Turbulent Velocity Variances Research Articles

An atmospheric turbulent velocity spectrum for three dimensions

A simple parametric model is developed that extends and unifies the usual phenomenological description of turbulent atmospheric velocity variances and correlations. The multidimensional spectral model thus defined allows any second‐order statistical quantity involving velocity to be calculated. The model parameters are determined by fitting them to published single‐point measurements of temporal spectra over land, which shows the ability of the model to efficiently and naturally account for observed differences in the low‐frequency behavior of spectra for different velocity components. The scheme is first tested by comparing its predictions for correlations to other data. The utility of the model is illustrated and its predictions are further tested by comparing to a set of optical ocean image data that exposes the two‐dimensional patterns of wind speed fluctuations in Taylorized flow. These exhibit the predicted anisotropy of the spectrum. Some detailed issues in the model for optical response to wind fluctuations are discussed.

Dependence of Turbulent and Mesoscale Velocity Variances on Scale and Stability

The scale dependence of velocity variances is studied using data collected from a grassland site, a heather site, and four forested sites. The dependence of velocity variances on averaging time, used to define the fluctuation quantities, is modeled. The crosswind velocity variance is emphasized, because it is more difficult to model than the other two components and is crucial input for applications such as dispersion modeling. The distinction between turbulence and mesoscale variances is examined in detail. Because mesoscale and turbulence motions are governed by different physics, meaningful study of the behavior of velocity variances requires adequate separation of turbulence and mesoscale motions from data. For stable conditions, the horizontal velocity variances near the surface exhibit a spectral gap, here corresponding to a very slow or nonexistent increase of variance with increasing averaging time. This “gap region,” when it occurs, allows separation of mesoscale and turbulence motions; however, the averaging times corresponding to this gap vary substantially with stability. A choice of typical averaging times for defining turbulent perturbations, such as 5 or 10 min, leads to the capture of significant mesoscale motions for very stable conditions and contributes to the disagreement with turbulence similarity theory. For unstable motions, the gap region for the horizontal velocity variances shrinks or becomes poorly defined, because large convective eddies tend to “fill in” the gap between turbulence and mesoscale motions. The formulation developed here allows turbulence and mesoscale motions to overlap into the same intermediate timescales. The mesoscale variances are less predictable, because a wide variety of physical processes contribute to mesoscale motions. Their magnitude and range of timescales vary substantially among sites. The variation of the behavior of turbulence variances among sites is significant but substantially less than that for the mesoscale motions.

An Intercomparison Study Using Electromagnetic Three-Component Turbulent Velocity Probes

Abstract An intercomparison study was performed with four Russian-made, electromagnetic probes capable of measuring three components of oceanic turbulent velocities and two single-axis velocity sensors familiar to western scientists, namely, a hot-film anemometer and an airfoil shear probe. The intercomparison measurements were conducted in a water flume tank in the Marine Scientific Production Corporation on Fishery Technology facility in Kaliningrad, Russia. Measurements were obtained in the turbulent region generated behind a grid at three different mean flow speeds (0.7, 1.1, and 1.7 m s−1). In all the intercomparison runs, data from the electromagnetic velocity probes behave in a manner expected from the sensor and filtering characteristics. On the average, turbulent velocity variances from the electromagnetic probes are about ±20% of those from both the hot-film and airfoil probes.

Observations of Turbulence in a Partially Stratified Estuary

The authors present a field study of estuarine turbulence in which profiles of Reynolds stresses were directly measured using an ADCP throughout a 25-h tidal day. The dataset that is discussed quantifies turbulent mixing for a water column in northern San Francisco Bay that experiences a sequence of states that includes a weak ebb and flood that are stratified, followed by a strong, and eventually unstratified, ebb and flood. These measurements show that energetic turbulence is confined to a bottom mixed layer by the overlying stratification. Examination of individual Reynolds stress profiles along with profiles of Richardson number and turbulent Froude number shows that the water column can be divided into regions based on the relative importance of buoyancy effects. Using the measured turbulence production rate P, the dissipation rate ϵ is estimated. The observed turbulence had values of ϵ/νN2 > 20 all of the time and ϵ/νN2 > 200 most of the time, suggesting that the observed motions were buoyancy affected turbulence rather than internal waves. However, at times, turbulent Froude numbers in much of the upper-water column were less than one, indicating important stratification effects. Taken as a whole, the data show that stratification affects the turbulent velocity variance q2 most severely; that is, observed reductions in u′w′ are largely associated with small values of q2 rather than with a dramatic reduction in the efficiency with which turbulent motions produce momentum fluxes. Finally, the dataset is compared to predictions made using the popular Mellor–Yamada level 2.5 closure. These comparisons show that the model tends to underestimate the turbulent kinetic energy in regions of strong stratification where the turbulence is strongly inhomogeneous and to overestimate the turbulent kinetic energy in weakly stratified regions. The length scale does not appear to compensate for these errors, and, as a result, similar errors are seen in the eddy viscosity predictions. It is hypothesized that the underestimation of q2 is due to an inaccurate parameterization of turbulence self-transport from the near-bed region to the overlying stratification.

Air‐sea fluxes and surface layer turbulence around a sea surface temperature front

The response of the lower marine atmospheric boundary layer to sharp changes in sea surface temperature was studied in the Frontal Air‐Sea Interaction Experiment (FASINEX) with aircraft and ships measuring mean and turbulence quantities, sea surface temperature, and wave state. Changing synoptic weather on 3 successive days provided cases of wind direction both approximately parallel and perpendicular to a surface temperature front. For the wind perpendicular to the front, both wind over cold‐to‐warm and warm‐to‐cold surface temperatures occurred. For the cold‐to‐warm case, the unstable boundary layer was observed to thicken, with increased convective activity on the warm side. For the warm‐to‐cold case, the surface layer buoyant stability changed from unstable to neutral or slightly stable, and the sea state and turbulence structure in the lower 100 m were immediately altered, with a large decrease in stress and slowing of the wind. Measurements for this case with two aircraft in formation at 30 and 100 m show a slightly increased stress divergence on the cold side. The turbulent velocity variances changed anisotropically across the front: the streamwise variance was practically unchanged, whereas the vertical and cross‐stream variances decreased. Model results, consistent with the observations, suggest that an internal boundary layer forms at the sea surface temperature front. The ocean wave, swell, and microwave radar backscatter fields were measured from several aircraft which flew simultaneously with the low‐level turbulence aircraft. Significant reductions in backscatter and wave height were observed on the cold side of the front.

A second-order closure model for flow through vegetation

By splitting the turbulent kinetic energy into two wavebands and adopting as the turbulence timescale the ratio k/ɛ of the kinetic energy in the low-frequency band to its turnover-rate, the second-order closure scheme of Launder et al. (1975) has been adapted for flow through vegetation. Predictions of the model compare satisfactorily with observations of the mean windspeed and (somewhat less satisfactorily) with the turbulent velocity variances in two very different canopies.

A Gaussian Plume Model of Atmospheric Dispersion Based on Second-Order Closure

A practical model of atmospheric dispersion of a passive tracer based on systematic reduction of the second-order closure transport equations using Gaussian shape assumptions is presented. The model is comparable with conventional Gaussian plume models in complexity, but still maintains the capability to also predict concentration fluctuation variance and to utilize direct measurements of turbulent velocity variances in a consistent manner. Comparison with laboratory data demonstrates the model's ability to produce reasonable predictions for the concentration field.

Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance

Recent papers by Wilson et al. (1981b) and Legg and Raupach (1982) give methods for the calculation of particle trajectories in turbulence with a gradient in vertical velocity variance Σ2w. However the two methods seem contradictory.

Nonlinear Eddy-Viscosity Turbulence Parameterization in Anelastic Three-Dimensional Flow: Some Mathematical Aspects

This paper considers some mathematical aspects of the nonlinear eddy-viscosity turbulence parameterization with quasi-isotropic partitioning of turbulent kinetic energy in three-dimensional anelastic flow. The parameterization, which several investigators have used with the Boussinesq approximation in simulating boundary layer flow and shallow cumulus convection, is generalized in a reasonable way, modifying the formulations of subgrid velocity variances and mean flow deformation to take nonzero three-dimensional divergence into account. It is shown that while strict dissipation of domain-integrated mean kinetic energy due to turbulence is insured for Boussinesq flow, a source/sink term analogous to the pressure-divergence term is also formally present for anelastic flow. Also, in seeking a straightforward parameterization of turbulent kinetic energy so as to insure mathematical realizability for the turbulent velocity variance and covariances, it is found that the formulation of Lilly (1967) meets these requirements provided that his proportionality factor is suitably restricted. In turn, this places a restriction on the relative magnitudes of two universal constants that arise in a more recent formulation of Deardorff (1973). (1973).