Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance

The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance _wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + t) = aw(t) + b _wE + (1 – a)T _L ( _wE ²)/z, where w(t) is the vertical velocity at time t, a random number from a Gaussian distribution with zero mean and unit variance, T _L the Lagrangian integral time scale for vertical velocity, a = exp(–t/T _L), and b = (1 – a ²)^1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, _wE and T _L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.     

Effects of heat and water vapor transport on eddy covariance measurement of CO2 fluxes

Flux densities of carbon dioxide were measured over an arid, vegetation-free surface by eddy covariance techniques and by a heat budget-profile method, in which CO₂ concentration gradients were specified in terms of mixing ratios. This method showed negligible fluxes of CO₂, consistent with the bareness of the experimental site, whereas the eddy covariance measurements indicated large downward fluxes of CO₂. These apparently conflicting observations are in quantitative agreement with the results of a recent theory which predicts that whenever there are vertical fluxes of sensible or latent heat, a mean vertical velocity is developed. This velocity causes a mean vertical convective mass flux (= _cw for CO₂, in standard notation). The eddy covariance technique neglects this mean convective flux and measures only the turbulent flux _c w. Thus, when the net flux of CO₂ is zero, the eddy covariance method indicates an apparent flux which is equal and opposite to the mean convective flux, i.e., _c w = – _c w. Corrections for the mean convective flux are particularly significant for CO₂ because _cw and _c w are often of similar magnitude. The correct measurement of the net CO₂ flux by eddy covariance techniques requires that the fluxes of sensible and latent heat be measured as well.     

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.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Wind stress over water waves: Field experiments on lake of Geneva

Summary A fixed platform (Fig.3), installed 100 m from the shoreline in 3 m water depth, was instrumented with velocity, temperature and wave-height sensors. 132 data (10 minutes averages) were analysed to calculate the wind stress; from these, 99 data were used to investigate the vertical distribution of the wind stress; all data are presented with Table 1.It was postulated that the total stress, _t being constant with height, is made up additively of two components, the wave-supporting stress, _w , and the turbulent stress, _c ; see Eq. 1. The vertical distribution of these two components is shown schematically in Fig. 1.The total stress, _t , evaluated outside the zone of wave influence, is given in the classical way with Fig. 4. The wave-supporting stress, _w (z), was evaluated from the data according to a relation proposed by Kitaigorodskii et al. (1984); it is given with Fig. 5. A height-dependency is clearly evident. The turbulent stress _c (z), was evaluated with data of the velocity gradient; it is given with Fig. 6. A height-dependency is not evident.The field data from the lake of Geneva give evidence that the additive relation of Eq. 1 seems to be justified.With 6 Figures     

Boundary-layer parameterizations for applied dispersion modeling over urban areas

Many applied dispersion models require the knowledge of boundary-layer parameters such as sensible heat flux,Q _H , friction velocity,u _*, and turbulent energy components, _w and _v . Formulas are suggested for calculating these parameters over a wide variety of types of ground surfaces, based on simple observations of wind speed near the ground and fractional cloud cover, and specification of constants such as roughness length, albedo, and soil moisture availability. Observations ofu _*,Q _H , _w , and _v during field experiments in St. Louis and Indianapolis are used to test the formulas for urban sites. Relative errors of about ±20% in the predictions are seen to occur whenu _*,Q _H , _w , and _v are large. However, when these quantities are small (e.g.,u _* < 0.2 m/s), the errors in the predictions are as large as the mean value of the quantity itself.In addition, it is concluded from studies of available field data and theories that the magnitude of _w is not well-known at elevations above about 100m during the late afternoon and night. Some simple parameterizations for _w . are suggested that are consistent with the observed steady decrease in ground-level concentration in the afternoon and the sudden increase in concentration that can occur a few hours after sunset due to wind shears associated with a low-level jet, for continuous plumes emitted from moderate to tall stacks.     

Free convection scaling over the ocean derived from buoy measurements during gate

The structure of atmospheric turbulence in the surface layer over the open ocean is examined under conditions of local free convection. The raw data consist of profile and fluctuation measurements of wind and temperature as obtained from a meteorological buoy. For near neutral conditions and for waves running approximately along the wind direction, wave-induced wind fluctuations can be described by a simplified linear theory based on Miles (1957). In this case, the spectrum of wind velocity is given as the sum of two parts; for the turbulent part, the parameterization as obtained by Kaimal et al. (1972) applies, while the wave-induced part is parameterized using a simplification of Miles' linear theory. For cases of local free convection, the measurements of the vertical component of the wind velocity are well described by similarity theory; as expected, _w /(-uw)^1/2 is proportional to (- z/L)^1/3. In order to scale the longitudinal wind velocity component, it seems to be reasonable to extend the list of relevant parameters by the height of the mixed layer z _i. We obtain _u /(- uw)^1/2 (z/z _i)^1/3(- z/L)^1/3 with only a poor correlation coefficient of r = 0.6. Overall, the results of local free convection scaling obtained from direct measurements show good agreement with those obtained from profile measurements. A comparison between direct and indirect determination of turbulent fluxes of momentum shows an unexplained difference of about 20%. This discrepancy is mainly due to a gap in the uw-cospectrum at the swell frequency.     

Turbulence mechanisms at an agricultural site

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

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

Measurements of solar radiation and estimation of optical depth in the high Andes of Peru

Summary During an expedition to the high Andes of Southern Peru in June–July 1977, measurements of direct solar radiation in four spectral bands (0.270–0.530–0.630–0.695–2.900 ) were conducted at six sites in elevations ranging from sea level to 5645 m. These measurements were evaluated in Langley plots to determine total optical depths () and irradiances at the top of the atmosphere. In addition, water vapor optical depths (_wv) were calculated from the mean radiosounding over Lima during the expedition, and Rayleigh (_ray) and ozone (_oz) optical depths were obtained from published tabulations. Subtracting _ray, _oz, and _wv from yielded estimates of aerosol optical depth _aer. The components _ray and _oz decrease from the shorter towards the longer wavelength bands and from the lower towards the higher elevation sites; _aer also decreases towards the higher elevations. Particularly pronounced is the decrease of _aer and from the lowlands of the Pacific coast to the highlands of the interior, reflecting the effect of a persistent lower-tropospheric inversion and the contrast from the marine boundary layer to the clear atmosphere of the high Andes.With 4 Figures     

Numerical simulation of particle trajectories in inhomogeneous turbulence,II: Systems with variable turbulent velocity scale

It is shown that for the purpose of trajectory simulation, the vertical velocityw _L (t) of a fluid element, which is moving in a system (such as a forest canopy, or the unstably stratified atmospheric surface layer) whose turbulent velocity scale _w is height-dependent, must be chosen from a frequency-distribution which is asymmetric aboutw _L = 0. If the gradient _w /z varies only slowly with height, correct trajectories may be obtained by adding a bias (where _L is the length scale) to a fluctuating velocity chosen from a symmetric distribution with variance _w ²(z).     

Near-field dispersion from instantaneous sources in the surface layer

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

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.     

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.     

A statistical-dynamical downscaling procedure for global climate simulations

Summary A statistical-dynamical downscaling procedure for global climate simulations is described. The procedure is based on the assumption that any regional climate is associated with a specific frequency distribution of classified large-scale weather situations. The frequency distributions are derived from multi-year episodes of low resolution global climate simulations. Highly resolved regional distributions of wind and temperature are calculated with a regional model for each class of large-scale weather situation. They are statistically evaluated by weighting them with the according climate-specific frequency. The procedure is exemplarily applied to the Alpine region for a global climate simulation of the present January climate.List of Symbols west-east mesh size in geographic coordinates south-north mesh size in geographic coordinates N number of large-scale weather classes n number of regional-scale event classes p pressure P probability Ø large-scale event regional-scale event q _v specific humidity potential temperature u west-east wind component v south-north wind componentAbbreviations AGL above ground level - LT local time - UTC universal time coordinated With 13 Figures     

The Mechanism of Reactive NO3 Uptake on Dry NaX (X=Cl, Br)

A simple kinetic mechanism of nitrate radicals uptake on dry sea-salt NaCl, NaBr surfaces is proposed. The mechanism includes adsorption/desorption equilibrium and unimolecular decomposition of the adsorbed complex: NO₃(g) + NaX(s) (NO₃-NaX)(s); (NO₃-NaX)(s) NaNO₃ + X(s) Two techniques were used: the matrix isolation ESR and mass spectrometry. The uptake coefficient () is found to be dependent on exposure time of salt to NO₃ for raw coating. The initial (t0) is higher than the observable steady-state _obs. At room temperature _obs is independent of [NO₃] at low [NO₃] = 3 × 10⁹ - 10¹¹ cm^-3, but it is inversely proportional to [NO₃] at concentrations higher than 10¹² cm^-3. At temperatures above 100 °C, _obs becomes independent of [NO₃] in a wider range of [NO₃]. An increased number of dislocations is supposed to exist in the case of raw coating. Due to a wide spread of the surface sites binding energy with the ionic lattice near dislocations, the part of surface complexes has lower binding energy and "burns" more rapidly. That burning determines the transition from (t0) down to _obs.The kinetic parameters and elementary rate coefficients are obtained. The recommended for low atmospheric NO₃ concentration are in the range of 0.002 ± 0.04 for NaCl and 0.1-0.3 for NaBr depending on a mechanism of the (t) relaxation.     

Drag and drag partition on rough surfaces

An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio _S/ of the stress _s on the underlying ground surface to total stress ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation _S/= 1/(1+), where = C_RC_S the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.     

Analytical investigations of horizontal meso-scale momentum equations with Newtonian nudging

Summary This study presents an analytical investigation of the local behaviour of the solution to a mesoscale model with Newtonian nudging when observed winds are time varying. The analysis examines each Fourier component of the time series of observed winds. Unlike the case with a constant observed wind, the nudged wind vector does not asymptotically approach the observed wind. In response to sinusoidal oscillation of the observed wind, the nudged wind vector is always on a half circle connecting the vector ends of the observed and un-nudged modelled winds. When nudging parameter 0, the nudged wind vector approaches the un-nudged wind; when , the nudged wind vector approaches the observed wind. For commonly used values of nudging parameter , the modelled wind field always carries errors.A target nudging scheme is devised in this study in order to ensure the model result is identical to observed winds with sinusoidal oscillation. Investigation shows that such a target wind exists for a finite value of , and the magnitude of the target-nudging term is about the same as that of a normal nudging term if f, wheref is the Coriolis parameter and is the frequency of the wind oscillation.With 7 Figures