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.     

Wind forcing due to synoptic storm activity over the North Pacific Ocean

Abstract

Six‐hourly surface wind analyses over the North Pacific Ocean covering the 10‐year period 1969–78 are used to describe synoptic storm activity in terms of parameters that are directly related to the atmospheric forcing of the ocean. The cube of the atmospheric friction velocity, u³ _* and the curl of the surface wind stress, curl τ, are used because of their relationship to turbulent vertical mixing and Ekman pumping in the ocean, respectively. In an attempt to isolate synoptic disturbances from mean fields, the time series of surface wind components at each individual grid point are partitioned into “high‐pass” (periods shorter than 10 days) and “low‐pass” (periods longer than 10 days) components by means of conventional filtering procedures. The two quantities u³ _* and curl τ are then calculated from (a) the high‐pass filtered wind components only, (b) a combination of the filtered wind components that include the interaction between the high‐ and low‐pass fields, and (c) the unfiltered wind components. These quantities describe the atmospheric forcing of the ocean that is attributable to (a) synoptic storm activity by itself, (b) synoptic storm activity in the presence of the low‐pass (mean) flow, and (c) the total spectrum of wind forcing, respectively.

Maps of the long‐term (10‐year) monthly mean u³ _* calculated from (a) and (b) are coherent across the mid‐latitude North Pacific and appear to coincide with the normal seasonal evolution of synoptic storm activity in that region. In mid‐latitudes, the values of u³ _* calculated from (a) and (b) are 27 and 83%, respectively, of the value of u³ _* itself. Thus, a major fraction of the production of turbulent energy available for mixing in the upper layers of the ocean comes from synoptic disturbances with a period shorter than 10 days. Maps of the long‐term monthly mean wind stress curl are quite different in that the mean wind stress curl calculated from (a) is essentially negligible. However, the mean curl calculated from (b) closely resembles the pattern of total curl (c), but with a magnitude of only 41% of (c). Thus, synoptic disturbances with a period shorter than 10 days are also responsible for a significant fraction of the Ekman pumping of the ocean.

Future studies with these data will attempt to determine whether a relationship exists between synoptic storm activity, as measured by the parameters developed in this study, and large‐scale sea‐surface temperature anomalies.     

Large-Scale Turbulence Structures and Their Contributions to the Momentum Flux and Turbulence in the Near-Neutral Atmospheric Boundary Layer Observed from a 213-m Tall Meteorological Tower

Large-scale turbulence structures in the near-neutral atmospheric boundary layer (ABL) are investigated on the basis of observations made from the 213-m tall meteorological tower at Tsukuba, Japan. Vertical profiles of wind speed and turbulent fluxes in the ABL were obtained with sonic anemometer-thermometers at six levels of the tower. From the archived data, 31 near-neutral cases are selected for the analysis of turbulence structures. For the typical case, event detection by the integral wavelet transform with a large time scale (180 s) from the streamwise velocity component (u) at the highest level (200 m) reveals a descending high-speed structure with a time scale of approximately 100 s (a spatial scale of 1 km at the 200-m height). By applying the wavelet transform to the u velocity component at each level, the intermittent appearance of large-scale high-speed structures extending also in the vertical is detected. These structures usually make a large contribution to the downward momentum transfer and induce the enhancement of turbulent kinetic energy. This behaviour is like that of “active” turbulent motions. From the analysis of the two-point space–time correlation of wavelet coefficients for the u velocity component, the vertical extent and the downward influence of large-scale structures are examined. Large fluctuations in the large-scale range (wavelet variance at the selected time scale) at the 200-m level tend to induce the large correlation between the higher and lower levels.     

Turbulence characteristics in the atmospheric surface layer during summer monsoon of 1997 over a semi-arid location in India

A land surface processes experiment (LASPEX) was conducted in the semi-arid region of Northwest India during January 1997–February 1998. Analysis of turbulent components of wind and air temperature collected in the surface layer (SL) at Anand (22°35′N, 72°55′E) during the Indian summer monsoon season from June to September 1997 is presented. Turbulent fluctuation of wind components and air temperature observed at Anand varied as a function of terrain features and stability of the surface layer. Under neutral conditions, the standard deviation of vertical velocity (σ _w ) and temperature (σ _T ) were normalized using respective surface layer scaling parameter u _* and T _* which fitted the expressions σ _w /u _* = 1.25 and σ _T /T _* ≈ 4. Micrometeorological spectrum of wind and temperature at 5 m above ground level (AGL) at Anand showed peaks at time scale of 1–3 min at the low-frequency end. The inertial sub-range characteristics (?2/3 slope) of the spectrum are exhibited mostly. However, in some occasions, slope of ?1 denoting brown noise was depicted by the wind and temperature spectrum, which indicated anisotropy in turbulence.     

Seasonal and diurnal variations of coherent structures over a deciduous forest

Coherent structures in turbulent flow above a midlatitude deciduous forest are identified using a wavelet analysis technique. Coupling between motions above the canopy (z/h=1.5, whereh is canopy height) and within the canopy (z/h=0.6) are studied using composite velocity and temperature fields constructed from 85 hours of data. Data are classified into winter and summer cases, for both convective and stable conditions. Vertical velocity fluctuations are in phase at both observation levels. Horizontal motions associated with the structures within the canopy lead those above the canopy, and linear analysis indicates that the horizontal motions deep in the canopy should lead the vertical motions by 90°. On average, coherent structures are responsible for only about 40% of overall turbulent heat and momentum fluxes, much less than previously reported. However, our large data set reveals that this flux fraction comes from a wide distribution that includes much higher fractions in its upper extremes. The separation distanceL _s between adjacent coherent structures, 6–10h, is comparable to that obtained in previous observations over short canopies and in the laboratory. Changes in separation between the summer and winter (leafless) conditions are consistent withL _s being determined by a local horizontal wind shear scale.     

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.     

An experimental investigation of a wind-generated suspension of particulate matter from a tailings disposal area

A wind tunnel investigation of the wind erosion of uranium mine-tailings material typical of a northern Ontario site has been carried out. The aim of the study was to measure the effects of various parameters, including mean and turbulent wind characteristics of the boundary layer and surface moisture content, upon the erosion process. The analysis of experimental data has yielded a mathematical model for predicting the net vertical mass fluxes. The results show that the dry vertical flux is proportional to u _* ^2.3and the wet flux to u _* ^5.0 Partical size analysis was also carried out.     

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.     

The characteristics of a laboratory produced turbulent Ekman layer

The characteristics of the atmospheric turbulent Ekman boundary layer have been qualitatively simulated in an annular rotating wind tunnel. Observed velocity spirals found to exist within the wind tunnel resembled qualitatively those found in the atmosphere in that a two-layer structure was evident, consisting of a log-linear portion topped by an outer spiral layer. The magnitude of the friction velocity u _* obtained from the log-linear profile agreed with that measured directly, i.e., that obtained from the relation: u _* = (u′w′)^1/2. Also, the effects of surface roughness on the characteristics of the boundary layer agreed with expected results. In cases where the parametric behaviour predicted by theory departed from the observed behaviour, the probable cause was the inherent size limitations of the wind tunnel. The ability to maintain dynamic similarity is constrained by the limited radius of curvature of the wind tunnel. The vertical distribution of turbulent intensity in the wind tunnel was found to agree qualitatively with an observed atmospheric distribution. Also, a vertical distribution of eddy diffusivity was calculated from tunnel data and found to give qualitatively what one might expect in the atmosphere.     

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.     

Triple-Hot-Film Anemometer Performance in Cases-99 and A Comparison With Sonic Anemometer Measurements

Two levels of triple-hot-film and sonic anemometers were deployed on a 5.5-m towerduring the Cooperative Atmospheric Surface Exchange Study (CASES-99) in October1999. Each triple-hot-film probe was collocated 50 mm from the sonic sensing path ona common boom. Various problems with using triple-hot-films in the atmosphere toresolve wind components are addressed including the derivation of a yaw angle correction using the collocated sensors. It was found that output voltage drift due to changes in environmental temperature could be monitored and corrected using an automated system. Non-unique solutions to heat transfer equations can be resolved using a collocated sonic anemometer. Multi-resolution decomposition of the hot-film data was used to estimate appropriate day and night averaging periods for turbulent flux measurements in and near the roughness sub-layer. Finally, triple-hot-film measurements of mean wind magnitude (M), turbulent kinetic energy (TKE), sensible heat flux (H), and local friction velocity (u_*) are compared to those of the collocated CSAT3 sonic anemometers. Overall, the mean wind magnitudes measured by the triple-hot-film and the collocated sonic sensorswere close, consistent and independent of stability or proximity to the ground. The turbulent statistics, TKE, u_*, and H, measured by the two sensor systems were reasonably close together at z = 5 m. However, the ratio of sonic measurement/hot-film measurement decreased toward the ground surface, especially during stable conditions.     

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375?C395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u _*/u _*R , where u _* is the friction velocity and u _*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

A note on albedo variations of the frozen surface of Lake Simcoe during march, 1978: Research note

Abstract

The relationships between monthly anomalies of sea surface temperature (SST) and monthly anomalies of several surface wind parameters are examined using ten years of data from the mid‐latitude North Pacific Ocean. The wind parameters involve both u³ _* and curl τ, where u_* is the atmospheric friction velocity and τ the surface stress. These quantities are calculated from surface wind components analysed on synoptic (6‐hourly) maps. In order to examine the effect of synoptic disturbances, the time series of surface wind components at each grid point is high‐pass filtered (passing periods less than 10 days) and the above wind parameters are calculated from both filtered and unfiltered wind components.

Two statistically significant relationships are found between monthly anomalies of SST and those of the various wind parameters. The first is a large coherent negative correlation between monthly anomalies of u³ _* calculated from the high‐pass filtered wind components and month‐to‐month changes in the SST anomalies in the Central Pacific. This relationship is attributed to the production of turbulent vertical mixing in the ocean by synoptic disturbances in the atmosphere. The second relationship is a large positive correlation between curl τ calculated from the unfiltered wind components and SST anomaly changes in the Eastern Pacific. This relationship, which is opposite to that expected from Ekman pumping, is attributed to a negative association between the wind stress curl and the meridional advection of heat by the eastern boundary current system. It is shown that these atmospheric forcing mechanisms explain up to 10 per cent of the variance of monthly SST anomalies in a large part of the mid‐latitude North Pacific Ocean. This amount is in addition to, but certainly less than, that which can be explained by anomalous horizontal advection through statistical relationships with sea‐level pressure anomalies (Davis, 1976).     

Structure Function Analysis of Two-Scale Scalar Ramps. Part II: Ramp Characteristics and Surface Renewal Flux Estimation

Ramp features in the turbulent scalar field are associated with turbulent coherent structures, which dominate energy and mass fluxes in the atmospheric surface layer. Although finer scale ramp-like shapes embedded within larger scale ramp-like shapes can readily be perceived in turbulent scalar traces, their presence has largely been overlooked in the literature. We demonstrate the signature of more than one ramp scale in structure functions of the turbulent scalar field measured from above bare ground and two types of short plant canopies, using structure-function time lags ranging in scale from isotropic to larger than the characteristic coherent structures. Spectral analysis of structure functions was used to characterize different scales of turbulent structures. By expanding structure function analysis to include two ramp scales, we characterized the intermittency, duration, and surface renewal flux contribution of the smallest (i.e., Scale One) and the dominant (i.e., Scale Two) coherent structure scales. The frequencies of the coherent structure scales increase with mean wind shear, implying that both Scale One and Scale Two are shear-driven. The embedded Scale One turbulent structure scale is ineffectual in the surface-layer energy and mass transport process. The new method reported here for obtaining surface renewal-based scalar exchange works well over bare ground and short canopies under unstable conditions, effectively eliminating the α calibration for these conditions and forming the foundation for analysis over taller and more complex surfaces.     

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windu _g . The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.     

Tilt errors and precipitation effects in trivane measurements of turbulent fluxes over open water

For 390 ten-minute samples of turbulent flux, made with a trivane above a lake, the vertical alignment is determined within 0.1 ° through azimuth-dependent averaging. One degree of instrumental misalignment is found to produce an average tilt error of 9 ± 4% for momentum flux, and 4 ± 2% for heat flux. The tilt error in the vertical momentum flux depends mainly ons _u/u_*, and cannot be much diminished with impunity by high-pass pre-filtering of the turbulence signals. The effects of rain on trivane measurements of vertical velocity are shown to be negligible at high wind speeds, and adaptable to correction in any case.The normalized vertical velocity variance,s _w/u_*, appears to be proportional to the square root ofz/L for unstable stratification. For a wind speed range of 2 to 15 m s^–1, the eddy correlation stresses measured at 4- and 8-m heights can be reasonably well estimated by using a constant drag coefficientC _d=1.3 X 10^-3, while cup anemometer profile measurements give an overestimate of eddy stress at high wind speeds. A good stress estimate is also obtained from the elevation variance; it is suggested that trivane measurement of this variance might be made from a mobile platform, e.g., a moderately stabilized spar buoy.     

Detection of turbulent coherent motions in a forest canopy part I: Wavelet analysis

Turbulence measurements performed at high frequencies yield data revealing intermittent and multi-scale processes. Analysing time series of turbulent variables thus requires extensive numerical treatment capable, for instance, of performing pattern recognition. This is particularly important in the case of the atmospheric surface layer and specifically in the vicinity of plant canopies, where largescale coherent motions play a major role in the dynamics of turbulent transport processes. In this paper, we examine the ability of the recently developedwavelet transform to extract information on turbulence structure from time series of wind velocities and scalars. It is introduced as a local transform performing a time-frequency representation of a given signal by a specific wavelet function; unlike the Fourier transform, it is well adapted to studying non-stationary signals. After the principles and the most relevant mathematical properties of wavelet functions and transform are given, we present various applications of relevance for our purpose: determination of time-scales, data reconstruction and filtering, and jump detection. Several wavelet functions are inter-compared, using simple artificially generated data presenting large-scale features similar to those observed over plant canopies. Their respective behaviour in the time-frequency domain leads us to assign a specific range of applications for each.     

A numerical study of the convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio –z _i /L _*=26. However, when heating is more moderate (so that –z _i /L _*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.     

Large-Eddy Simulation for the Mechanism of Pollutant Removal from a Two-Dimensional Street Canyon

Large-eddy simulation (LES) is conducted to investigate the mechanism of pollutant removal from a two-dimensional street canyon with a building-height to street-width (aspect) ratio of 1. A pollutant is released as a ground-level line source at the centre of the canyon floor. The mean velocities, turbulent fluctuations, and mean pollutant concentration estimated by LES are in good agreement with those obtained by wind-tunnel experiments. Pollutant removal from the canyon is mainly determined by turbulent motions, except in the adjacent area to the windward wall. The turbulent motions are composed of small vortices and small-scale coherent structures of low-momentum fluid generated close to the plane of the roof. Although both small vortices and small-scale coherent structures affect pollutant removal, the pollutant is largely emitted from the canyon by ejection of low-momentum fluid when the small-scale coherent structures appear just above the canyon where the pollutant is retained. Large-scale coherent structures also develop above the canyon, but they do not always affect pollutant removal.