Using direct numerical simulation, we investigate stationary and homogeneous shear-driven turbulence in various stratifications, ranging from neutral to very stable. To attain and maintain a stationary flow, we throttle the mean shear so that the net production stays constant for all times. This results in a flow that is characterized solely by its mean shear and its mean buoyancy gradient, independent of initial conditions. The method of throttling is validated by comparison with experimental spectra in the case of neutral stratification. With increasing stratification comes the emergence of vertically sheared large-scale horizontal motions that preclude a straightforward interpretation of flow statistics. However, once these motions are excluded, simply by subtracting the horizontal average, the underlying flow appears amenable to the standard methods of turbulence analysis. It is shown that a direct acknowledgement of the confining influence of the periodic simulation box can lead to a meaningful physical interpretation of the large scales. Once an appropriate confinement scale is identified, many features, including horizontal spectra, flux–gradient relationships and length scales, of stratified sheared turbulence can be readily understood, both qualitatively and quantitatively, in terms of Monin–Obukhov similarity theory. Finally, the similarity-theory framework is used to interpret the scaling of the vertical diapycnal diffusivity in stratified turbulence.

The present study considers the impact of various choices pertaining to the numerical solution of the governing equations on large-eddy simulation (LES) prediction and the association of these choices with flow physics. These include the effect of dissipative versus nondissipative advection discretizations, different implementations of the constant-coefficient Smagorinsky subgrid-scale model, and grid resolution. Simulations corresponding to the trade wind precipitating shallow cumulus composite case of the Rain in Cumulus over the Ocean (RICO) field experiment were carried out. Global boundary layer quantities such as cloud cover, liquid water path, surface precipitation rate, power spectra, and the overall convection structure were used to compare the effects of different discretization implementations. The different discretization implementations were found to exert a significant impact on the LES prediction even for the cases where the process of precipitation was not included. Increasing numerical dissipation decreases cloud cover and surface precipitation rates. For nonprecipitating cases, grid convergence is achieved for grid spacings of 20 m. Cloud cover was found to be particularly sensitive, exhibiting variations between different resolution runs even when the mean liquid water profile had converged.

The buoyancy-adjusted stretched-vortex subgrid-scale (SGS) model is assessed for a number of large-eddy simulations (LESs) corresponding to diverse atmospheric boundary layer conditions. The cases considered are free convection, a moderately stable boundary layer [first Global Energy and Water Exchanges (GEWEX) Atmospheric Boundary Layer Study (GABLS)] case, shallow cumulus [Barbados Oceanographic and Meteorological Experiment (BOMEX)], shallow precipitating cumulus [Rain in Cumulus over the Ocean (RICO)] and nocturnal stratocumulus [Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS-II) field study RF01]. An identical LES setup, including advection discretization and SGS model parameters, is used for all cases, which is a stringent test on the ability of LES to accurately capture diverse conditions without any flow-adjustable parameters. The LES predictions agree well with observations and previously reported model results. A grid-resolution convergence study is carried out, and for all cases the mean profiles exhibit good grid-resolution independence, even for resolutions that are typically considered coarse. Second-order statistics, for example, variances, converge at finer resolutions compared to domain means. The simulations show that 90% of the turbulent kinetic energy (at each level) must be resolved to obtain sufficiently converged mean profiles. This empirical convergence criterion can be used as a guide in designing future LES runs.

In this study, the eddy diffusivity/mass flux (EDMF) approach is used to combine parameterizations of nonprecipitating moist convection and boundary layer turbulence. The novel aspect of this EDMF version is the use of a probability density function (PDF) to describe the moist updraft characteristics. A single bulk dry updraft is initialized at the surface and integrated vertically. At each model level, the possibility of condensation within the updraft is considered based on the PDF of updraft moist conserved variables. If the updraft partially condenses, it is split into moist and dry updrafts, which are henceforth integrated separately. The procedure is repeated at each of the model levels above. The single bulk updraft ends up branching into numerous moist and dry updrafts. With this new approach, the need to define a cloud-base closure is circumvented. This new version of EDMF is implemented in a single-column model (SCM) and evaluated using large-eddy simulation (LES) results for the Barbados Oceanographic and Meteorological Experiment (BOMEX) representing steady-state convection over ocean and the Atmospheric Radiation Measurement (ARM) case representing time-varying convection over land. The new EDMF scheme is able to represent the properties of shallow cumulus and turbulent fluxes in cumulus-topped boundary layers realistically. The parameterized updraft properties partly account for the behavior of the tail of the PDF of moist conserved variables. It is shown that the scheme is not particularly sensitive to the vertical resolution of the SCM or the main model parameters.

This study presents a series of steady-state large-eddy simulations (LESs) to study the stratocumulus to shallow cumulus cloud transition. To represent the different stages of what can be interpreted as an Eulerian view of the transition, each simulation is assigned a unique sea surface temperature (SST) and run until statistically steady. The LES runs are identical in every other aspect. These idealized boundary-driven steadystate LESs allow for a simple parametric assessment of cloud-controlling factors in isolation from initial conditions and time-lag effects inherent in the Lagrangian view of the transition. The analysis of the thermodynamic energy budget reveals that, as the cloud regime transitions from stratocumulus to shallow cumulus, changes in the cloud radiative cooling term are balanced by changes in the subsidence warming term. This leads to a linear regression between the cloud fraction (CF) and an integral that scales, to a first-order approximation, as the lower-tropospheric stability (LTS). The study also considers the response of the boundary layer to a step change in SST that triggers the transition from stratocumulus to shallow cumulus. An examination of the time-lag conditional average centered on events when cumulus thermals are penetrating the stratocumulus deck suggests that the net effect of cumulus thermals in the transition is not to dry the stratocumulus deck but rather to moisten it. It is shown that the Gaussian probability density function (pdf) model of Sommeria and Deardorff describes the evolution of CF well during this step-change transition, suggesting that the systematic decrease in cloud cover is essentially associated with the mean drying of the air just below the cloud top.