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Evaluation of turbulent Prandtl ( Schmidt ) number parameterizations for stably stratified environmental flows
| Content Provider | Semantic Scholar |
|---|---|
| Author | Elliott, Zachary A. Venayagamoorthy, Subhas Karan |
| Copyright Year | 2011 |
| Abstract | In this study, we first evaluate four different formulations of the turbulent Prandtl (Schmidt) number Prt = νt/Γt where νt is the eddy viscosity and Γt is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Prt are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. algebraic) turbulence model for νt in a one-dimensional, turbulent channel flow is considered to evaluate 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. We perform model-to-model comparisons to highlight 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 linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Prt, given a model for νt in stably stratified flows. Direct numerical simulation (DNS) data of stably stratified homogeneous turbulence are also used to study the parameters in two-equation RANS turbulence models such as the buoyancy parameter Cε3, and Prt in the k-ε model. Both Ri and the turbulent Froude number Frk = ε/(Nk), where ε is the turbulent kinetic energy dissipation rate and k is the turbulent kinetic energy, are used as correlating parameters to characterize stratification in the k-ε model. We show that it may be more appropriate to use Frk as the parameter of choice for modeling the stratification parameters 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. These proposed modifications are implemented in a one-dimensional water column model called the General Ocean Turbulence Model (GOTM) and used to simulate stably stratified channels flows. 1 Department of Civil & Environmental Engineering Colorado State University 1372 Campus Delivery Fort Collins, CO 80523-1372 Tel: (970)491-1915 e-mail: vskaran@colostate.edu |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://hydrologydays.colostate.edu/Abstracts_11/Elliott_abs.pdf |
| Alternate Webpage(s) | http://www.engr.colostate.edu/~vskaran/EV_DAO_published_final.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Computer simulation Direct numerical simulation Directional Valve Device Component Email Flow Gradient Kinetics Large eddy simulation Numerical analysis Population Parameter Richardson number Schmidt decomposition Spatial variability Stratification Turbulence kinetic energy Turbulence modeling Uniform Resource Identifier |
| Content Type | Text |
| Resource Type | Article |
