Wind Tunnel simulation of diffusion in a convective boundary layer

A study of turbulent dispersion of passive tracers in unstable boundary layers, conducted in the Meteorological Wind Tunnel of the Fluid Dynamics and Diffusion Laboratory at Colorado State University, is described. The measured mean and turbulent velocities are found to be similar to those measured in atmospheric convective boundary layers. The diffusion pattern, from ground-level and elevated sources over both a smooth floor and a rough floor, is found to be the same as that measured in the water-tank experiments of Deardorff and Willis (1975) and in numerical models. The measurements show an initial rapid descent of plumes from elevated sources and a subsequent plume rise at t^* > 0.5 h/w^*. Ground-level concentrations from elevated sources are found to be larger, at certain distances from the source, than those from a ground-level source of equal strength. The measurements of the cross-wind spread _v are in agreement with the Prairie Grass measurements and confirm earlier predictions that the initial cross-wind spread for ground-level sources is larger than that for elevated sources.     

Turbulent dispersion in coastal atmospheric boundary layers: An application of a Lagrangian model

A Lagrangian model is applied to simulate the dispersion of passive tracers (in particular, water vapour) in coastal atmospheric boundary layers under onshore wind conditions. When applied to convective boundary layers over uniform surfaces, the model gives results in agreement with those of similar studies. Numerical simulation of turbulent dispersion in coastal areas also reproduces the basic features known from experimental studies. Under onshore wind conditions, the humidity field is plume-shaped with the maximum vertical transport being over land downstream of the coast line. The model shows that the surface sensible heat flux over land, the static stability of the onshore air flow and the onshore wind speed are the most important factors determining the basic features of turbulent dispersion in coastal areas.     

Markov chain simulations of vertical dispersion from elevated sources into the neutral planetary boundary layer

A Lagrangian statistical-trajectory model based on a Markov chain relation is used to investigate vertical dispersion from elevated sources into the neutral planetary boundary layer. The model is fully two-dimensional, in that both vertical and longitudinal velocity fluctuations, and their correlation, are simulated explicitly. The best observational information currently available is used to characterize the mean and turbulent structure of the neutral boundary layer. In particular, a realistic vertical profile of the Lagrangian integral time scale is proposed, based partly on a review of direct measurements and partly on a comparison of the model predictions with published diffusion data. The model predictions are shown to agree well with a variety of dispersion observations. The model is used to study vertical diffusion as a function of release height H, friction velocity u* and surface roughness z ₀ for downwind distances up to 10 km from the source. The equivalent Gaussian dispersion parameter Σ _z is shown to decrease slightly with an increase in H, and to increase with increases in z ₀ or u*. It is demonstrated that relationships valid in a field of homogeneous turbulence can be applied to vertical dispersion in the atmosphere if the release occurs above the region of strongest gradients in the mean and turbulent parameters. Scaling in terms of the standard deviation in elevation angle of the wind at the release point leads to a universal curve which provides accurate estimates of Σ _z over a wide range of values of H, z ₀ and the meteorological parameters.     

Note on a Parametric Relation for Separating Flow over a Rough Hill

A parametrization method used to account for the effects of flow separation and wall roughness on the lower boundary condition for turbulent boundary layers is investigated against direct numerical simulation and laser Doppler anemometry data. The numerical simulation represents flow over a smooth, flat surface with a prescribed external adverse pressure gradient. The water-channel experiments cover flow over smooth and rough hills for two specified Reynolds numbers. Global optimization algorithms based on four different direct search methods are used to assess the parametrization function, C, in terms of local mean velocity profiles and the parametrization parameters u _* (friction velocity), ∂ _x p (local pressure gradient), z ₀ (effective roughness) and d (zero-plane displacement). The study investigates regions of attached and reversed flows, and forty-two velocity profiles are compared with the proposed expression for the function C, including two profiles that satisfy the solution of Stratford.     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Estimation of the Lagrangian Velocity Structure Function Constant C0 by Large-Eddy Simulation

The inertial subrange Kolmogorov constant C ₀, which determines the effective turbulent diffusion in velocity space, plays an important role in the Lagrangian modelling of pollutants. A wide range of values of the constant are found in the literature, most of them determined at low Reynolds number and/or under different assumptions. Here we estimate the constant C ₀ by tracking an ensemble of Lagrangian particles in a planetary boundary layer simulated with a large-eddy simulation model and analysing the Lagrangian velocity structure function in the inertial subrange. The advantage of this technique is that it easily allows Reynolds numbers to be achieved typical of convective turbulent flows. Our estimates of C ₀ is C ₀=4.3±0.3 consistent with values found in the literature     

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Observation of lake breeze penetration and subsequent development of the thermal internal boundary layer for the Nanticoke II Shoreline Diffusion Experiment

The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing _gq/_*, _u /w _* and _w /w _* between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /_* values showed reasonable agreement; however, _u /w _* and _w /W_* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer

The dissipation rate of turbulent kinetic energy, , and the temperature structure function parameter, C _T ², have been measured over water from the near surface (Z = 3 m) to the top of the boundary layer. The near surface values of and C _T ² were used to calculate the velocity and temperature Monin-Obukhov scaling parameters u _* and T _*. The data collected during unstable lapse rates were used to evaluate the feasibility of extrapolating the values of and C _T ² as a function of height with empirical scaling formulae. The dissipation rate scaling formula of Wyngaard et al. (l971 a) gave a good fit to an average of the data for Z < 0.8 Z _i. In the surface layer the scaling formula of Wyngaard et al. (1971b) disagreed with the C _T ² values by as much as 50%. This disagreement is due to an unexpected reduction in the measured values of C _T ² forZ < 30 m. At this point it is not clear if the discrepancy is a unique property of the marine boundary layer or if it is simply some unknown instrumental or analytical problem. The mixed layer scaling results were similar to the overland results of Kaimal et al. (1976).     

A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows

The existence of universal power laws at low wavenumbers (K) in the energy spectrum (E_u) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong- and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E_u at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solution for E_u, the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet E_u spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in E_u(= C_uuu² _* K^-1, where C_uu is a constant and u_* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's inactive eddy motion hypothesis, and the Perry et al. analysis.     

Characteristics of the Lyman-alpha humidiometer and measurements of turbulent humidity fluctuations over the ocean

The characteristics of a Lyman-alpha humidiometer have been carefully examined in an air-conditioned test chamber. The results confirm that when carefully used, this humidiometer is suitable for measurements of turbulent humidity fluctuations. Measurements with a Lyman-alpha humidiometer were carried out in the surface boundary layer over the ocean. The relation between turbulent intensity ( _a = a ^ov2) and the friction humidity (a _*) can be expressed as _a = l.6a _*. The spectrum of turbulent humidity for wind speeds larger than 3 m s ^–1 conforms to the similarity law in the surface boundary layer. The spectrum has two characteristic normalized frequencies, namely, a higher peak and a secondary peak (or a shoulder).     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient     

Formulation of stability-dependent empirical relations for turbulent intensities from surface layer turbulence measurements for dispersion parameterization in a lagrangian particle dispersion model

Season- and stability-dependent turbulence intensity (σ _u /u _*, σ _v /u _*, σ _w /u _*) relationships are derived from experimental turbulence measurements following surface layer scaling and local stability at the tropical coastal site Kalpakkam, India for atmospheric dispersion parameterization. Turbulence wind components (u′, v′, w′) measured with fast response UltraSonic Anemometers during an intense observation campaign for wind field modeling called Round Robin Exercise are used to formulate the flux–profile relationships using surface layer similarity theory and Fast Fourier Transform technique. The new relationships (modified Hanna scheme) are incorporated in a Lagrangian Particle Dispersion model FLEXPART-WRF and tested by conducting simulations for a field tracer dispersion experiment at Kalpakkam. Plume dispersion analysis of a ground level hypothetical release indicated that the new turbulent intensity formulations provide slightly higher diffusivity across the plume relative to the original Hanna scheme. The new formulations for σ _u , σ _v , σ _w are found to give better agreement with observed turbulent intensities during both stable and unstable conditions under various seasonal meteorological conditions. The simulated concentrations using the two methods are compared with those obtained from a classical Gaussian model and the observed SF₆ concentration. It has been found that the new relationships provide comparatively higher diffusion across the plume relative to the model default Hanna scheme and provide downwind concentration results in better agreement with observations.     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.     

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale ( ):l = e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w_*), h/w_*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.     

Corrections to the Mathematical Formulation of a Backwards Lagrangian Particle Dispersion Model

This technical note introduces some corrections to the Lagrangian particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367–389, 1986). Careful mathematical derivation following the detailed explanations in that paper uncovered some unit inconsistencies that were the result of mistaken function definitions. Errors are noted in the drift correction, or “probability current” of the particle dispersion model as well as in parameterization of turbulence terms, which are necessary inputs to the model. The probability current comprises Gaussian, convective, and solenoidal components, with derivation errors discovered in the latter two components. All errors are presented along with new formulations that are mathematically consistent, correct the original problems, and adhere to the underlying Gaussian nature of the particle dispersion phenomenon. The corrections shown here should provide more accurate results for particle dispersion models based upon the work of Rotach et al., as well as resolve points of confusion for future researchers referring to that work.     

Displaced-Beam Small Aperture Scintillometer Test. Part I: The Wintex Data-Set

The friction velocity (u_*) and the sensible heat flux density (H) determined with a displaced-beam small aperture scintillometer (DBSAS) and a hot-film eddy correlation system are compared. Random errors in the DBSAS are relatively small, compared to scatter found with two eddy-correlation systems. Assuming that the hot-film system yields the true fluxes, theDBSAS appears to overestimate u_* when u_* is less than 0.2 m s^-1 and to underestimate u_* at high wind speeds. This implies that the DBSAS measurements of theinner scale length of turbulence, l₀, a direct measure for the dissipation rate of kinetic turbulent energy, are biased. Possible causes for these results are discussedin detail. A correction procedure is presented to account for effects of random noise and of so-called inactive turbulence or sensor vibrations. The errors in u_* cause errors in the DBSAS measurements of the structure parameter of temperature C_T ². The derived H appears to be less sensitive to errors in l₀ and C_T ², because errors in these quantities tend to cancel out.     

Dynamics of lateral boundary meso-scale jet in the ocean and atmosphere

By using an ageostrophic shallow water model, it is pointed out that a kind of lateral boundary meso-scales jet can be established near the plateau or coast. The characteristic width of this kind of jet is proportional to the scale ofL _c=L₀(C₀/V_g), whereL ₀=C ₀/f is the radius of Rossby deformation,C ₀=(g ^* H)^1/2 the speed of gravity wave and g^* the reduced gravity. In general,L _c is of the order of one hundred kilometes and tens of kilometers in the atmosphere and in the ocean respectively. The large-scale geostrophic current is an important background condition for forming this kind of jet. From this view point it seems that this kind of atmospheric meso-scale jet only occurs in late spring and summer in the eastern part of Asia, because there is a large-scale south monsoon over there. For the ocean, this kind of meso-scale jet seems to be a semi-persistant system and not to show a significant seasonal variation, and it can be established on both sides of the ocean.     

The turbulent structure of the internal boundary layer near the shore

The mean structure within the internal boundary layer (IBL) near the shore, which develop from the coast in the presence of a sea breeze, has been described in Part I of this study (Ogawa and Ohara, 1984). This paper presents the results of the similarity and energy budget analysis for the purpose of parameterization of the turbulent structure within the IBL. The analysis of the turbulent kinetic energy balance, turbulent intensities and spectra show that the wind is strongly affected by mechanical turbulence in comparison with the past results in a fully developed convective layer where thermal convection dominated. The standard deviations of the wind velocities normalized by the friction velocity u _* (surface-layer scaling parameter) are functions only of the normalized height z/Z _i within 160 m of the shoreline, where Z _i is the IBL. On the other hand, the standard deviations of temperature normalized by _* (mixing-layer scaling parameter) have less scatter with distance than those normalized by T _* (surface-layer scaling parameter). The data showed that both u _* (not a mixed-layer parameter), and Z _i (not a surface-layer parameter) are necessary to describe the turbulent characteristics of the IBL near the shore.Deceased March, 1984.