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Dynamics and energetics underlying mixing efficiency in homogeneous stably stratified turbulence

Young R. Yi* and Jeffrey R. Koseff

  • Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA

  • *yryi@stanford.edu
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Phys. Rev. Fluids 7, 084801 – Published 12 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084801

Abstract

We studied homogeneous stably stratified turbulence in a triply periodic domain over a wide range of stratification strengths. We evaluated the statistically stationary, volume-averaged budgets of Reynolds stresses, turbulent potential energy, and turbulent vertical density flux. By separately studying the three components of the turbulent kinetic energy (TKE), we examined the role of pressure-strain correlations and observed connections between changes in the energetics to regime shifts of the mixing coefficient (Γ) as a function of the turbulent Froude number (Frk). As we increase stratification, we find that pressure-strain correlations become more important in producing the vertical component of TKE (kw). At the stratification strength where direct production and pressure-strain correlations equally generate kw, we observe the maximum value of Γ, and it remains constant as stratification is increased further. However, when we greatly increase stratification from this point, the pressure-strain correlations become the dominant source of kw with direct production becoming negligible, and this change is accompanied by the mixing coefficient decreasing from its maximum value. Finally, we find that this final transition for the mixing coefficient coincides with a sign change of the pressure scrambling term in the vertical density flux budget.

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References (43)

  1. C. Wunsch and R. Ferrari, Vertical mixing, energy, and the general circulation of the oceans, Annu. Rev. Fluid Mech. 36, 281 (2004).
  2. W. D. Smyth, H. T. Pham, J. N. Moum, and S. Sarkar, Pulsating turbulence in a marginally unstable stratified shear flow, J. Fluid Mech. 822, 327 (2017).
  3. A. Adcroft, W. Anderson, V. Balaji, C. Blanton, M. Bushuk, C. O. Dufour, J. P. Dunne, S. M. Griffies, R. Hallberg, M. J. Harrison, I. M. Held, M. F. Jansen, J. G. John, J. P. Krasting, A. R. Langenhorst, S. Legg, Z. Liang, C. McHugh, A. Radhakrishnan, B. G. Reichl et al., The GFDL global ocean and sea ice model OM4.0: Model description and simulation features, J. Adv. Model. Earth Syst. 11, 3167 (2019).
  4. C. de Lavergne, G. Madec, J. Le Sommer, A. J. G. Nurser, and A. C. Naveira Garabato, The impact of a variable mixing efficiency on the abyssal overturning, J. Phys. Oceanogr. 46, 663 (2015).
  5. A. Mashayek, H. Salehipour, D. Bouffard, C. P. Caulfield, R. Ferrari, M. Nikurashin, W. R. Peltier, and W. D. Smyth, Efficiency of turbulent mixing in the abyssal ocean circulation, Geophys. Res. Lett. 44, 6296 (2017).
  6. L. Cimoli, C. P. Caulfield, H. L. Johnson, D. P. Marshall, A. Mashayek, A. C. Naveira Garabato, and C. Vic, Sensitivity of deep ocean mixing to local internal tide breaking and mixing efficiency, Geophys. Res. Lett. 46, 14622 (2019).
  7. T. R. Osborn, Estimates of the local rate of vertical diffusion from dissipation measurements, J. Phys. Oceanogr. 10, 83 (1980).
  8. H. Salehipour and W. R. Peltier, Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence, J. Fluid Mech. 775, 464 (2015).
  9. S. K. Venayagamoorthy and J. R. Koseff, On the flux Richardson number in stably stratified turbulence, J. Fluid Mech. 798, R1 (2016).
  10. G. N. Ivey and J. Imberger, On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing, J. Phys. Oceanogr. 21, 650 (1991).
  11. A. F. Waterhouse, J. A. MacKinnon, J. D. Nash, M. H. Alford, E. Kunze, H. L. Simmons, K. L. Polzin, L. C. St. Laurent, O. M. Sun, R. Pinkel, L. D. Talley, C. B. Whalen, T. N. Huussen, G. S. Carter, I. Fer, S. Waterman, A. C. Naveira Garabato, T. B. Sanford, and C. M. Lee, Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate, J. Phys. Oceanogr. 44, 1854 (2014).
  12. G. N. Ivey, K. B. Winters, and J. R. Koseff, Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech. 40, 169 (2008).
  13. M. C. Gregg, E. A. D'Asaro, J. J. Riley, and E. Kunze, Mixing efficiency in the ocean, Annu. Rev. Mar. Sci. 10, 443 (2018).
  14. C. P. Caulfield, Open questions in turbulent stratified mixing: Do we even know what we do not know? Phys. Rev. Fluids 5, 110518 (2020).
  15. C. P. Caulfield, Layering, instabilities, and mixing in turbulent stratified flows, Annu. Rev. Fluid Mech. 53, 113 (2021).
  16. S. G. Monismith, J. R. Koseff, and B. L. White, Mixing efficiency in the presence of stratification: When is it constant? Geophys. Res. Lett. 45, 5627 (2018).
  17. A. Garanaik and S. K. Venayagamoorthy, On the inference of the state of turbulence and mixing efficiency in stably stratified flows, J. Fluid Mech. 867, 323 (2019).
  18. A. Maffioli, G. Brethouwer, and E. Lindborg, Mixing efficiency in stratified turbulence, J. Fluid Mech. 794, R3 (2016).
  19. L. H. Shih, J. R. Koseff, G. N. Ivey, and J. H. Ferziger, Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations, J. Fluid Mech. 525, 193 (2005).
  20. G. D. Portwood, S. M. de Bruyn Kops, and C. P. Caulfield, Asymptotic Dynamics of High Dynamic Range Stratified Turbulence, Phys. Rev. Lett. 122, 194504 (2019).
  21. T. S. Lundgren, Linearly forced isotropic turbulence, in Annual Research Briefs (Center for Turbulence Research, Stanford, CA, 2003), pp. 461–473
  22. C. Rosales and C. Meneveau, Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties, Phys. Fluids 17, 095106 (2005).
  23. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).
  24. C. Canuto, A. Quarteroni, M. Y. Hussaini, and T. A. Zang, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics, Scientific Computation (Springer, Berlin, 2007).
  25. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, Scientific Computation (Springer, Berlin, 2006).
  26. M. Bassenne, J. Urzay, G. I. Park, and P. Moin, Constant-energetics physical-space forcing methods for improved convergence to homogeneous-isotropic turbulence with application to particle-laden flows, Phys. Fluids 28, 035114 (2016).
  27. K.-S. Choi and J. L. Lumley, The return to isotropy of homogeneous turbulence, J. Fluid Mech. 436, 59 (2001).
  28. A. J. Simonsen and P.-Å. Krogstad, Turbulent stress invariant analysis: Clarification of existing terminology, Phys. Fluids 17, 088103 (2005).
  29. M. L. Waite and P. Bartello, Stratified turbulence dominated by vortical motion, J. Fluid Mech. 517, 281 (2004).
  30. E. Lindborg, The energy cascade in a strongly stratified fluid, J. Fluid Mech. 550, 207 (2006).
  31. G. Brethouwer, P. Billant, E. Lindborg, and J.-M. Chomaz, Scaling analysis and simulation of strongly stratified turbulent flows, J. Fluid Mech. 585, 343 (2007).
  32. E. Lindborg and G. Brethouwer, Stratified turbulence forced in rotational and divergent modes, J. Fluid Mech. 586, 83 (2007).
  33. A. Maffioli, Vertical spectra of stratified turbulence at large horizontal scales, Phys. Rev. Fluids 2, 104802 (2017).
  34. J. A. Palmore and O. Desjardins, Technique for forcing high Reynolds number isotropic turbulence in physical space, Phys. Rev. Fluids 3, 034605 (2018).
  35. S. Almalkie and S. M. de Bruyn Kops, Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence, J. Turbul. 13, N29 (2012).
  36. C. J. Howland, J. R. Taylor, and C. P. Caulfield, Mixing in forced stratified turbulence and its dependence on large-scale forcing, J. Fluid Mech. 898, A7 (2020).
  37. E. Bou-Zeid, X. Gao, C. Ansorge, and G. G. Katul, On the role of return to isotropy in wall-bounded turbulent flows with buoyancy, J. Fluid Mech. 856, 61 (2018).
  38. E. C. Itsweire, J. R. Koseff, D. A. Briggs, and J. H. Ferziger, Turbulence in stratified shear flows: Implications for interpreting shear-induced mixing in the ocean, J. Phys. Oceanogr. 23, 1508 (1993).
  39. P. Billant and J.-M. Chomaz, Self-similarity of strongly stratified inviscid flows, Phys. Fluids 13, 1645 (2001).
  40. A. Maffioli and P. A. Davidson, Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number, J. Fluid Mech. 786, 210 (2016).
  41. S. M. de Bruyn Kops and J. J. Riley, The effects of stable stratification on the decay of initially isotropic homogeneous turbulence, J. Fluid Mech. 860, 787 (2019).
  42. G. P. Chini, G. Michel, K. Julien, C. B. Rocha, and C. P. Caulfield, Exploiting self-organized criticality in strongly stratified turbulence, J. Fluid Mech. 933, A22 (2022).
  43. T. Passot and A. Pouquet, Numerical simulation of compressible homogeneous flows in the turbulent regime, J. Fluid Mech. 181, 441 (1987).

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Phys. Rev. Fluids 7, 084801– Published 12 August, 2022
  • Received 24 January 2022
  • Accepted 21 July 2022
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