To improve the modeling of turbulence and mixing in strongly stratified natural flows such as lakes and oceans, the proposed work involves developing an analytical model based on rapid distortion theory (RDT). Although turbulence can be intense in parts of natural flows, strong stratification can reduce vertical transport and mixing in the interior of lakes and oceans. Turbulence models based on the Reynolds-averaged Navier-Stokes (RANS) equations have provided useful predictions of stratified flows; however, they require adjustment to account for the interaction of internal waves and turbulence, and models that employ the gradient-transport assumption cannot predict upgradient fluxes, which can affect transport in strongly stratified flows significantly.
In contrast to RANS models, RDT is naturally suited for predicting turbulence in a strongly stratified flow. While the gradient-transport approximation works best for a stratified flow when the time scales of the turbulence are much smaller than the time scale of gravitational adjustment (i.e., weak stratification), RDT applies when the stratification is strong. Although RDT does not predict the vortex mode seen at large times in some studies, it has successfully predicted many features of strongly stratified flows, including upgradient fluxes and preferential transport of temperature in a heat-salt system. The proposed work exploits this success to elucidate the physics and improve the modeling of strongly stratified flows.
The objectives of the proposed work are to (1) apply RDT to homogeneous turbulence in strong stratification to determine (a) the mixing efficiency and its dependence on molecular diffusivity, (b) the effects of time-varying forcing in sheared and unsheared flows, and (c) the evolution of turbulence in a velocity and density field modeled after internal waves and (2) extend RDT to increase its relevance for natural flows by (a) applying it to a patch of turbulence with and without shear and (b) investigating the effect of moderate stratification and developing and testing a turbulence model based on RDT. Work for the first objective involves straightforward, though important, extensions of previous applications. Along with applying previous research on RDT for inhomogeneous turbulence to a stratified patch, work for the second objective involves relaxing the assumption of strong stratification by analytically evaluating the neglected nonlinear terms and adding a variable eddy diffusivity, which will be computed from the RDT solution, to extend the RDT to moderate stratification.
The intellectual merit of the proposed work stems from the success of RDT in reproducing key features of several stratified flows and the PI?s experience with RDT and mixing in stratified flows in general. The theoretical problems are designed to answer key questions for stratified flows (objective 1) as well as relax the assumptions behind RDT to increase its applicability objective 2). Results from this research are expected to complement current models of stratified flows and offer insights on how to improve them. The broader impacts include training a graduate student; involving undergraduates from Iowa State University's Program for Women in Science and Engineering in the research; conducting outreach to schools; continuing collaborations with Drs. Hideshi Hanazaki, Hidekatsu Yamazaki, and William Merryfield; and improving the parameterization of sub-grid scale processes in models of lakes and oceans. The last of these will be aided by collaborating with Dr. Merryfield, an ocean modeler.
