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Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations

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Abstract

Diapycnal (irreversible) mixing is analyzed using thirty direct numerical simulations (at \(1024^3\) resolution) of homogeneous rotating stratified turbulence (RST) in the absence of imposed shear or forcing. The influence of varied rotation and stratification rates on the energetics (in particular the dissipation rates of kinetic and potential energies) is presented. Data is also analyzed within a new parametric framework, using the turbulent Froude and Rossby numbers \(Fr_t = \epsilon /Nk\), \(Ro_t = \epsilon / f k\), where k is the turbulent kinetic energy, \(\epsilon\) its rate of dissipation, N the buoyancy frequency and f the Coriolis parameter. This framework is used to illustrate relative magnitudes of the stratification and rotation in geophysical flows and provide a useful tool for explicating the relationship between \(Fr_t\) and \(Ro_t\) as relevant dynamic parameters in the geophysical setting. Results indicate that unforced rotation does not impact the magnitude of the irreversible mixing coefficient (\(\Gamma =\epsilon _P/\epsilon\)) when compared to results without rotation, where \(\epsilon _P\) is the rate of potential energy dissipation. Moreover, it is shown that the recent scaling laws for mixing efficiency in stably stratified turbulence in the absence of rotation, as exemplified in Garanaik & Venayagamoorthy (J. Fluid Mech. 867, 2019, pp. 323-333), are applicable as well for homogeneous and decaying RST. Results also highlight the ambiguity of the ratio N/f as a control parameter for the classification of small-scale RST, and thus for evaluating diapycnal mixing.

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Acknowledgements

SKV and MRK gratefully acknowledge funding from the Office of Naval Research (N00014-18-1-2773 and N00014-22-1-2043). AP is thankful to the Laboratory for Atmospheric and Space Physics (LASP) and in particular to Bob Ergun for support. DR wishes to acknowledge the Colorado State University Cooperative Institute for Research in the Atmosphere at the National Oceanic and Atmospheric Administration (NOAA)/Oceanic and Atmospheric Research (OAR)/Earth Systems Research Laboratories (ESRL), Global Systems Division Number: NA14OAR4320125. Computation and storage of some numerical data was provided by the National Center for Atmospheric Research (NCAR), for which we are grateful. NCAR is funded by the National Science Foundation (NSF). RM acknowledges support from the project ‘EVENTFUL’ (ANR-20-CE30-0011), funded by the French ‘Agence Nationale de la Recherche’ - ANR through the program AAPG-2020.

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  1. Matthew Klema, S. Karan Venayagamoorthy, Annick Pouquet, Duane Rosenberg and Raffaele Marino have contributed equally to this work.

Authors and Affiliations

  1. Civil and Environmental Engineering Department, Colorado State University, Fort Collins, CO, 80523, USA

    Matthew Klema & S. Karan Venayagamoorthy

  2. Department of Physics and Engineering, Fort Lewis College, Durango, CO, 81301, USA

    Matthew Klema

  3. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, 80309, USA

    Annick Pouquet

  4. National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307, USA

    Annick Pouquet

  5. Cooperative Institute for Research in the Atmosphere, NOAA, G/GSD, 325 Broadway, Boulder, CO, 80305, USA

    Duane Rosenberg

  6. Laboratoire de Mécanique des Fluides et d’Acoustique, UMR5509, F-69134, Université de Lyon, CNRS, École Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, 69134, Écully, France

    Raffaele Marino

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Klema, M., Venayagamoorthy, S.K., Pouquet, A. et al. Effect of rotation on mixing efficiency in homogeneous stratified turbulence using unforced direct numerical simulations. Environ Fluid Mech 23, 1115–1130 (2023). https://doi.org/10.1007/s10652-022-09869-y

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