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Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

Published online by Cambridge University Press:  12 April 2011

ESTEBAN GONZALEZ-JUEZ ,
ALAN R. KERSTEIN  and
DAVID O. LIGNELL
ESTEBAN GONZALEZ-JUEZ
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA
ALAN R. KERSTEIN*
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA
DAVID O. LIGNELL
Affiliation:
Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA
*
†Email address for correspondence: [email protected]
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Abstract

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat flux Nu scales with the stability parameter Rρ, Rayleigh number Ra and Prandtl number Pr as Nu ~ (Ra/Rρ)0.37±0.03 when Pr varies from 3 to 100 and as Nu ~ (Ra/Rρ)0.31Pr0.22±0.04 when Pr varies from 0.01 to 1. Here Ra/Rρ can be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxes Rf is independent of Pr, scales with the Lewis number Le as Rf ~ Le0.41±0.04 when Rρ is large enough and deviates from this expression for low values of Rρ, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson number Ri ≪ 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface and Rf = Rρ. Near Ri ~ 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces when Ri ≫ 1.

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 218 - 254
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
Ashurst, W. T. & Kerstein, A. R. 2005 One-dimensional turbulence: variable-density formulation and application to mixing layers. Phys. Fluids 17, 025107.CrossRefGoogle Scholar
Atkinson, J. F. 1994 Interfacial fluxes at a grid-stirred diffusive interface. Intl J. Heat Mass Transfer 37, 2089–2099.CrossRefGoogle Scholar
Canuto, V. M., Cheng, Y. & Howard, A. M. 2008 a A new model for double diffusion plus turbulence. Geophys. Res. Lett. 35, 2613.CrossRefGoogle Scholar
Canuto, V. M., Cheng, Y., Howard, A. M. & Esau, I. N. 2008 b Stably stratified flows: a model with no Ri(cr). J. Atmos. Sci. 65, 2437–2447.CrossRefGoogle Scholar
Canuto, V. M., Howard, A., Cheng, Y. & Dubovikov, M. S. 2001 Ocean turbulence. Part I. One-point closure model – momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413–1426.2.0.CO;2>CrossRefGoogle Scholar
Canuto, V. M., Howard, A., Cheng, Y. & Dubovikov, M. S. 2002 Ocean turbulence. Part II. Vertical diffusivities of momentum, heat, salt, mass, and passive scalars. J. Phys. Oceanogr. 32, 240–264.2.0.CO;2>CrossRefGoogle Scholar
Chabrier, G. & Baraffe, I. 2007 Heat transport in giant (exo)planets: a new perspective. Astrophys. J. Lett. 661, L81–L84.CrossRefGoogle Scholar
Crapper, P. F. 1975 Measurements across a diffusive interface. Deep Sea Res. 22, 537–545.Google Scholar
Crapper, P. F. 1976 Fluxes of heat and salt across a diffusive interface in the presence of grid generated turbulence. Intl J. Heat Mass Transfer 19, 1371–1378.CrossRefGoogle Scholar
Dreeben, T. D. & Kerstein, A. R. 2000 Simulation of vertical slot convection using one-dimensional turbulence. Intl J. Heat Mass Transfer 43, 3823–3834.CrossRefGoogle Scholar
Echekki, T., Kerstein, A. R., Dreeben, T. D. & Chen, J. Y. 2001 One-dimensional turbulence simulation of turbulent jet diffusion flames: model formulation and illustrative applications. Combust. Flame 125, 1083–1105.CrossRefGoogle Scholar
Fernando, H. J. S. 1989 Buoyancy transfer across a diffusive interface. J. Fluid Mech. 209, 1–34.CrossRefGoogle Scholar
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23, 455–493.CrossRefGoogle Scholar
Funfschilling, D., Brown, E., Nikolaenko, A. & Ahlers, G. 2005 Heat transport by turbulent Rayleigh–Bénard convection in cylindrical samples with aspect ratio one and larger. J. Fluid Mech. 536, 145–154.CrossRefGoogle Scholar
Gargett, A. E. 1989 Ocean turbulence. Annu. Rev. Fluid Mech. 21, 419–451.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.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, 611–624.CrossRefGoogle Scholar
Kelley, D. E. 1990 Fluxes through diffusive staircases: a new formulation. J. Geophys. Res. 95, 3365–3371.CrossRefGoogle Scholar
Kelley, D. E., Fernando, H. J. S., Gargett, A. E., Tanny, J. & Oezsoy, E. 2003 The diffusive regime of double-diffusive convection. Prog. Oceanogr. 56, 461–481.CrossRefGoogle Scholar
Kerstein, A. R. 1991 Linear-eddy modelling of turbulent transport. Part 6. Microstructure of diffusive scalar mixing fields. J. Fluid Mech. 231, 361–394.CrossRefGoogle Scholar
Kerstein, A. R. 1999 a One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows. J. Fluid Mech. 392, 277–334.CrossRefGoogle Scholar
Kerstein, A. R. 1999 b One-dimensional turbulence. Part 2. Staircases in double-diffusive convection. Dyn. Atmos. Oceans 30, 25–46.CrossRefGoogle Scholar
Kerstein, A. R. 2007 BasicODT. Available at: http://groups.google.com/group/odt-research/.Google Scholar
Kerstein, A. R. 2009 One-dimensional turbulence: stochastic simulation of multi-scale dynamics. Lect. Notes Phys. 756, 291–337.CrossRefGoogle Scholar
Kerstein, A. R., Ashurst, W. T., Wunsch, S. & Nilsen, V. 2001 One-dimensional turbulence: vector formulation and application to free shear flows. J. Fluid Mech. 447, 85–109.CrossRefGoogle Scholar
Kerstein, A. R. & Wunsch, S. 2006 Simulation of a stably stratified atmospheric boundary layer using one-dimensional turbulence. Bound.-Layer Meteorol. 118, 325–356.CrossRefGoogle Scholar
Krishnamoorthy, N. 2008 Reaction models and reaction state parametrization for turbulent nonpremixed combustion. PhD thesis, University of Utah.Google Scholar
Larson, N. G. & Gregg, M. C. 1983 Turbulent dissipation and shear in thermohaline intrusions. Nature 306, 26–32.CrossRefGoogle Scholar
Law, A. M. & Kelton, W. D. 2000 Simulation Modeling and Analysis. McGraw-Hill.Google Scholar
Linden, P. F. 1971 Salt fingers in the presence of grid-generated turbulence. J. Fluid Mech. 49, 611–624.CrossRefGoogle Scholar
Linden, P. F. 1974 A note on the transport across a diffusive interface. Deep Sea Res. 21, 283–287.Google Scholar
Linden, P. F. & Shirtcliffe, T. G. L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417–432.CrossRefGoogle Scholar
Marmorino, G. O. & Caldwell, D. R. 1976 Heat and salt transport through a diffusive thermohaline interface. Deep Sea Res. 23, 59–67.Google Scholar
McDermott, R. J. 2005 Toward one-dimensional turbulence subgrid closure for large-eddy simulation. PhD thesis, University of Utah.Google Scholar
McDougall, T. J. 1981 Double-diffusive convection with a nonlinear equation of state. Part II. Laboratory experiments and their interpretation. Prog. Oceanogr. 10, 91–121.CrossRefGoogle Scholar
Merryfield, W. J. 1995 Hydrodynamics of semiconvection. Astrophys. J. 444, 318–337.CrossRefGoogle Scholar
Newell, T. A. 1984 Characteristics of a double-diffusive interface at high density stability ratios. J. Fluid Mech. 149, 385–401.CrossRefGoogle Scholar
Padman, L. 1994 Momentum fluxes through sheared oceanic thermohaline steps. J. Geophys. Res. 99, 22491–22499.CrossRefGoogle Scholar
Padman, L. & Dillon, T. M. 1991 Turbulent mixing near the Yermak Plateau during the coordinated Eastern Arctic experiment. J. Geophys. Res. 96, 4769–4782.CrossRefGoogle Scholar
Paparella, F., Spiegel, E. A. & Talon, S. 2002 Shear and mixing in oscillatory doubly diffusive convection. Geophys. Astrophys. Fluid Dyn. 96, 271–289.CrossRefGoogle Scholar
Ricks, A. J., Hewson, J. C., Kerstein, A. R., Gore, J. P., Tieszen, S. R. & Ashurst, W. T. 2010 A spatially developing one-dimensional turbulence study of soot and enthalpy evolution in meter-scale buoyant turbulent flames. Combust. Sci. Technol. 182, 60–101.CrossRefGoogle Scholar
Schmidt, R. C., Kerstein, A. R., Wunsch, S. & Nilsen, V. 2003 Near-wall LES closure based on one-dimensional turbulence modeling. J. Comput. Phys. 186, 317–355.CrossRefGoogle Scholar
Shirtcliffe, T. G. L. 1973 Transport and profile measurements of the diffusive interface in double diffusive convection with similar diffusivities. J. Fluid Mech. 57, 27–43.CrossRefGoogle Scholar
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137–168.CrossRefGoogle Scholar
St. Laurent, L. S. & Schmitt, R. W. 1999 The contribution of salt fingers to vertical mixing in the North Atlantic Tracer Release Experiment. J. Phys. Oceanogr. 29, 1404–1424.2.0.CO;2>CrossRefGoogle Scholar
Stern, M. E. 1982 Inequalities and variational principles in double-diffusive turbulence. J. Fluid Mech. 114, 105–121.CrossRefGoogle Scholar
Suárez, F., Tyler, S. W. & Childress, A. E. 2010 A fully coupled, transient double-diffusive convective model for salt-gradient solar ponds. Intl J. Heat Mass Transfer 53, 1718–1730.CrossRefGoogle Scholar
Takao, S. & Narusawa, U. 1980 An experimental study of heat and mass transfer across a diffusive interface. Intl J. Heat Mass Transfer 23, 1283–1285.CrossRefGoogle Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Intl J. Heat Mass Transfer 8, 759–760.CrossRefGoogle Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6, 37–54.CrossRefGoogle Scholar
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Worster, M. G. 2004 Time-dependent fluxes across double-diffusive interfaces. J. Fluid Mech. 505, 287–307.CrossRefGoogle Scholar
Wunsch, S. & Kerstein, A. R. 2001 A model for layer formation in stably stratified turbulence. Phys. Fluids 13, 702–712.CrossRefGoogle Scholar
Wunsch, S. & Kerstein, A. R. 2005 A stochastic model for high-Rayleigh-number convection. J. Fluid Mech. 528, 173–205.CrossRefGoogle Scholar