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On the turbulent Prandtl number in homogeneous stably stratified turbulence
| Content Provider | Scilit |
|---|---|
| Author | Venayagamoorthy, Subhas K. Stretch, Derek D. |
| Copyright Year | 2010 |
| Description | In this paper, we derive a general relationship for the turbulent Prandtl number $Pr_{t}$ for homogeneous stably stratified turbulence from the turbulent kinetic energy and scalar variance equations. A formulation for the turbulent Prandtl number, $Pr_{t}$, is developed in terms of a mixing length scale $L_{M}$ and an overturning length scale $L_{E}$, the ratio of the mechanical (turbulent kinetic energy) decay time scale $T_{L}$ to scalar decay time scale $T_{ρ}$ and the gradient Richardson number Ri. We show that our formulation for $Pr_{t}$ is appropriate even for non-stationary (developing) stratified flows, since it does not include the reversible contributions in both the turbulent kinetic energy production and buoyancy fluxes that drive the time variations in the flow. Our analysis of direct numerical simulation (DNS) data of homogeneous sheared turbulence shows that the ratio $L_{M}/L_{E}$ ≈ 1 for weakly stratified flows. We show that in the limit of zero stratification, the turbulent Prandtl number is equal to the inverse of the ratio of the mechanical time scale to the scalar time scale, $T_{L}/T_{ρ}$. We use the stably stratified DNS data of Shih et al. (J. Fluid Mech., vol. 412, 2000, pp. 1–20; J. Fluid Mech., vol. 525, 2005, pp. 193–214) to propose a new parameterization for $Pr_{t}$ in terms of the gradient Richardson number Ri. The formulation presented here provides a general framework for calculating $Pr_{t}$ that will be useful for turbulence closure schemes in numerical models. |
| Related Links | http://www.engr.colostate.edu/~vskaran/JFM_Prt_VS_published.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/01E838A1E4A63FAF853599BDF77CAA12/S002211200999293Xa.pdf/div-class-title-on-the-turbulent-prandtl-number-in-homogeneous-stably-stratified-turbulence-div.pdf |
| Ending Page | 369 |
| Page Count | 11 |
| Starting Page | 359 |
| ISSN | 00221120 |
| e-ISSN | 14697645 |
| DOI | 10.1017/s002211200999293x |
| Journal | Journal of Fluid Mechanics |
| Volume Number | 644 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2010-02-10 |
| Access Restriction | Open |
| Subject Keyword | Journal of Fluid Mechanics Fluids and Plasmas Physics Numerical Simulation Time Scale Stably Stratified Turbulent Prandtl Number |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mechanics of Materials Condensed Matter Physics Mechanical Engineering |
