Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation.Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.

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The particle tracking (PT) technique is used to study turbulent diffusion of particle pairs in a three-dimensional turbulent flow generated by two oscillating grids. The experimental data show a range where the Richardson–Obukhov law 〈r2〉 = Cεt3 is satisfied, and the Richardson–Obukhov constant is found to be C = 0.5. A number of models predict much larger values. Furthermore, the distance–neighbour function is studied in detail in order to determine its general shape. The results are compared with the predictions of three models: Richardson (1926), Batchelor (1952) and Kraichnan (1966a). These three models predict different behaviours of the distance–neighbour function, and of the three, only Richardson's model is found to be consistent with the measurements. We have corrected a minor error in Kraichnan's (1996a) Lagrangian history direct interaction calculations with the result that we had to increase his theoretical value from C = 2.42 to C = 5.5.

Bolund measurements were used for a blind comparison of microscale flow models. Fifty-seven models ranging from numerical to physical were used, including large-eddy simulation (LES) models, Reynolds-averaged Navier-Stokes (RANS) models, and linearized models, in addition to wind-tunnel and water-channel experiments. Many assumptions of linearized models were violated when simulating the flow around Bolund. As expected, these models showed large errors. Expectations were higher for LES models. However, of the submitted LES results, all had difficulties in applying the specified boundary conditions and all had large speed-up errors. In contrast, the physical models both managed to apply undisturbed 'free wind' boundary conditions and achieve good speed-up results. The most successful models were RANS with two-equation closures. These models gave the lowest errors with respect to speed-up and turbulent kinetic energy (TKE) prediction.

Modeling of the systematic errors in the second-order moments of wind speeds measured by continuous-wave (ZephIR) and pulsed (WindCube) lidars is presented. These lidars use the conical scanning technique to measure the velocity field. The model captures the effect of volume illumination and conical scanning. The predictions are compared with the measurements from the ZephIR, WindCube, and sonic anemometers at a flat terrain test site under different atmospheric stability conditions. The sonic measurements are used at several heights on a meteorological mast in combination with lidars that are placed on the ground. Results show that the systematic errors are up to 90% for the vertical velocity variance, whereas they are up to 70% for the horizontal velocity variance. For the ZephIR, the systematic errors increase with height, whereas for the WindCube, they decrease with height. The systematic errors also vary with atmospheric stability and are low for unstable conditions. In general, for both lidars, the model agrees well with the measurements at all heights and under different atmospheric stability conditions. For the ZephIR, the model results are improved when an additional low-pass filter for the 3-s scan is also modeled. It is concluded that with the current measurement configuration, these lidars cannot be used to measure turbulence precisely.

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R 2 120:740. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. ParisiFrisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

We present a general approach for estimating systematic and random errors in eddy correlation fluxes and flux gradients measured by aircraft in the convective boundary layer as a function of the length of the flight leg, or of the cutoff wavelength of a highpass filter. The estimates are obtained from empirical expressions for various length scales in the convective boundary layer and they are experimentally verified using data from the First ISLSCP (International Satellite Land Surface Climatology Experiment) Field Experiment (FIFE), the Air Mass Transformation Experiment (AMTEX), and the Electra Radome Experiment (ELDOME). We show that the systematic flux and flux gradient errors can be important if fluxes are calculated from a set of several short flight legs or if the vertical velocity and scalar time series are high-pass filtered. While the systematic error of the flux is usually negative, that of the flux gradient can change sign. For example, for temperature flux divergence the systematic error changes from negative to positive about a quarter of the way up in the convective boundary layer. 1o Introduction Analysis of aircraft eddy correlation flux measurements from the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) has indicated that significant systematic errors can be introduced by high-pass filtering the vertical velocity w and scalar s time series used in calculating the eddy correlation fluxes and possibly by inadequate length of the flight legs [Betts et al., 1990; Kelly et al., 1992; Grossman, 19924, b]. Not only is the flux itself affected, but also the vertical divergence of the flux, which is a term in the budget equation for so Although this issue is of immediate relevance to the FIFE results, as presented in the special issue of the Journal of Geophysical Research, 97 (D17), 1992, it is of critical importance for any field program involving aircraft flux measurements. Therefore we present here a general approach for consideration of systematic errors in fluxes measured in the convective boundary layer (CBL) as a function of the length of the flight leg, or of the cutoff wavelength of a high-pass filter. One measure of the importance of the systematic error is to compare it with the random error, which we also estimateø We build on the results of Lenschow and $tankov [1986] and of Lenschow et al. [1994] to predict the