# Numerical simulations of stably stratified turbulent flow / Lucinda H. Shih.

##### By: Shih, Lucinda H.

Publisher: Stanford University, Dept. of Civil and Environmental Engineering 2003Description: 198 pages.Dissertation note: Thesis (Ph. D.)--Stanford University, 2004. Summary: Numerical simulations of idealized geophysical flows are valuable complements to data garnered from field observations and laboratory experiments. It is in many respects easier to examine the effects of specific flow parameters in numerical experiments, and insights from such studies can be used to inform future laboratory or field studies, as well as lower-resolution general ocean or atmosphere models. To this end, two basic types of stratified flows were numerically simulated in this study. The first flow is stratified homogeneous shear turbulence, which is the simplest type of flow which contains many of the important phenomena that characterize geophysical flows. Direct numerical simulations (DNS) reveal that final states of tu rbulence vary with initial shear rate at low but not high Reynolds numbers, indicating the importance of employing instantaneous rather than initial values to parameterize flows. Also, while it may be more convenient to use a global parameter such as the gradient Richardson number to characterize stratification for modeling purposes, a local, temporally-evolving parameter such as the turbulent Froude number is more illustrative of physical flow processes. The results from the homogeneous shear flow simulations are used to assess predictions for turbulent fluxes. Accurate quantification of turbulent fluxes is vital to understanding the global heat budget of the atmosphere and ocean. Traditionally, oceanographers have used e/(z/A2), a measure of turbulence intensity, to parameterize flows. The DNS data is found to divide neatly into diffusive, intermediate, and energetic regimes of turbulence activity based on e/(vN2). The Osborn (1980) prediction for scalar diffusivity kp as a function of t / { v N 2), which assumes stationary conditions, was found to be reasonable in the intermediate regime I where the flux Richardson number Rf indicates that the flow is approximately stationary. Modifying the Osborn prediction to allow the mixing efficiency R f to vary with the flow parameters (e.g.e/(uN2)) extends the validity of the prediction into the energetic regime E. This prediction holds for laboratory data from higher Prandtl number (Pr) experiments as well; in order to collapse the laboratory and the numerical data, however, a factor of P r 1//5 is required. These results show that even for unsteady flows, kp and kv can be computed from instantaneous estimates of e/(vN2), or an equivalent measure of the intensity of the turbulence in stratified flows, such as a combination of the integral scale Reynolds number and the turbulent Froude number Re/yFrl. The latter parameterization is in many respects preferable to e/(vN2), since dimensional analysis requires two independent parameters to fully describe the stratified turbulent flow. Using a Reynolds number and a Froude number renders more distinct the effects of viscosity and stratification; given the Reynolds number independence of high Reynolds number flows, it is possible to express the turbulent diffusivity as functions of Froude number alone. A parallel large eddy simulation (LES) code for the second type of flow studied in this dissertation, stratified channel flow, has been updated and modified for use in studying processes significant to the near-coastal ocean. Turbulence generated by bottom shear interacts as expected with varying stratification; weakly stratified flows are quickly mixed, while stronger thermoclines suppress the growth of turbulent structures. In the freestream portion of the channel flow, turbulence behaves similarly to turbulence in homogeneous shear flow. The turbulent Froude number is again found to be useful in characterizing this type of stratified flow. An important physical process common to oceans and lakes is that of Langmuir circulations, which are large, coherent, and often turbulent sets of counterrotating vortices generated by wind-wave effects. Langmuir circulations are added to the channel flow simulation, via the Craik-Leibovich vortex forcing mechanism, to study their influence on mixing in stratified flow. The presence of the vortex forcing mechanism above a thermocline accelerates surface mixed layer deepening, moderated by increased stratification, and is important for realistic modeling of vertical mixing in surface waters.Item type | Current location | Call number | Copy number | Status | Date due | Item holds |
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Mesa Lab | 102116 (Browse shelf) | 1 | Available |

Submitted to the Department of Civil and Environmental Engineering.

Copyright by the author.

Thesis (Ph. D.)--Stanford University, 2004.

Numerical simulations of idealized geophysical flows are valuable complements to data garnered from field observations and laboratory experiments. It is in many respects easier to examine the effects of specific flow parameters in numerical experiments, and insights from such studies can be used to inform future laboratory or field studies, as well as lower-resolution general ocean or atmosphere models. To this end, two basic types of stratified flows were numerically simulated in this study.

The first flow is stratified homogeneous shear turbulence, which is the simplest type of flow which contains many of the important phenomena that characterize geophysical flows. Direct numerical simulations (DNS) reveal that final states of tu rbulence vary with initial shear rate at low but not high Reynolds numbers, indicating the importance of employing instantaneous rather than initial values to parameterize flows. Also, while it may be more convenient to use a global parameter such as the gradient Richardson number to characterize stratification for modeling purposes, a local, temporally-evolving parameter such as the turbulent Froude number is more illustrative of physical flow processes.

The results from the homogeneous shear flow simulations are used to assess predictions for turbulent fluxes. Accurate quantification of turbulent fluxes is vital to understanding the global heat budget of the atmosphere and ocean. Traditionally, oceanographers have used e/(z/A2), a measure of turbulence intensity, to parameterize flows. The DNS data is found to divide neatly into diffusive, intermediate, and energetic regimes of turbulence activity based on e/(vN2). The Osborn (1980) prediction for scalar diffusivity kp as a function of t / { v N 2), which assumes stationary conditions, was found to be reasonable in the intermediate regime I where the flux Richardson

number Rf indicates that the flow is approximately stationary. Modifying the Osborn prediction to allow the mixing efficiency R f to vary with the flow parameters (e.g.e/(uN2)) extends the validity of the prediction into the energetic regime E. This prediction holds for laboratory data from higher Prandtl number (Pr) experiments

as well; in order to collapse the laboratory and the numerical data, however, a factor of P r 1//5 is required.

These results show that even for unsteady flows, kp and kv can be computed from instantaneous estimates of e/(vN2), or an equivalent measure of the intensity of the turbulence in stratified flows, such as a combination of the integral scale Reynolds number and the turbulent Froude number Re/yFrl. The latter parameterization is in many respects preferable to e/(vN2), since dimensional analysis requires two independent parameters to fully describe the stratified turbulent flow. Using a Reynolds number and a Froude number renders more distinct the effects of viscosity and stratification; given the Reynolds number independence of high Reynolds number flows, it is possible to express the turbulent diffusivity as functions of Froude number alone.

A parallel large eddy simulation (LES) code for the second type of flow studied in this dissertation, stratified channel flow, has been updated and modified for use in studying processes significant to the near-coastal ocean. Turbulence generated by bottom shear interacts as expected with varying stratification; weakly stratified flows are quickly mixed, while stronger thermoclines suppress the growth of turbulent structures. In the freestream portion of the channel flow, turbulence behaves similarly to turbulence in homogeneous shear flow. The turbulent Froude number is again found to be useful in characterizing this type of stratified flow.

An important physical process common to oceans and lakes is that of Langmuir circulations, which are large, coherent, and often turbulent sets of counterrotating vortices generated by wind-wave effects. Langmuir circulations are added to the channel flow simulation, via the Craik-Leibovich vortex forcing mechanism, to study

their influence on mixing in stratified flow. The presence of the vortex forcing mechanism above a thermocline accelerates surface mixed layer deepening, moderated by increased stratification, and is important for realistic modeling of vertical mixing in surface waters.