Rapid distortion theory for mixing efficiency of a flow stratified by one or two scalars |
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| Institution: | 1. Department of Physics, University of Alberta, Edmonton, AB, T6G 2E1, Canada;2. Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA;3. Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, USA;4. Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA;1. Colorado School of Mines, Hydrologic Science and Engineering Program, 1500 Illinois Street, Golden, CO 80215, USA;2. Colorado School of Mines, Department of Applied Mathematics and Statistics, 1500 Illinois Street, Golden, CO 80215, USA;3. Colorado School of Mines, Geology and Geological Engineering Department, 1500 Illinois Street, Golden, CO 80215, USA;4. Integrated Ground Water Modeling Center, 1500 Illinois Street, Golden, CO 80215, USA;1. Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, MC-250, Urbana, IL, 61801-2350, USA;2. Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 306 North Wright St, MC-702, Urbana, IL, 61801-2918, USA;1. The University of Sydney, School of Aerospace, Mechanical and Mechatronic Engineering, Sydney, Australia;2. University of Strathclyde, Department of Mechanical and Aerospace Engineering, Glasgow, G1 1XW, United Kingdom;1. Ralph M Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA |
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| Abstract: | The mixing efficiency of unsheared homogeneous turbulence in flows stratified by one or two active scalars was calculated with rapid distortion theory (RDT). For the case with one scalar the mixing efficiency η depends on the Schmidt number Sc = ν/D and the Grashof number Gr = NL2/ν, where ν is the kinematic viscosity, D is the molecular diffusivity, N is the buoyancy frequency, and L is a length scale representative of the large eddies. For the case with two scalars the efficiency also depends on the density ratio Rρ, which compares the density difference caused by temperature and the density difference caused by salt. In the one scalar case when Gr is large, η decreases as Sc increases. The mixing efficiency increases with Gr up to a maximum value, as in numerical simulations and experiments. The maximum mixing efficiency of approximately 30% for low Sc is consistent with simulations, while the maximum efficiency of 6% for heated water is consistent with laboratory measurements. However, RDT underpredicts the maximum efficiency for saltwater and also the value of Gr at which the efficiency becomes constant. The predicted behavior of the mixing efficiency for two active scalars is similar to that for one scalar, and the efficiency decreases as Rρ decreases, as in experiments and semi-empirical models. These calculations show that results from simulations with low Sc likely overestimate the efficiency of turbulence in strongly stratified flows in lakes and oceans. |
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| Keywords: | Mixing efficiency Stratification Turbulence |
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