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Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS

Published online by Cambridge University Press:  25 January 2021

Yuchen Ma Open the ORCID record for Yuchen Ma [Opens in a new window]  and
W. R. Peltier
Yuchen Ma*
Affiliation:
Department of Physics, University of Toronto, 60 St George Street, Toronto, ON, M5S 1A7, Canada
W. R. Peltier
Affiliation:
Department of Physics, University of Toronto, 60 St George Street, Toronto, ON, M5S 1A7, Canada
*
†Email address for correspondence: [email protected]
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Abstract

We employ direct numerical simulations of salt fingering engendered turbulent mixing to derive a parameterization scheme for the representation of this physical process in low-resolution ocean models and compare the results with those previously suggested on empirical grounds. In this analysis we differentiate between the reversible and irreversible contributions to diapycnal diffusivity associated with the turbulence generated by this mechanism. The necessity of such a distinction has been clearly recognized in connection with shear-driven density stratified turbulence processes: only irreversible processes can contribute to the effective turbulent diapycnal diffusivity. We expand the formalism herein to the more complicated salt-fingering case as a first step towards analysis of the general case. The irreversible fluxes are determined in the case of salt fingering related turbulence by examining high-resolution direct numerical simulation (DNS)-derived turbulence data sets based upon two different models: namely the ‘unbounded gradient model’ and the ‘interface model’ with depth-dependent gradients of temperature and salinity. By fitting the irreversible diapycnal fluxes in the unbounded gradient model (for equilibrium states) as a function of density ratio (the governing non-dimensional parameter), we derive a functional form that can be used as a basis for a next generation salt-fingering parametrization scheme. By applying this scheme to the interface model, we demonstrate that the local fluxes predicted agree well with those obtained from the numerical simulations based upon this more complex model. We compare this new DNS-derived turbulence parameterization with those that have been derived empirically.

JFM classification

Convection: Double diffusive convection Instability: Transition to turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A9
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Baines, P.G. & Gill, A.E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37 (2), 289–306.CrossRefGoogle Scholar
Batchelor, G.K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5 (1), 113–133.CrossRefGoogle Scholar
Caulfield, C.P. & Peltier, W.R. 2000 The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech. 413, 1–47.CrossRefGoogle Scholar
Fischer, P.F., Kruse, G.W. & Loth, F. 2002 Spectral element methods for transitional flows in complex geometries. J. Sci. Comput. 17 (1–4), 81–98.CrossRefGoogle Scholar
Fischer, P.F., Kruse, G.W., Lottes, J.W. & Kerkemeier, S.G. 2008 Nek5000 Web Page. Available at: http://nek5000.mcs.anl.gov.Google Scholar
Griffies, S.M., Levy, M., Adcroft, A.J., Danabasoglu, G., Hallberg, R.W., Jacobsen, D., Large, W.G. & Ringler, T. 2015 Theory and numerics of the community ocean vertical mixing (CVMix) project. Tech Rep.Google Scholar
Holyer, J.Y. 1984 The stability of long, steady, two-dimensional salt fingers. J. Fluid Mech. 147, 169–185.CrossRefGoogle Scholar
Inoue, R., Yamazaki, H., Wolk, F., Kono, T. & Yoshida, J. 2007 An estimation of buoyancy flux for a mixture of turbulence and double diffusion. J. Phys. Oceanogr. 37 (3), 611–624.CrossRefGoogle Scholar
Kimura, S., Smyth, W. & Kunze, E. 2011 Turbulence in a sheared, salt-fingering-favorable environment: anisotropy and effective diffusivities. J. Phys. Oceanogr. 41 (6), 1144–1159.CrossRefGoogle Scholar
Large, W.G., McWilliams, J.C. & Doney, S.C. 1994 Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32 (4), 363–403.CrossRefGoogle Scholar
Maday, Y., Patera, A.T. & Rønquist, E.M. 1990 An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow. J. Sci. Comput. 5 (4), 263–292.CrossRefGoogle Scholar
Mashayek, A., Caulfield, C.P. & Peltier, W.R. 2017 Role of overturns in optimal mixing in stratified mixing layers. J. Fluid Mech. 826, 522–552.CrossRefGoogle Scholar
Mashayek, A. & Peltier, W.R. 2013 Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency? J. Fluid Mech. 725, 216–261.CrossRefGoogle Scholar
McDougall, T.J. & Taylor, J.R. 1984 Flux measurements across a finger interface at low values of the stability ratio. J. Mar. Res. 42 (1), 1–14.CrossRefGoogle Scholar
Middleton, L. & Taylor, J.R. 2020 A general criterion for the release of background potential energy through double diffusion. J. Fluid Mech. 893, R3.CrossRefGoogle Scholar
Nakano, H. & Yoshida, J. 2019 A note on estimating Eddy diffusivity for oceanic double-diffusive convection. J. Oceanogr. 75, 375–393.CrossRefGoogle Scholar
Osborn, T.R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10 (1), 83–89.2.0.CO;2>CrossRefGoogle Scholar
Peltier, W.R. & Caulfield, C.P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135–167.CrossRefGoogle Scholar
Peltier, W.R., Ma, Y. & Chandan, D. 2020 The KPP trigger of rapid AMOC intensification in the nonlinear Dansgaard-Oeschger relaxation oscillation. J. Geophys. Res.-Oceans. 125, e2019JC015557.CrossRefGoogle Scholar
Radko, T. 2003 A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech. 497, 365–380.CrossRefGoogle Scholar
Radko, T. 2008 The double-diffusive modon. J. Fluid Mech. 609, 59–85.CrossRefGoogle Scholar
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.CrossRefGoogle Scholar
Radko, T. & Smith, D.P. 2012 Equilibrium transport in double-diffusive convection. J. Fluid Mech. 692, 5–27.CrossRefGoogle Scholar
Salehipour, H., Caulfield, C.-P. & Peltier, W.R. 2016 Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech. 803, 591–621.CrossRefGoogle Scholar
Salehipour, H. & Peltier, W.R. 2015 Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech. 775, 464–500.CrossRefGoogle Scholar
Schmitt, R.W. 1979 Flux measurements on salt fingers at an interface. J. Mar. Res. 37, 419–436.Google Scholar
Schmitt, R.W. 1981 Form of the temperature-salinity relationship in the central water: evidence for double-diffusive mixing. J. Phys. Oceanogr. 11 (7), 1015–1026.2.0.CO;2>CrossRefGoogle Scholar
Schmitt, R.W. 1988 Mixing in a thermohaline staircase. In Elsevier Oceanography Series, vol. 46, pp. 435–452. Elsevier.Google Scholar
Schmitt, R.W. & Evans, D.L. 1978 An estimate of the vertical mixing due to salt fingers based on observations in the north Atlantic central water. J. Geophys. Res.-Oceans 83 (C6), 2913–2919.CrossRefGoogle Scholar
Schmitt, R.W., Ledwell, J.R., Montgomery, E.T., Polzin, K.L. & Toole, J.M. 2005 Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science 308 (5722), 685–688.CrossRefGoogle ScholarPubMed
Shen, C.Y. 1989 The evolution of the double-diffusive instability: salt fingers. Phys. Fluids A 1 (5), 829–844.CrossRefGoogle Scholar
Shen, C.Y. 1995 Equilibrium salt-fingering convection. Phys. Fluids 7 (4), 706–717.CrossRefGoogle Scholar
Shen, C.Y. & Veronis, G. 1997 Numerical simulation of two-dimensional salt fingers. J. Geophys. Res.-Oceans 102 (C10), 23131–23143.CrossRefGoogle Scholar
Singh, O.P. & Srinivasan, J. 2014 Effect of rayleigh numbers on the evolution of double-diffusive salt fingers. Phys. Fluids 26 (6), 062104.CrossRefGoogle Scholar
Smith, R., et al. . 2010 The parallel ocean program (POP) reference manual: ocean component of the community climate system model (CCSM) and community earth system model (CESM). LAUR-01853, vol. 141, pp. 1–140.Google Scholar
St. Laurent, L. & Schmitt, R.W. 1999 The contribution of salt fingers to vertical mixing in the North Atlantic tracer release experiment. J. Phys. Oceanogr. 29 (7), 1404–1424.2.0.CO;2>CrossRefGoogle Scholar
Stellmach, S., Traxler, A., Garaud, P., Brummell, N. & Radko, T. 2011 Dynamics of fingering convection. Part 2. The formation of thermohaline staircases. J. Fluid Mech. 677, 554–571.CrossRefGoogle Scholar
Traxler, A., Stellmach, S., Garaud, P., Radko, T. & Brummell, N. 2011 Dynamics of fingering convection. Part 1. Small-scale fluxes and large-scale instabilities. J. Fluid Mech. 677, 530–553.CrossRefGoogle Scholar
Turner, J.S. 1967 Salt fingers across a density interface. In Deep Sea Research and Oceanographic Abstracts, vol. 14, pp. 599–611. Elsevier.CrossRefGoogle Scholar
Walin, G. 1964 Note on the stability of water stratified by both salt and heat. Tellus 16 (3), 389–393.Google Scholar
Wells, M.G. & Griffiths, R.W. 2003 Interaction of salt finger convection with intermittent turbulence. J. Geophys. Res.-Oceans 108 (C3).CrossRefGoogle Scholar
Winters, K.B., Lombard, P.N., Riley, J.J. & D'Asaro, E.A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.CrossRefGoogle Scholar
Zhang, J., Schmitt, R.W. & Huang, R.X. 1998 Sensitivity of the GFDL modular ocean model to parameterization of double-diffusive processes. J. Phys. Oceanogr. 28 (4), 589–605.2.0.CO;2>CrossRefGoogle Scholar