification only studied). The ratio of the non-dimensional humidity gradient to the corresponding non-dimensional potential temperature gradient (equivalent to k _h /k _w ) is found to be unity for (z – d)/L _v less than about –0.1 and about 1.4 for near neutral stratification, but the scatter of the data is very large.     

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

This paper describes a wind-tunnel experiment on the dispersion of trace heat from an effectively planar source within a model plant canopy, the source height being h _s = 0.80 h _c , where h _c is the canopy height. A sensor assembly consisting of three coplanar hot wires and one cold wire was used to make simultaneous measurements of the temperature and the streamwise and vertical velocity components. It was found that:

1. The thermal layer consisted of two parts with different length scales, an inner sublayer (scaling with h _s and h _c ) which quickly reached streamwise equilibrium downstream of the leading edge of the source, and an outer sublayer which was self-preserving with a length scale proportional to the depth of the thermal layer.
2. Below 2h _c , the vertical eddy diffusivity for heat from the plane source (K _HP ) was substantially less than the far-field limit of the corresponding diffusivity for heat from a lateral line source at the same height as the plane source. This shows that dispersion from plane or other distributed sources in canopies is influenced, near the canopy, by turbulence ‘memory’ and must be considered as a superposition of both near-field and far-field processes. Hence, one-dimensional models for scalar transport from distributed sources in canopies are wrong in principle, irrespective of the order of closure.
3. In the budgets for temperature variance, and for the vertical and streamwise components of the turbulent heat flux, turbulent transport was a major loss between h _s and h _c and a principal gain mechanism below h _s , as also observed in the budgets for turbulent energy and shear stress.
4. Quadrant analysis of the vertical heat flux showed that sweeps and ejections contributed about equal amounts to the heat flux between h _s and h _c , though among the more intense events, sweeps were dominant. Below h _s , almost all the heat was transported by sweeps.

     

Flux determination over a smooth surface under strongly unstable conditions

Careful micrometeorological measurements on an empty parking lot allowed determination of the surface fluxes of sensible heatH and of momentum by applying profile equations derived from Monin-Obukhov similarity theory with two sets of the stability correction function for momentum _m and sensible heat _h . These fluxes were compared with reference values ofH independently determined by means of an eddy correlation technique. In general, better agreement was found betweenH values derived from profiles with the stability functions of Brutsaert (1992) and referenceH values, than when the Businger-Dyer functions were used to deriveH. The disagreement in the latter comparison was especially serious under strongly unstable conditions, with the value ofy=–z/L (wherez is the height andL is the Obukhov length) larger than 10. A closer look at the procedure for calculatingH from the profiles revealed that the large differences between theH values derived with these two different versions of the stability correction functions were caused by the small differences of the _h values, and not by the larger differences of the _m values. This result stems from the strong sensitivity of the resultingH values on the choice of _h .     

An Approximate Analytical Solution Of Flux-Profile Relationships For The Atmospheric Surface Layer With Different Momentum And Heat Roughness Lengths

An approximate method for calculating the relationship between z/L(z = reference height, L = Obukhov length) and the bulk Richardsonnumber is presented. If this relationship is known, the momentum andheat fluxes can be computed easily without any iteration. The avoidance of iteration can speed up computationsin large-scale models considerably (up to 10 times) and cases which do not converge or converge very slowly cannot occur. The proposed formulae take into account the difference between momentum (z_0M) and heat roughnesslengths (z_0H). Because the roughness lengths are not neglected at any step of the derivation, the resulting analytical formulae can be used not only between the surface and the reference height but also between two finite levels z₁ andz₂ (by replacing z_0M and z_0H by z₁ and z by z₂). Theequations remain correct even in the limit z₁ z₂.The formulae are based upon the (partially modified) Businger–Dyer flux–profile relationships and,consequently, they are restricted to predominantly homogeneous terrain.These new approximations are an improvement over the existing solutions because they are simpler than most of the formulae in the literature and are able to match the numerical exact solution for different parameter sets (Businger, Dyer, Högström) with an maximum error of about 2% for a wide range of z/L, z/z_0M and z_0M/z_0H.Furthermore, in stable conditions, schemes with and without a finitecritical bulk Richardson number can be approximated. The possibleambiguity of the exact solution =f(RI_B) in (moderately) stable conditions is discussed briefly. The performance of the new formulae is compared to the exact numerical solution and to different formulae proposed in the literature.     

Momentum and heat transfers in the surface layer over a frozen sea

Wind and temperature profiles from a 10-m mast were measured over the frozen Baltic Sea. The Monin-Obukhov similarity theory applies well to runs carefully selected according to stationarity criteria. This provides relatively low-scattered results with the roughness length z ₀ 0.04 cm, the drag coefficient C _D 1.5 × 10^-3 and the Stanton number C _H 1.00 × 10^-3 under near-neutral conditions. The roughness length, however, behaves in a peculiar way under intense stratification conditions. The reasons proposed for this could lead to an extension of the theory. The mechanisms for momentum and heat transfers are also examined, revealing that there are two different regimes, the smooth and the rough, for the wall friction but not for the heat transfer. Further, the scatter of the data for momentum and heat transfer under the aerodynamically rough regime can be explained by the distinction between the type of thermal stability conditions.     

Turbulence measurements during mistral winds with a 1-dimensional sonic anemometer

Fluctuations in the vertical wind velocity and air temperature were measured with a 1-dimensional sonic anemometer and fine thermocouple over a flat agricultural site in the Rhone Valley, France. Strong Mistral winds with speeds up to 20 m s^–1 kept atmospheric conditions very close to neutral and ensured stationarity. Friction velocities estimated both by eddy correlation (sonic plus Gill Bivane) and inertialdissipation (sonic only) methods agreed within 1 and 5 % respectively of traditional profile measurements over the measured range of 0.2 to 1.2 m s^–1. The coefficient of eddy transport for heat exceeded that of momentum by a factor of 1.38 (± 0.05), a result almost identical to that obtained in the Kansas experiment (Businger et al., 1971). For - 0.15 >= z/L >= 0.05, the ratio _w /u _* was 1.69 and 1.34 for unstable and stable conditions, respectively. For ¦z/L¦ >= 0.05, the ratio /T _* was 1.40 independent of whether neutrality was approached from either stable or unstable conditions.     

On the bulk parameterization of surface fluxes for various conditions and parameter ranges

A comparison between various parameterizations for the bulk transfercoefficient for heat and momentum is carried out for a wide range ofatmospheric stability and values of the roughness lengths for momentum and heat,z_0m and z_0h respectively.It is confirmed that the parameterization of Launiainen compares wellto a numerical iterative solution for the Obukhov length L as function of the gradients of wind speed and temperatureover a limited range of z_0m/z_0h and stability conditions.For _0m/z_0h > 500, an alternativeinterpolation formulation of Holtslag and Ek,in combination with the formulation of Launiainen, provides a better approximation.     

The thermodynamic speed limit and its violation in axisymmetric numerical simulations of tornado‐like vortices

Abstract

Processes that regulate the central pressure and maximum wind speeds of tornado‐like vortices are explored with an axisymmetric numerical model. The model consists of a rotating cylinder of fluid enclosed within rigid boundaries. The momentum diffusivity is a fixed function of height. In the rotating reference frame, relative motion is induced by a buoyancy force in the vicinity of the rotation axis, leading to the formation of a central vortex. The work done by the central buoyancy force on a parcel rising along the axis defines theoretical and empirical wind speed bounds on both the updraft and the low‐level vortex. Certain processes are found that allow for the vortex to greatly exceed this wind speed bound, or the so‐called thermodynamic speed limit; however, in most of the parameter space the vortex wind speeds are close to the thermodynamic speed limit.

The most effective limit‐breaking process involves a supercritical end‐wall vortex with an axial jet. In steady state, the supercritical vortex sustains wind speeds 2.0 times the speed limit. A transient end‐wall vortex, with the vortex breakdown travelling rapidly downwards toward the surface, is able to achieve wind speeds 5.0 times the speed limit. Warming of the subsiding vortex core past the vortex breakdown increases the maximum steady‐state azimuthal wind speed by about 20% from what it would be otherwise. Axial momentum diffusion is not found to significantly enhance the surface pressure deficit in any of the simulations.     

Experiments on scalar dispersion within a model plant canopy,part III: An elevated line source

An experiment is reported in which heat was released as a passive tracer from an elevated lateral line source within a model plant canopy, with h _s = 0.85 h _c (h _s and h _c being the source and canopy heights, respectively). A sensor assembly consisting of three coplanar hot wires and one cold wire was used to measure profiles of mean temperature % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGaeqiUdehaaiaacMcaaaa!390C!\[(\overline \theta )\], temperature variance (Σ_θ ²), vertical and streamwise turbulent heat fluxes, and third moments of wind and temperature fluctuations. Conclusions were:

1. Despite the very heterogeneous flow within the canopy, the observed dispersive heat flux (due to spatial correlation between time-averaged temperature and vertical velocity) was small. However, there is evidence from the plume centroid (which was lower than h _s at the source) of systematic recirculating motions within the canopy.
2. The ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS% baaSqaaiabeI7aXjaab2gacaqGHbGaaeiEaaqabaGccaGGVaWaa0aa% aeaacqaH4oqCaaWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaa!41DF!\[\sigma _{\theta {\text{max}}} /\overline \theta _{{\text{max}}} \] (of maximum values on vertical profiles) decreased from 1 near the source to an asymptotic value of 0.4 far downstream, in good agreement with previous experimental and theoretical work for concentration fluctuations in the surface layer well above the canopy.
3. The eddy diffusivity for heat from the line source (K _HL ) increased, downstream of the source, to a nearly constant ‘far-field’ vertical profile. Within the canopy, the far-field K _HL was an order of magnitude larger than K _HP , the equivalent diffusivity for a plane source; well above the canopy, the two were equal. The time scale defined by (far-field K _HL )/(vertical velocity variance) was independent of height within the canopy.
4. Budgets for temperature variance, vertical heat flux and streamwise heat flux are remarkably similar to the equivalent budgets for an elevated line source in the surface layer well above the canopy, except in the lower part of the canopy in the far field, where vertical transport is much more important than in the surface layer.
5. A random flight simulation of the mean height and depth of the temperature plume was generally in good agreement with experiment. However, details of the temperature and streamwise turbulent heat flux profiles were not correct, suggesting that the model formulation needs to be improved.

     

The influence of stratification on heat and momentum turbulent transfer in antarctica

Data from the Antarctic winter at Halley Base have been used in order to evaluate qualitatively and quantitatively how the stratification in the low atmosphere (evaluated with the gradient Richardson number, Ri) influences the eddy transfers of heat and momentum. Vertical profiles of wind and temperature up to 32 m, and turbulent fluxes ( , and ) measured from three ultrasonic thermo-anemometers installed at 5, 17 and 32 m are employed to calculate Ri, the friction velocity (u _*) and the eddy diffusivities for heat (K _h ) and momentum (K _m ). The results show a big dependence of stability onK _m ,K _h andu _*, with a sharp decrease of these turbulent parameters with increasing stability. The ratio of eddy diffusivities (K _h /K _m ) is also analyzed and presents a decreasing tendency as Ri increases, reaching values even less than 1, i.e., there were situations where the turbulent transfer of momentum was greater than that of heat. Possible mechanisms of turbulent mixing are discussed.     

A model of airflow above changes in surface heat flux,temperature and roughness for neutral and unstable conditions

A numerical model of airflow in the lowest 50–100 m of the atmosphere above changes in surface roughness and temperature or heat flux has been developed based on boundary layer approximations, the Businger-Dyer hypotheses for the non-dimensional wind shear and heat flux and a mixing length hypothesis.Results have been obtained for several situations, in particular, airflow with neutral upstream conditions encountering a step change in surface temperature or heat flux with no roughness change. In these cases large increases in shear stress at the outer edge of the internal boundary layer are predicted. The case of unstable upstream flow encountering a step change to zero heat flux is also considered.Two situations that may be encountered near the shores of the Great Lakes are considered.Notation B Businger-Dyer constant (= 16.0) in form for _M, _H - c _p Specific heat at constant pressure - g Acceleration due to gravity - H Upward vertical heat flux - H ₀ , H ₁ Surface heat fluxes for x < 0, x 0 - k von Kármán's constant ( = 0.4) - l Mixing length - L Monin-Obukhov length - L ₀ Upstream value of L - m Ratio of roughness lengths (= z ₁/z ₀) - RL ^* Non-dimensional parameter, see Equations (20, 22 and 24) - RL ₁ ^* Same as RL ^* but with z ₁ scaling (= mRL ^*) - T Scaled temperature - T ₀ (z) Upstream temperature profile - u ₀, u ₁(x) Surface friction velocities for x < 0, x 0 - U, W Horizontal and vertical mean velocities - U ₀ (z) Upstream velocity profile - x, z Horizontal and vertical coordinates - z _i Local roughness length