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Measurements of mixing parameters in atmospheric stably stratified parallel shear flow

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Abstract

The mixing coefficient Г = B/ε, defined as the ratio of the magnitude of buoyancy flux B to the rate of turbulent kinetic energy (TKE) dissipation ε, plays a key role in modeling atmospheric and oceanic flows. Г is sometimes estimated using yet another fundamental quantity, the flux Richardson number (or mixing efficiency) Rif = B/P, where P is the rate of production of TKE. In practice, Г and Rif are commonly assumed as constants, but studies show that they depend on multiple parameters determined by the type of flow, for example, the gradient Richardson number Rig for stratified shear flows. During the MATERHORN field program, direct measurements of velocity and temperature profiles as well as B, ε, and P were made over an extended period using a densely instrumented flux tower. A ~ 90 min period of stratified parallel shear flow was identified in the data record, including recurrent intervals of nominally stationary flow. Measurements during this period supported the study of mixing parameters as reported in this paper. Even for this case of nature resembling an ideal flow, Г was found to be dependent on multiple parameters. Nevertheless, for periods robustly identified as shear flow in equilibrium with embedded turbulence, the measurements were in agreement with those of past stratified shear flow experiments in the laboratory. This result points to the challenges of parameterizing turbulent mixing in environmental flow models.

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Acknowledgements

The MATERHORN program supported the technology development necessary to obtain the experimental data presented here and was funded under a Multidisciplinary University Research Initiative of the Office of Naval Research (Award # N00014-11-1-0709). PC was supported by the U.S. Department of Defense through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. EK was supported by Israel Science Foundation (Grant 408/15). During the data analysis, HJSF was funded by U.S. National Science Foundation grants (AGS-1528451 and AGS-1565535). Dan Liberzon and Chris Hocut provided crucial support during various phases of the experiment. We acknowledge two anonymous reviewers for making comments that led to improvement of manuscript.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    Patrick Conry, Eliezer Kit & Harindra J. S. Fernando

  2. Department of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel

    Eliezer Kit

  3. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Harindra J. S. Fernando

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Correspondence to Patrick Conry.

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Conry, P., Kit, E. & Fernando, H.J.S. Measurements of mixing parameters in atmospheric stably stratified parallel shear flow. Environ Fluid Mech 20, 1177–1197 (2020). https://doi.org/10.1007/s10652-018-9639-z

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