Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

In this study, the stability dependence of turbulent Prandtl number ($$Pr_t$$ P r t ) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $$Pr_t$$ P r t and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.

Fine-Resolution WRF Simulation of Stably Stratified Flows in Shallow Pre-Alpine Valleys: A Case Study of the KASCADE-2017 Campaign

In an overall approach aiming at the development and qualification of various tools designed to diagnose and/or forecast the flows at the local scale in complex terrain, we qualified a numerical model based on the WRF platform and operated in a two-way nested domain mode, down to a horizontal resolution of 111 m for the smallest domain. The area in question is the Cadarache valley (CV), in southeast France, which is surrounded by hills and valleys of various sizes. The CV dimensions (1 km wide and 100 m deep) favor the development of local flows greatly influenced by the diurnal cycle and are prone to thermal stratification, especially during stable conditions. This cycle was well documented due to permanent observations and dedicated field campaigns. These observations were used to evaluate the performance of the model on a specific day among the intensive observation periods carried out during the KASCADE-2017 campaign. The model reproduced the wind flow and its diurnal cycle well, notably at the local CV scale, which constitutes considerable progress with respect to the performances of previous WRF simulations conducted in this area with kilometric resolution, be it operational weather forecasts or dedicated studies conducted on specific days. The diurnal temperature range is underestimated however, together with the stratification intensity of the cold pool observed at night. Consequently, the slope drainage flows along the CV sidewalls are higher in the simulation than in the observations, and the resulting scalar fields (such as specific humidity) are less heterogeneous in the model than in the observations.

Mixing Coefficient in Stably Stratified Flows

Turbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.

Simulation of stratified flows over a ridge using a lattice Boltzmann model

A three-dimensional thermal lattice Boltzmann model (TLBM) using multi-relaxation time method was used to simulate stratified atmospheric flows over a ridge. The main objective was to study the efficacy of this method for turbulent flows in the atmospheric boundary layer, complex terrain flows in particular. The simulation results were compared with results obtained using a traditional finite difference method based on the Navier–Stokes equations and with previous laboratory results on stably stratified flows over an isolated ridge. The initial density profile is neutral stratification in the boundary layer, topped with a stable cap and stable stratification aloft. The TLBM simulations produced waves, rotors, and hydraulic jumps in the lee side of the ridge for stably stratified flows, depending on the governing stability parameters. The Smagorinsky turbulence parameterization produced typical turbulence spectra for the velocity components at the lee side of the ridge, and the turbulent flow characteristics of varied stratifications were also analyzed. The comparison of TLBM simulations with other numerical simulations and laboratory studies indicated that TLBM is a viable method for numerical modeling of stratified atmospheric flows. To our knowledge, this is the first TLBM simulation of stratified atmospheric flow over a ridge. The details of the TLBM, its implementation of complex boundaries and the subgrid turbulence parameterizations used in this study are also described in this article.