John C. Wyngaard

Flux-Profile Relationships in the Atmospheric Surface Layer

Abstract Wind and temperature profiles for a wide range of stability conditions have been analyzed in the context of Monin-Obukhov similarity theory. Direct measurements of heat and momentum fluxes enabled determination of the Obukhov length L, a key independent variable in the steady-state, horizontally homogeneous, atmospheric surface layer. The free constants in several interpolation formulas can be adjusted to give excellent fits to the wind and temperature gradient data. The behavior of the gradients under neutral conditions is unusual, however, and indicates that von Karmans constant is ∼0.35, rather than 0.40 as usually assumed, and that the ratio of eddy diffusivities for heat and momentum at neutrality is ∼1.35, compared to the often-suggested value of 1.0. The gradient Richardson number, computed from the profiles, and the Obukhov stability parameter z/L, computed from the measured fluxes, are found to be related approximately linearly under unstable conditions. For stable conditions the Richar...

Turbulence Structure in the Convective Boundary Layer

Abstract Results from a boundary layer experiment conducted over a flat site in northwestern Minnesota are discussed. Wind and temperature fluctuations near the ground were measured with AFCRLs fast-response instrumentation on a 32 m tower. Measurements between 32 m and the inversion base zi were made with MRU probes attached at five different heights to the tethering cable of a 1300 m2 kite balloon. The daytime convective boundary layer appears to be well-mixed with evidence of significant heat and momentum entrainment through the capping inversion. The spectra of velocity components are generalized within the framework of mixed-layer similarity. The characteristic wavelength for w increases linearly with height up to z = 0.l zi following free convection prediction, but approaches a limiting value of 1.5 zi, in the upper half of the boundary layer. The characteristic wavelengths for u and v are maintained at approximately 1.5 zi down to heights very close to the ground. This limiting wavelength correspo...

Local Free Convection, Similarity, and the Budgets of Shear Stress and Heat Flux

Abstract Equations for the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived. The behavior of the production and turbulent transport (flux divergence) terms in each budget is determined directly from measurements obtained over a wide range of stability conditions during the 1968 Kansas field program of AFCRL. The data are presented in the dimensionless form suggested by Monin-Obukhoy similarity theory, and follow universal functions quite well. The theory is extended to the “local free convection” regime which exists under very unstable conditions, and specific power law forms are predicted. Several of these are verified and values are given for the proportionality factors in the power laws. The flux divergence terms are small, implying that in each budget the local production and destruction rates are in balance. The third moments which represent the vertical fluxes of stress and heat flux a...

Toward Numerical Modeling in the “Terra Incognita”

Abstract In mesoscale modeling the scale l of the energy- and flux-containing turbulence is much smaller than the scale Δ of the spatial filter used on the equations of motion, and in large-eddy simulation (LES) it is much larger. Since their models of the subfilter-scale (SFS) turbulence were not designed to be used when l and Δ are of the same order, this numerical region can be called the “terra incognita.” The most common SFS model, a scalar eddy diffusivity acting on the filtered fields, emerges from the conservation equations for SFS fluxes when several terms, including all but one of the production terms, are neglected. Analysis of data from the recent Horizontal Array Turbulence Study (HATS) shows that the neglected production terms can be significant. Including them in the modeled SFS flux equations yields a more general SFS model, one with a tensor rather than a scalar eddy diffusivity. This more general SFS model is probably not necessary in fine-resolution LES or in coarse-resolution mesoscale...

Evaluation of Turbulent Transport and Dissipation Closures in Second-Order Modeling

Abstract We show that the turbulence statistics from our (96)3 large-eddy-simulation (LES) studies of a convective boundary layer are in excellent agreement with those from the Deardorff–Willis laboratory convection tank. Using these LES data, we evaluate contemporary parameterizations for turbulent transport and dissipation in second-order closure models of the convective boundary layer. The gradient-diffusion parameterization for turbulent transport fares poorly, due in large part to the direct influence of buoyancy. This leads to poor predictions of the vertical profiles of some turbulence statistics. We also find that the characteristic length scales for the mechanical and thermal dissipation rates typically used in second-order closure models are a factor of 2–3 too small; this leads to underpredictions of turbulence kinetic energy levels. Finally, we find that the flux and variance budgets for conservative scalars are substantially different in top-down and bottom-up diffusion. In order to reproduce...

Spectral Analysis of Large-Eddy Simulations of the Convective Boundary Layer

Abstract To examine the fidelity of the simulated turbulent flow, we analyzed the spectra of 96×&96×96 large-eddy-simulation results. We derived expressions for the inertial-range spectra of a filtered wind field, compared our computed spectra with the theoretical predictions, and drew two main conclusions. First, the wave cutoff filter is more appropriate for our large-eddy-simulation model than the Gaussian filter. Second, only a certain combination of the subgrid-scale parameters for the dissipation rate and eddy viscosity provides good inertial-range spectra. We offer an explanation for the unreasonably large sugrid temperature and moisture variances reported in Deardorffs 1974 lame-eddy-simulation results, and show that moment statistics up to third order are not sensitive to moderate changes in the subgrid-scale parameters.

Statistics of Conservative Scalars in the Convective Boundary Layer

Abstract We represent the three-dimensional, time-dependent field of a passive, conservative scalar in the conservative boundary layer as the sum of “top-down” and “bottom-up” components created by the scalar fluxes through the top and bottom, respectively. A simple similarity hypothesis for these component fields allows us to extract their statistics from large-eddy simulations of the boundary layer. We find that the top-down and bottom-up fields are strongly correlated, but that their statistics are quite different. Analysis of the budgets of their fluxes and variances shows clearly some of the differences between top-down and bottom-up diffusion. We present simple formulas for scalar variance profiles which are in good agreement with observations.

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.

An analysis of closures for pressure-scalar covariances in the convective boundary layer

Abstract Perhaps the most commonly used closure in second-moment models of turbulence is Rottas return-to-isotropy expression, which was originally developed to pararmeterize the pressure-velocity gradient correlation in the Reynolds stress conservation equations. It is not clear that this closure alone is adequate for application to convective turbulence, however, because of the pervasive effects of buoyancy on turbulence structure. We study the closure problem for the pressure covariance in the scalar flux equation using a data set we generated through large-eddy simulation (LES) of a convective boundary layer. We resolve the pressure field into turbulence–turbulence, mean-shear, buoyancy, Coriolis, and subgrid-scale components, and find that the buoyancy and turbulence–turbulence components dominate in the convective boundary layer. The buoyancy contribution to the pressure-gradient/scalar covariance is one-half of the buoyant production term in the flux equation, to a good approximation, while the tu...

Parameterizing turbulent diffusion through the joint probability density

The “convective mass flux” parameterization often used in meteorological modeling expresses the vertical flux of a transported scalar as proportional to the product of the difference in mean values of the scalar in updrafts and downdrafts and their characteristic velocity. The proportionality factor is a constant to be specified. We show that this proportionality factor also appears in the “relaxed eddy accumulation” technique of Businger and Oncley. That associates the surface-layer flux of a scalar with the product of the standard deviation of vertical velocity and the mean concentration difference between updrafts and downdrafts.We show that this constant (b) is determined uniquely by the joint probability density (jpd) of vertical velocity and the scalar. Using large-eddy simulation, we generate this jpd for a conservative scalar diffusing through a convective boundary layer. It has quite different forms in “top-down” and “bottom-up” diffusion geometries. The bottom-up jpd is fairly well represented by a jointly Gaussian form and implies b ~ 0.6, in good agreement with the surface-layer value reported by Businger and Oncley. The top-down jpd is strikingly non-Gaussian and gives b ~ 0.47. Updrafts carry the bulk of the scalar flux - 70% in the bottom-up case, 60% in the top-down case.