Local Similarity Relationships In The Urban Boundary Layer

To investigate turbulent structures in an urban boundary layer (UBL) with many tallbuildings, a number of non-dimensional variable groups based on turbulent observationsfrom a 325-m meteorological tower in the urban area of Beijing, China, are analyzedin the framework of local similarity. The extension of surface-layer similarity to localsimilarity in the stable and unstable boundary layer is also discussed. According to localsimilarity, dimensionless quantities of variables: e.g., velocity and temperature standarddeviations _i/u_*l (i=u,v,w) and_T/T_*l,correlation coefficients of uw and wT covariance, gradients of wind and temperature_m and _h, and dissipation rates of turbulent kinetic energy (TKE) andtemperature variance and _N can be represented as a functiononly of a local stability parameter z/, where is the local Obukhovlength and z is the height above ground. The average dissipation rates of TKE andtemperature variance are computed by using the u spectrum, and the uw and wTcospectra in the inertial subrange. The functions above were found to be in a goodagreement with observational behaviour of turbulence under unstable conditions, butthere were obvious differences in the stable air.     

Ab initio study on carbon Kinetic Isotope Effect (KIE) in the reaction of CH4+Cl•

Recent studies suggest that the destruction of methane by Cl in the marine boundary layer could be accounted for as another major sink besides the methane destruction by OH. High level ab initio molecular orbital calculations have been carried out to study the CH₄+Cl reaction, the carbon Kinetic Isotope Effect (KIE) is calculated using Conventional Transition-State Theory (CTST) plus Wigner and Eckart semiclassical tunneling corrections. The calculated KIE is around 1.026 at 300 K and has a small temperature variation. This is by far the largest KIE among different processes involving atmospheric methane destruction (e.g., OH, soil). A calculated mass balance of atmospheric methane including the KIE for the CH₄+Cl reaction is found to favor those methane budgets with enhanced biological methane sources, which have relatively lighter carbon isotope composition.     

Numerische Integrationen einer Gleichung für die turbulente Diffusion in der Atmosphäre

Zusammenfassung Es werden numerische Integrationen der dreidimensionalen Fickschen Diffusionsgleichung mit höhenabhängigen Diffusionskoeffizienten und Windgeschwindigkeit für den stationären Fall und eine kontinuierlich emittierende Punktquelle durchgeführt. Für die drei typischen Ausbreitungsverhältnisse Starke Durchmischung, Bodeninversion und Inversion über der Quelle, charakterisiert durch die Diffusionskoeffizienten und die Windgeschwindigkeit, werden die Einflüsse unterschiedlicher Quellhöhe, Sinkgeschwindigkeit und Ablagerungsgeschwindigkeit studiert.

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Summary Numerical integrations of the threedimensional Fickean diffusion equation with height dependent diffusion coefficients and wind velocity are performed in the stationary case with a continuous point source. For the three typical cases strong mixing, surface inversion and inversion above the source characterized by the diffusion coefficients and wind velocity, the effects of source height, sinking velocity and deposition velocity are discussed.

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Résumé Les auteurs ont procédé à l'intégration numérique de l'équation à trois dimensions de la diffusion, équation établie par Fick. Ils ont, pour cela, utilisé des coefficients de diffusion variant avec l'altitude et la vitesse du vent et distingué l'état stationnaire et le cas d'une source d'émission ponctuelle et continue. Ils étudient en outre les influences de hauteurs différentes de la source, de la rapidité de subsidence et de la vitesse de sédimentation. Ils ont tenu compte pour cela des trois conditions typiques de diffusion mélange très accentué, inversion au sol et inversion au-dessus de la source.

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Mit 7 Textabbildungen     

On the temperature coefficient of PCO 2 in seawater

The commonly reported temperature coefficient of P. the equilibrium partial pressure of CO₂, is (P/T) _A,C ,which is about 15 ppm/°C, or 5% of the atmospheric partial pressure of CO₂. This coefficient, however, applies only to deep water, not to surface water which can exchange CO₂ with the atmosphere. The coefficient (P/T) _A,C ,, where designates constancy of the sum of atmospheric and surface-ocean CO₂, is the appropriate value for air-sea exchange. Numerical values are mass-dependent because the depth of the exchanging ocean layer must be specified. For a 100-m surface layer, the value is ca. 1.5 ppm/°C, or 0.5% of ambient CO₂. Editor's Note:In view of the interdisciplinary importance of the carbon dioxide-climate problem, this note on seawater chemistry should be of interest to specialists beyond the discipline of ocean chemistry.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

Effect of land management on ecosystem carbon fluxes at a subalpine grassland site in the Swiss Alps

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.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

Stable boundary layers: Observations,models and variability part I: Modelling and measurements

Selected field measurements of evening stable boundary layers are presented in detail comparable with published Large Eddy Simulation results. Such models appear to match idealized theories more closely than do some boundary-layer observations. Any attempt to compare detailed observations with idealized models therefore highlights the variability of the real boundary layer.Here direct turbulence measurements across the stable boundary layer from a heterogeneous and an ideal site are contrasted. Recommendations are made for the information needed to distinguish heterogeneous and ideal cases.The companion paper (Part II) discusses further the issues of data, analysis in the presence of variability, and the effects of averaging over heterogeneous terrain.Part of UK Meteorological Office Atmospheric Process Research Division.     

Turbulence Characteristics Over Complex Terrain In West China

Meteorological data of velocity components and temperature have been measured on a mast of height 4.9 m at one site in the Heihe River Basin Field Experiment (HEIFE) conducted in west China. Mean and individual turbulence parameters, power spectra/cospectra, phase angles and their changes withfetch downwind of a change in surface roughness were analyzed. The turbulence characteristics depend strongly on the prevailing wind direction, which in turn is associated with changes in the upwind surface roughness pattern. The results show that values of horizontal velocity standard deviations sigma;_u,v scaled with local friction velocity u under different stratifications are larger than those over flat terrain, while the values of _w/u have the same values as over flat terrain. The differences between variance values of the horizontal velocity components, u and v, over inhomogeneous terrain were found to be significantly smaller than those over flat terrain. Since energy densities of the w spectra, uw and wT cospectra at low frequencies are relatively lower than those of longitudinal velocity spectra, total energies of w spectra, uw and wT cospectra tend to be in equilibrium with the local terrain. The values of phase angles at the low frequency end of the frequency showed obvious differences associated with changes of roughness.     

An observational aircraft-based study of sea-breeze frontogenesis

In the summer of 1988/89 flights were carried out in the Coorong coastal area of South Australia to investigate sea-breeze fronts. The flights yielded data sets of the structure of the fronts in the cross-frontal direction with a spatial resolution of approximately 3 m. The study is focused on the budgets of sensible and latent heat in the vicinity of the front and on frontogenesis/frontolysis processes which are closely related to budget considerations.The frontogenesis relationships and the budgets were established on a 2 km length scale by low-pass filtering of the space series. As the wind components were measured with high accuracy, all processes which determine frontogenesis could be evaluated and are displayed in x,z-cross-sections: these are the confluence, shear and diabatic effects, all of which play a role in q/x-, q/z-, /x- as well as /z-frontogenesis. A detailed analysis is given for two different states of frontal development. The presented results shed much light on the governing physical processes in the frontal region with strong emphasis on the effects of confluence-generated updrafts, on shear instabilities causing bulges and clefts in the frontal surface as well as producing the elevated frontal head, and on processes related to differential heating and moistening.     

Arctic hazes in summer over Greenland and the North American Arctic: II. Nature and concentrations of accumulation-mode and giant particles

Airborne measurements made during August 1985 over Greenland and its environs show that both accumulation-mode (0.1 m D2.0 m) and giant (D2 m) particles were present in relatively high concentrations in arctic haze layers and that the accumulation-mode particles dominated light scattering. Particles with diameters (D) between 1 and 4 m consisted predominately of mixed materials, small and dense inclusions, and probably organic compounds containing sulfur. Many of the particles from 0.1 to 1 m in diameter were also of mixed composition, with sulfuric acid, ammonium sulfate and organics probably the dominant constituents.     

Hidden information within series of measurements — four examples from atmospheric science

Whether in classical networks such as meteorological networks of in more recent ones of atmospheric chemistry, a wealth of data is at hand. These data have been evaluated in a manner depending on the purpose of the network. However, much more information is hidden in these time series and waits for discovery. Only the imagination of scientists is needed. Four examples are given which lead to new information about the atmospheric aerosol and the behaviour of the atmosphere. These examples are: Atmospheric turbidity from sunshine recordings, Meteorological drainage area from the variance of observations, Location of point sources from air mass trajectories, and Total vertical ozone from turbidity measurements.     

Propagation of the sea-surface temperature anomalies in the Tropical Atlantic

Summary The evolving modes of the sea-surface temperature (SST) in the Tropical Atlantic on the short interannual (IA) timescale were obtained by performing the extended empirical orthogonal function (EEOF) analyses on this variable separately for the 106-year (1871–1976) and 20-year (1881–1900; 1901–1920; 1921–1940; 1941–1960) periods. The equatorial and inter-hemispheric patterns manifest in the first EEOF mode of each analysis as part of the short IA evolution of the SST anomalies in the Tropical Atlantic. Another outstanding feature of the first EEOF mode of each analysis concerns the propagations of the SST anomalies in the meridional direction within the 20°N–20°S band and in the zonal direction in the sector 40°W–20°W. For all analyses, the SST anomalies propagate northward from the equator to 15°N and southward from 20°N to 15°N, with the same sign anomalies merging approximately at 15°N. On the other hand, the SST anomalies propagate westward in the sector 40°W–20°W with a propagation rate close to that of the phase speed of the fastest baroclinic Rossby wave in the ocean. So, the observed propagations of the SST anomalies in the 20°N–20°S band might result from the combined effect of the surface oceanic currents in this band and the baroclinic Rossby waves in the ocean.     

Land use and local climate: A case study near Santa Cruz, Bolivia

Summary The Tierras Bajas regions of eastern Santa Cruz, Bolivia have undergone among the most rapid rates of concentrated deforestation during the 1980s and 1990s. We investigate the sensitivity of local climate to these land cover changes as observed from Landsat images acquired between 1975 and 1999. The Simple Biosphere model (SiB2) is used to assess the effects of both morphological and physiological changes in vegetation and the implications for fluxes of water, energy and carbon between the vegetation and the atmosphere during the rainy season.Conversion from tropical forest to cropland implicates morphological changes in vegetation as the primary drivers for a daily maximum warming of about 2°C and a slight nighttime cooling, suggesting that clearing of tropical forests for agricultural use may increase the diurnal temperature range, mainly by increasing the maximum temperature. On the other hand, the conversion of wooded grassland to cropland resulted in a similar daily warming and drying but exclusively due to vegetation physiological activity.The area-averaged monthly mean response for each conversion type resulted in a warming of about 0.6°C for the conversion of broadleaf evergreen and 1.2°C for conversion of wooded grassland. These temperature differences represent an augmentation in the local heat source associated with a reduction in evapotranspiration due to land cover conversion and do not reflect variations forced by changes in atmospheric circulation.When averaged over the entire domain, the effect of landscape conversion results in a reduction of the latent heat flux and an increase in sensible heat flux, producing a large-scale apparent heat source of 0.5°C during January. This warming is in line with an increasing trend observed in monthly mean temperature in Santa Cruz, Bolivia during the same period.     

Thermal comfort of man in different urban environments

Summary On July 29, 1985, a hot summer day, biometeorological measurements were performed simultaneously in three different urban structures within the city of Munich and in the trunk space of a nearby tall spruce forest. Based on the results of these experiments the following thermophysiologically relevant biometeorological indices were calculated: Predicted mean vote, skin wettedness and physiologically equivalent temperature. These three indices are derived from different models for the human energy balance. They allow the assessment of the thermal components of the microclimates at the selected sites with regard to application in urban planning. The results quantitatively show the great heat stress in the urban structure street canyon, exposed to south, whereas in the trunk space of the tall spruce forest there is nearly an optimal climate even on hot summer days. Between these extremes the results for street canyon, exposed to north show a little higher heat load than for backyard with trees.

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Zusammenfassung An einem heißen Sommertag, dem 29. Juli 1985, wurden in drei Stadtstrukturen in München und im Stammraum eines nahegelegenen Fichtenhochwaldes zeitgleich biometeorologische Messungen durchgeführt. Mit den Meßergebnissen wurden folgende thermophysiologisch relevante biometeorologische Indizes berechnet: Predicted mean vote, Hautbenetzungsgrad und physiologisch äquivalente Temperatur. Diese drei Indizes beruhen auf verschiedenen Modellen zur menschlichen Energiebilanz. Mit den drei Indizes wurden die thermischen Komponenten der Mikroklimate an den ausgewählten Meßplätzen im Hinblick auf Stadtplanungsaufgaben bewertet. Die Ergebnisse zeigen quantitativ die relativ große Hitzebelastung bei der Stadtstruktur Straßenschlucht, nach Süd exponiert, während im Stammraum des Fichtenhochwaldes selbst an heißen Sommertagen nahezu optimale Bedingungen herrschen. Zwischen diesen Extremen liegen die Ergebnisse für die anderen Meßplätze, wobei für Straßenschlucht, nach Nord exponiert die Wärmebelastung etwas höher als für Innenhof mit Bäumen ist.

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With 6 Figures     

Occurrence of roll circulations in a shallow boundary layer

Meteorological measurements taken at the Näsudden wind turbine site during slightly unstable conditions have been analyzed. The height of the convective boundary layer (CBL) was rather low, varying between 60 and 300 m. Turbulence statistics near the ground followed Monin-Obukhov similarity, whereas the remaining part of the boundary layer can be regarded as a near neutral upper layer. In 55% of the runs, horizontal roll vortices were found. Those were the most unstable runs, with -z _i/L > 5. Spectra and co-spectra are used to identify the structures. Three roll indicators were identified: (i) a low frequency peak in the spectrum of the lateral component at low level; (ii) a corresponding increase in the vertical component at mid-CBL; (iii) a positive covariance {ovvw} together with positive wind shear in the lateral direction (V/z) in the CBL. By applying these indicators, it is possible to show that horizontal roll circulations are likely to be a common phenomenon over the Baltic during late summer and early winter.     

Stable Isotope Ratios: Hurricane Olivia

The oxygen and hydrogen isotopic compositions of rains from HurricaneOlivia (1994) in the eastern Pacific were measured. The rains werecollected on 24 and 25 September during airplane flights conducted at anelevation of 3 km. Hurricane Olivia peaked in intensity to a category-4storm between the two dates. Isotope ratios of rains from HurricaneOlivia were markedly lower ( ¹⁸O = –13.9to –28.8) than that of rain collected from a thunderstormat an elevation of 2.3 km outside the influence of Olivia (¹⁸O = –3.8). A distinct decrease in isotoperatios from the first day to the next ( ¹⁸O =–18.4 to –21.9) in Hurricane Olivia wasattributed to decreased updraft velocities and outflow aloft. Thisshifted the isotopic water mass balance so that fewer hydrometeors werelifted and more ice descended to flight level. A decrease in the averagedeuterium excess from the first day to the next (d = 15.5 to 7.1)was attributed to an increase in the relative humidity of the watervapor `source' area. We hypothesize that the `source' region for therain was in the boundary layer near the storm center and that becausethe hurricane was at peak intensity prior to the second day the relative humidity was higher.     

On the enhanced smoothing over topography in some mesometeorological models

An equation is derived for the components of the horizontal (turbulent) frictional force in the -coordinate system with special attention to mesometeorological flow models. The starting point is the horizontal equation of motion in its flux-form in the -system in which we replace (following Reynolds' procedure) the velocity components u,v and % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbai % aaaaa!37B8! \[ \dot \sigma \] aswell as other relevant quantities by terms of the form u = + u,..., = ± + % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbai % Gbauaaaaa!37C3! \[ \dot \sigma ' \] , etc. ( = time average of u; u = fluctuating part of u.) Next, the equation is averaged with respect to time and terms which we believe are small in mesometeorological flows, are neglected. On expressing by an appropriate expression that involves w, the result shows the appearance of two new terms which, have not been considered previously in the published literature. While the expression earlier used in the literature involved the -derivative of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG3bGbauaaaaaaaa!380B!\[\overline {u'w'} \] alone, the new terms add the -derivatives of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EC!\[\overline {u'^2 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG2bGbauaaaaaaaa!380A!\[\overline {u'v'} \] for the x-component of the force, and the -derivatives of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG2bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37ED!\[\overline {v'^2 } \]} and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG2bGbauaaaaaaaa!380A!\[\overline {u'v'} \] for the y-component, where and are the slopes of the -surfaces in the x- and y-directions, respectively. Further, a few numerical simulations of the sea-breeze over topography are carried out with and without the correction terms. It is shown that when corrections terms are not included the effective smoothing is stronger above the sloping regions and may amount to as high as 50 percent of the convergence with slopes of ~.04. The ìnclusìon of the new terms does not lead to any special computational difficulties and for that reason there is no compelling reason to neglect them, all the more so because, as is shown, the addition of the new terms results in a consistent apportioning of the degree of horizontal diffusion.On leave from CIMMS, Norman, OK.Now visiting Dept. of Met., Helsinki, Finland.     

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