High resolution direct numerical simulations are used to investigate the dynamics of turbulence in flows subject to strong stable stratification, which are common in natural settings. Results are presented for two categories of simulations, uniform and non-uniform density stratification. For all simulated flows, the density stratification was held constant in time, and there was no ambient shear. Flows with uniform density stratification are first analyzed to help provide clear insight to physical processes, followed by flows with non-uniform density stratification which better represent the stratification occurring in nature.

Global and regional ocean simulations rely on eddy viscosities and diffusivities to represent the unresolved turbulent mixing of momentum and scalars. The simulated flow and the transport of quantities such as heat and carbon are quite sensitive to how the turbulence is modeled. Particularly, the eddy diffusivity model of Osborn (1980) is widely used to represent the vertical buoyancy flux, which requires accurate knowledge of the mixing coefficient--defined as the ratio of the dissipation rates of available turbulent potential energy (TPE) and turbulent kinetic energy (TKE). While a constant value of 0.2 is often prescribed for the mixing coefficient, there is significant evidence for parameterizing it as a function of dimensionless numbers that characterize the state of the turbulence. Using direct numerical simulations, we studied stably stratified turbulence under three different sets of forcing: (i) linear axisymmetric forcing; (ii) three types of shear forcing; and (iii) combined momentum and buoyancy forcing. By analyzing the budgets of the normal Reynolds stresses and the vertical buoyancy flux, we observed that terms involving the pressure field (i.e., pressure-strain correlations and pressure scrambling) exhibited significant changes as the turbulent mixing became more efficient. Each of these three sets of flows exhibited quantitative physical differences in their mixing characteristics. Our findings suggested the need for improved models of the turbulent mixing in stratified flows, which we achieved by revising existing scaling relationships for the mixing coefficient and exploring anisotropic model forms for the turbulent momentum and scalar fluxes.

Stratified flows are important in determining how various atmospheric and environmental processes occur. The book investigates these processes and focuses on the methods by which pollutants are mixed and dispersed in natural and industrial environments.

A research program was carried out to investigate turbulent mixing in stably stratified shear flows with the hope of gaining an improved understanding of stably stratified nocturnal boundary layers. The program was mainly laboratory experimental, supplemented by theoretical and numerical developments. The flow configuration consisted of a three-layer system, with upper turbulent layer driven over the lower stratified, quiescent, layer while an intermediate (inversion) layer sandwiched between these two layers. The studies included the nature of instabilities, intermittent generation of turbulence, sustenance and decay of turbulence under varying background conditions (essentially determined by the Richardson number) and ensuing turbulent mixing in the inversion layer. An unprecedented volume of laboratory data were gathered during the program, which enabled to delve into the mechanics and energetics of mixing in stable boundary layers. The laboratory results were compared with, and was used to gain insights on, field observations. Also, the parameterizations developed were compared with those currently used in numerical models. A meso-scale numerical model also was used to check the efficacy of some of the laboratory-based parameterizations.