Turbulent Mixing In Stably Stratified Wall-Bounded Flows


Stably stratified wall-bounded turbulent flows are ubiquitous in nature such as in estuaries, lakes, oceans and atmospheric boundary layer. In such flows, the simultaneous existence of density stratification and solid wall results in anomalous mixing of momentum and active scalar (density) compared to other turbulent flows. Hence, there is no surprise that stratified wall-bounded flows are usually considered as one of the most complex flows. The focus of this study is to analyze stably stratified wall-bounded turbulent flows to highlight a number of issues that have implications for predicting turbulent mixing in these flows. By invoking the equilibrium assumption between the production rate of the turbulent kinetic energy (P), the dissipation rate of the turbulent kinetic energy (ε) and the turbulent potential energy dissipation rate (εPE) as P ≈ ε + εPE, we first propose that the irreversible flux Richardson number Rf = εPE /(ε +εPE) can be approximated with the reversible form of the flux Richardson number Rf = −B/P (where B is the buoyancy flux), especially for low gradient Richardson numbers. Second, we propose that the turbulent viscosity νt ≈ 1/(1-Rf) ε /S2, where S is the mean shear rate. We then extend our analysis to propose appropriate velocity and length scales. Tests using direct numerical simulation (DNS) data of stably stratified turbulent channel flow are performed to evaluate our propositions. The comparisons are excellent. Finally, by invoking the equilibrium assumption between the buoyancy flux (B) and the dissipation rate of the turbulent potential energy (εPE) as −B ≈ εPE we infer the turbulent diffusivity as κt ≈ εPE /N2, where N is the buoyancy frequency. The comparison of the proposed turbulent diffusivity with the exact turbulent diffusivity computed from DNS data is good especially in the near-wall region but the agreement deteriorates far away from the wall, indicating the breakdown of the equilibrium assumption which is attributed to the presence of linear internal wave motions in this far-wall region.

Feb 11, 2015 3:30 PM — 4:30 PM
Bechtel Collaboratory, Discovery Learning Center
Engineering Center, University of Colorado at Boulder, Boulder, CO 80309

Colorado State University