P. J. Mason

Large-Eddy Simulation of the Convective Atmospheric Boundary Layer

Abstract Large-eddy simulations of a free convective atmospheric boundary layer with an overlying capping inversion are considered. Attention is given to the dependence of the results upon the various factors influencing the simulation: the subgrid model, the domain size, and the mesh resolution. By providing artificial constraints upon the convection the results also provide extra insight into the underlying dynamics. The gross features of the boundary layer, such as the overall energy budget, are not sensitive to the details of the simulations but a number of important factors are revealed. It has been found that near the surface the subgrid diffusivity must be larger than is usually supposed, in order for the vertical velocity skewness to have the correct sign. This region of the flow has a significant subgrid-scale heat flux and it seems that the subgrid model requires improvement in such cases. A revised model which under statically unstable conditions allows the mixing-length of the subgrid-scale tu...

Large-Eddy Simulation of the Convective Boundary Layer: A Comparison of Four Computer Codes

To test the consistency of large-eddy simulation we have run four existing large-eddy codes for the same case of the convective atmospheric boundary layer. The four models differ in various details, such as: the subgrid model, numerics and boundary conditions.

Large-Eddy Simulation of the stably-stratified atmospheric boundary layer

Large-Eddy Simulation of stable boundary layers (SBLs) has been considered particularly difficult, indeed perhaps impossible with present computational resources. Here we present a new series of successful simulations of SBLs over uniform, flat terrain, using an approach previously successful for neutral and convective conditions, and showing that essentially the same model can handle all three main dry types of atmospheric boundary layer. We consider both technical requirements for successful and accurate SBL simulations and the observed characteristics of the simulated SBL. We discuss the evolution (in some cases to quasi-steady states) and compare with theory and experimental data. Effects of static-stability on the flow are analyzed using one-point and two-point statistics. Results show the development of a shear-driven SBL, with little sign of distinctively wavelike motions. The flow statistics are found to be consistent with local scaling, and that framework is used to compare with other data and theoretical models.

Boundary-layer flow over low hills

In 1975 Jackson and Hunt observed that there had, until that time, been few attempts to relate measurements of wind velocity on hills to the local topography. The succeeding ten years have seen substantial research effort aimed at rectifying this omission. The field measurements, in conjunction with theoretical, numerical and wind tunnel studies now provide a good basis for a preliminary description of neutrally stratified boundary-layer flow over low hills. There are still gaps in the description and understanding of the flow but many more data are now available. The present review attempts to summarize recent field experiments that have been conducted on boundary-layer flow over low hills and to review what we have learnt from them.

Surface-layer flow in complex terrain: Comparison of models and full-scale observations

Four models of surface boundary-layer flow in complex terrain are compared with observations made at Blashaval Hill, North Uist, Scotland. The field experiment is described by Mason and King (1985). Three of the models are derived from the two-dimensional theory of Jackson and Hunt (1975) and are described in Mason and King (1985), Walmsley et al. (1986) and Troen and Petersen (1989). The fourth is a mass-consistent code based on Traci et al. (1979). The model results are in good agreement with each other and are generally within the observed range of variation ( ~ ± 16%) in normalized wind speed. For most wind direcions (7 of 11), model results of normalized wind speed at the summit were within 7% of the observed mean values. For some wind directions, calculations using the “Guidelines” of Walmsley et al. (1989) suggested that variations in surface roughness were important. This led us to apply one of our models incorporating nonuniform surface roughness. The lack of significant improvement for cases when water lay upstream of Blashaval Hill is attributed to compensating changes at summit and reference sites and to very local effects on the wind data. Sensitivity to topography lying to the west and northwest of Blashaval was also investigated. Results suggested an influence from those distant topographic features for some wind directions. When those features were incorporated, maximum errors in normalized wind speed at the summit were reduced from 18 to 13%.

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)2 up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z0eff. The form of the varation of z0eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.

Flow over the summit of an isolated hill

Observations of the mean flow and turbulence statistics over the summit of an isolated, roughly circular hill, Nyland hill, are presented, Nyland hill rises 70 m above the surrounding terrain and has a base diameter of about 500 m. The summit of the hill is very smooth and allows representative measurements to be made close to the surface. The flow speed 8 m above the summit is increased by a factor of 2 over the upstream speed 8 m above level terrain, and flow separation occurs in the lee of the hill. The mean velocity profile over the summit shows an increase in velocity with height up to about 2 m and then a near constant velocity between 2 and 16 m. The flow perturbation relative to the upstream profile is thus a maximum at about 2 m. The measurements of turbulence structure show how the influence of the hill depends on the length scale of the turbulent eddies involved. Scales greater than the scale of the hill are modified through the flow speed-up whilst scales shorter than the hill suffer complex changes. The short-scale turbulence over the summit is only in local equilibrium in the lowest fraction of a metre. Above this equilibrium region, there is a complex adjustment towards the rapid distortion dynamics which appear to dominate at heights above about 8 m. The detailed results are compared with previous studies and available theories.

Thermal Convection in a Rotating Fluid Subject to a Horizontal Temperature Gradient: Spatial and Temporal Characteristics of Fully Developed Baroclinic Waves

Abstract Detailed studies of the azimuthal structure of fully developed waves in a differentially heated rotating fluid annulus have been carried out with the aid of instrumentation capable of providing frequent determinations of the temperature variation around a circle concentric with the walls of the annulus. Owing to the cyclic nature of the data they are conveniently analyzed in terms of azimuthal Fourier modes. The time-averaged azimuthal spectra thus obtained show that in the regular regime, where the flow is dominated by a single mode of wavenumber M, say, significant “energy” is found not only in the harmonics required to describe the jet stream structure of the flow but also in the sideband modes of wavenumber M=1 which describe the observed azimuthal modulations in the amplitude and/or phase of the wave. At the high-wavenumber end of those spectra for which an inertial subrange can be resolved the “spectral energy” follows a (wavenumber)−3 law. The time-dependent behavior of the phases of the s...

The sensitivity of large-eddy simulation of turbulent shear flow to subgrid models

Previous large-eddy simulations of turbulent shear flows have shown significant sensitivity to some aspects of the subgrid-scale turbulence models. In particular, Mason and Thomson (1992) demonstrated a marked improvement in simulations through the inclusion of stochastic stress variations in the subgrid model. Here a series of simulations is presented with a view to exploring the general sensitivity to such a subgrid model and in particular to the size and nature of the stochastic stress variations. The model proposed by Mason and Thomson is found to be fairly satisfactory but some quantitative uncertainty remains.

Stochastic Backscatter for Cloud-Resolving Models. Part I: Implementation and Testing in a Dry Convective Boundary Layer

Abstract In simulations of deep convection with cloud-resolving models the turbulence is often rather poorly resolved, and the influence of the subfilter-scale parameterization used in such circumstances is probably greater than in better-resolved simulations. Therefore a study to investigate the influence of stochastic backscatter was performed and presented in two papers. This first paper focuses on a description of the stochastic backscatter model and its effect on a neutral and a dry convective boundary layer. The second paper then deals with two cases of deep convection. The dry convective boundary layer is typical of the subcloud layer in deep convection and this study allows for influences on this layer to be investigated separately. As a simple case of convection it also allows for general effects to be identified. The implementation of stochastic backscatter was improved to ensure an appropriate scale of backscatter that is independent of any mesh refinements and always spatially isotropic. It ca...