# Turbulence parameterizations for numerical simulations of stably stratified environmental flows

## Date

2011

## Authors

Elliott, Zachary, author

Venayagamoorthy, Subhas Karan, advisor

Julien, Pierre Y., committee member

Dasi, Lakshmi Prasad, committee member

## Journal Title

## Journal ISSN

## Volume Title

## Abstract

Almost all environmental and geophysical flows such as lakes, reservoirs, estuaries, and the atmosphere are turbulent and are also often characterized by stable density stratification. The presence of buoyancy forces due to stratification has a substantial effect on the flow development and turbulent mixing processes, influencing the distribution of pollutants and suspended matter in these flows. Mathematical and computer models can be used to simulate and produce numerical solutions to these flows, providing results that would otherwise not be feasibly attainable in a laboratory setting and that can be used for engineering prediction, design, and analysis purposes. Turbulence models use computational procedures to close the system of mean flow equations and account for the effects of turbulence and stratification through the specification of parameters that characterize the behavior of the flow. In this research, an attempt is made to assess and improve turbulence parameterizations for stably stratified environmental flows. An important parameter describing the transfer of momentum and scalar fluxes in stratified turbulent flows is the turbulent Prandtl number Prt. Specifically, four different formulations of the turbulent Prandtl number Prt are evaluated for stably stratified flows. All four formulations of Prt are strictly functions of the gradient Richardson number Ri, a parameter that provides a measure of the strength of the stratification. A zero-equation turbulence model for the turbulent viscosity νt in a one-dimensional turbulent channel flow is considered to assess the behavior of the different formulations of Prt. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems, such as atmospheric boundary layer flows and tidally-driven estuarine flows, to quantify the behavior of each of the four formulations of Prt. It is discussed as to which of the models of Prt allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from fixed continuous stratification as well as fixed two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to highlight the importance of choosing an appropriate parameterization of Prt, given a model for νt in stably stratified flows. Other more complete and dynamic models rely on additional parameters that allow stratified turbulent flow to be modeled as a function of local turbulence quantities rather than mean global properties of the flow. This research also focuses on implementing and testing proposed changes that explicitly account for buoyancy effects in two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. Direct numerical simulation (DNS) data of stably stratified homogeneous turbulence are used to study the parameters in two-equation RANS turbulence models such as the buoyancy parameter Cε3 and the turbulent Prandtl number Prt in the k-ε model. Both the gradient Richardson number Ri and the turbulent Froude number Frk are used as correlating parameters to characterize stratification in the k-ε model. It is shown that it may be more appropriate to use Frk as the parameter of choice for the stratification parameter in the k-ε model since it is based on the local properties of the turbulence as opposed to Ri, which is a mean property of the flow. The proposed modifications and alterations to Cε3 and Prt as functions of Ri and Frk are implemented in a one-dimensional water column model called General Ocean Turbulence Model (GOTM) and used to simulate stably stratified channel flows. The results from numerical simulations using the modified versions of the k-ε model are compared to stably stratified channel flow DNS data to assess their efficacy.

## Description

2011 Spring.

Includes bibliographical references.

Includes bibliographical references.

## Rights Access

## Subject

mixing

numerical modeling

scalar flux

stable stratification

turbulence

turbulent Prandtl number