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Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS. (English) Zbl 07319130
Summary: 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.
76F06 Transition to turbulence
76F25 Turbulent transport, mixing
76Rxx Diffusion and convection
Nek5000; POP
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[1] Baines, P.G. & Gill, A.E.1969On thermohaline convection with linear gradients. J. Fluid Mech.37 (2), 289-306.
[2] Batchelor, G.K.1959Small-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. · Zbl 0085.39701
[3] Caulfield, C.P. & Peltier, W.R.2000The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech.413, 1-47. · Zbl 0982.76050
[4] Fischer, P.F., Kruse, G.W. & Loth, F.2002Spectral element methods for transitional flows in complex geometries. J. Sci. Comput.17 (1-4), 81-98. · Zbl 1001.76075
[5] Fischer, P.F., Kruse, G.W., Lottes, J.W. & Kerkemeier, S.G.2008 Nek5000 Web Page. Available at: http://nek5000.mcs.anl.gov.
[6] 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.
[7] Holyer, J.Y.1984The stability of long, steady, two-dimensional salt fingers. J. Fluid Mech.147, 169-185. · Zbl 0588.76069
[8] Inoue, R., Yamazaki, H., Wolk, F., Kono, T. & Yoshida, J.2007An estimation of buoyancy flux for a mixture of turbulence and double diffusion. J. Phys. Oceanogr.37 (3), 611-624.
[9] Kimura, S., Smyth, W. & Kunze, E.2011Turbulence in a sheared, salt-fingering-favorable environment: anisotropy and effective diffusivities. J. Phys. Oceanogr.41 (6), 1144-1159.
[10] Large, W.G., Mcwilliams, J.C. & Doney, S.C.1994Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev. Geophys.32 (4), 363-403.
[11] Maday, Y., Patera, A.T. & Rønquist, E.M.1990An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow. J. Sci. Comput.5 (4), 263-292. · Zbl 0724.76070
[12] Mashayek, A., Caulfield, C.P. & Peltier, W.R.2017Role of overturns in optimal mixing in stratified mixing layers. J. Fluid Mech.826, 522-552. · Zbl 1430.76221
[13] Mashayek, A. & Peltier, W.R.2013Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?J. Fluid Mech.725, 216-261. · Zbl 1287.76127
[14] Mcdougall, T.J. & Taylor, J.R.1984Flux measurements across a finger interface at low values of the stability ratio. J. Mar. Res.42 (1), 1-14.
[15] Middleton, L. & Taylor, J.R.2020A general criterion for the release of background potential energy through double diffusion. J. Fluid Mech.893, R3. · Zbl 1460.76740
[16] Nakano, H. & Yoshida, J.2019A note on estimating Eddy diffusivity for oceanic double-diffusive convection. J. Oceanogr.75, 375-393.
[17] Osborn, T.R.1980Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr.10 (1), 83-89.
[18] Peltier, W.R. & Caulfield, C.P.2003Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech.35 (1), 135-167. · Zbl 1041.76024
[19] Peltier, W.R., Ma, Y. & Chandan, D.2020The KPP trigger of rapid AMOC intensification in the nonlinear Dansgaard-Oeschger relaxation oscillation. J. Geophys. Res.-Oceans. 125, e2019JC015557.
[20] Radko, T.2003A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech.497, 365-380. · Zbl 1065.76086
[21] Radko, T.2008The double-diffusive modon. J. Fluid Mech.609, 59-85. · Zbl 1147.76058
[22] Radko, T.2013Double-Diffusive Convection. Cambridge University Press.
[23] Radko, T. & Smith, D.P.2012Equilibrium transport in double-diffusive convection. J. Fluid Mech.692, 5-27. · Zbl 1250.76076
[24] Salehipour, H., Caulfield, C.-P. & Peltier, W.R.2016Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech.803, 591-621.
[25] Salehipour, H. & Peltier, W.R.2015Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech.775, 464-500. · Zbl 1403.76028
[26] Schmitt, R.W.1979 Flux measurements on salt fingers at an interface. J. Mar. Res.37, 419-436.
[27] Schmitt, R.W.1981Form of the temperature-salinity relationship in the central water: evidence for double-diffusive mixing. J. Phys. Oceanogr.11 (7), 1015-1026.
[28] Schmitt, R.W.1988 Mixing in a thermohaline staircase. In Elsevier Oceanography Series, vol. 46, pp. 435-452. Elsevier.
[29] Schmitt, R.W. & Evans, D.L.1978An estimate of the vertical mixing due to salt fingers based on observations in the north Atlantic central water. J. Geophys. Res.-Oceans83 (C6), 2913-2919.
[30] Schmitt, R.W., Ledwell, J.R., Montgomery, E.T., Polzin, K.L. & Toole, J.M.2005Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science308 (5722), 685-688.
[31] Shen, C.Y.1989The evolution of the double-diffusive instability: salt fingers. Phys. Fluids A1 (5), 829-844.
[32] Shen, C.Y.1995Equilibrium salt-fingering convection. Phys. Fluids7 (4), 706-717. · Zbl 1032.76549
[33] Shen, C.Y. & Veronis, G.1997Numerical simulation of two-dimensional salt fingers. J. Geophys. Res.-Oceans102 (C10), 23131-23143.
[34] Singh, O.P. & Srinivasan, J.2014Effect of rayleigh numbers on the evolution of double-diffusive salt fingers. Phys. Fluids26 (6), 062104.
[35] 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.
[36] St. Laurent, L. & Schmitt, R.W.1999The contribution of salt fingers to vertical mixing in the North Atlantic tracer release experiment. J. Phys. Oceanogr.29 (7), 1404-1424.
[37] Stellmach, S., Traxler, A., Garaud, P., Brummell, N. & Radko, T.2011Dynamics of fingering convection. Part 2. The formation of thermohaline staircases. J. Fluid Mech.677, 554-571. · Zbl 1241.76228
[38] Traxler, A., Stellmach, S., Garaud, P., Radko, T. & Brummell, N.2011Dynamics of fingering convection. Part 1. Small-scale fluxes and large-scale instabilities. J. Fluid Mech.677, 530-553. · Zbl 1241.76229
[39] Turner, J.S.1967 Salt fingers across a density interface. In Deep Sea Research and Oceanographic Abstracts, vol. 14, pp. 599-611. Elsevier.
[40] Walin, G.1964Note on the stability of water stratified by both salt and heat. Tellus16 (3), 389-393.
[41] Wells, M.G. & Griffiths, R.W.2003Interaction of salt finger convection with intermittent turbulence. J. Geophys. Res.-Oceans108 (C3).
[42] Winters, K.B., Lombard, P.N., Riley, J.J. & D’Asaro, E.A.1995Available potential energy and mixing in density-stratified fluids. J. Fluid Mech.289, 115-128. · Zbl 0858.76095
[43] Zhang, J., Schmitt, R.W. & Huang, R.X.1998Sensitivity of the GFDL modular ocean model to parameterization of double-diffusive processes. J. Phys. Oceanogr.28 (4), 589-605.
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