Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T20:10:35.372Z Has data issue: false hasContentIssue false
  • English
  • Français

Salinity transfer in bounded double diffusive convection

Published online by Cambridge University Press:  10 March 2015

Yantao Yang ,
Erwin P. van der Poel ,
Rodolfo Ostilla-Mónico ,
Chao Sun ,
Roberto Verzicco ,
Siegfried Grossmann  and
Detlef Lohse
Yantao Yang*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Erwin P. van der Poel
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Rodolfo Ostilla-Mónico
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Chao Sun
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Roberto Verzicco
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
Siegfried Grossmann
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared with experiments by Hage & Tilgner (Phys. Fluids, vol. 22, 2010, 076603) for several sets of parameters and reasonable agreement is found. This, in particular, holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have a minor influence on the salinity flux but affects the Reynolds number and the morphology of the flow. In addition to the numerical calculation, we apply the Grossmann–Lohse theory for Rayleigh–Bénard flow to the present problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.

JFM classification

Convection: Convection Convection: Double diffusive convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 476 - 491
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279–314.CrossRefGoogle Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65 (3), 851–1112.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2001 Thermal convection for large Prandtl numbers. Phys. Rev. Lett. 86 (15), 3316–3319.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66 (1), 016305.CrossRefGoogle ScholarPubMed
Grossmann, S. & Lohse, D. 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16 (12), 4462–4472.CrossRefGoogle Scholar
Hage, E. & Tilgner, A. 2010 High Rayleigh number convection with double diffusive fingers. Phys. Fluids 22 (7), 076603.CrossRefGoogle Scholar
Hort, W., Linz, S. J. & Lücke, M. 1992 Onset of convection in binary gas mixtures: role of the Dufour effect. Phys. Rev. A 45 (6), 3737–3748.CrossRefGoogle ScholarPubMed
Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40 (1), 185–208.CrossRefGoogle Scholar
Krishnamurti, R. 2003 Double-diffusive transport in laboratory thermohaline staircases. J. Fluid Mech. 483, 287–314.CrossRefGoogle Scholar
Kunze, E. 2003 A review of oceanic salt-fingering theory. Prog. Oceanogr. 56, 399–417.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.Google Scholar
Linden, P. F. 1973 On the structure of salt fingers. Deep-Sea Res. 20 (4), 325–340.Google Scholar
Linden, P. F. 1978 The formation of banded salt finger structure. J. Geophys. Res. 83 (C6), 2902–2912.CrossRefGoogle Scholar
Liu, J. & Ahlers, G. 1996 Spiral-defect chaos in Rayleigh–Bénard convection with small Prandtl numbers. Phys. Rev. Lett. 77 (15), 3126–3129.CrossRefGoogle ScholarPubMed
Liu, J. & Ahlers, G. 1997 Rayleigh–Bénard convection in binary-gas mixtures: thermophysical properties and the onset of convection. Phys. Rev. E 55 (6), 6950–6968.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
Mirouh, G. M., Garaud, P., Stellmach, S., Traxler, A. L. & Wood, T. S. 2012 A new model for mixing by double-diffusive convection (semi-convection). I. The conditions for layer formation. Astrophys. J. 750 (1), 61.CrossRefGoogle Scholar
Ostilla-Mónico, R., Yang, Y., van der Poel, E. P., Lohse, D. & Verzicco, R. 2015 A multiple resolutions strategy for direct numerical simulation of scalar turbulence. J. Comp. Phys. (submitted) arXiv:1502.01874.CrossRefGoogle Scholar
Paparella, F. & von Hardenberg, J. 2012 Clustering of salt fingers in double-diffusive convection leads to staircase like stratification. Phys. Rev. Lett. 109, 014502.CrossRefGoogle Scholar
Pringle, S. E. & Glass, R. J. 2002 Double-diffusive finger convection: influence of concentration at fixed buoyancy ratio. J. Fluid Mech. 462, 161–183.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
Radko, T. & Stern, M. E. 2000 Finite-amplitude salt fingers in a vertically bounded layer. J. Fluid Mech. 425, 133–160.CrossRefGoogle Scholar
Rosenblum, E., Garaud, P., Traxler, A. & Stellmach, S. 2011 Turbulent mixing and layer formation in double-diffusive convection: three-dimensional numerical simulations and theory. Astrophys. J. 731 (1), 66.CrossRefGoogle Scholar
Schmitt, R. W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26, 255–285.CrossRefGoogle Scholar
Schmitt, R. W. 2011 Thermohaline convection at density ratios below one: a new regime for salt fingers. J. Mar. Res. 69, 779–795.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, 685–688.CrossRefGoogle ScholarPubMed
Shirtcliffe, T. G. L. & Turner, J. S. 1970 Observations of the cell structure of salt fingers. J. Fluid Mech. 41 (04), 707–719.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42 (6), 3650–3653.CrossRefGoogle ScholarPubMed
Spiegel, E. A. 1972 Convection in stars II. Special effects. Annu. Rev. Astron. Astrophys. 10 (1), 261–304.CrossRefGoogle Scholar
Sreenivas, K. R., Singh, O. P. & Srinivasan, J. 2009 On the relationship between finger width, velocity, and fluxes in thermohaline convection. Phys. Fluids 21 (2), 026601.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
Stern, M. E. 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12 (2), 172–175.CrossRefGoogle Scholar
Stevens, R. J. A. M., van der Poel, E. P., Grossmann, S. & Lohse, D. 2013 The unifying theory of scaling in thermal convection: the updated prefactors. J. Fluid Mech. 730, 295–308.CrossRefGoogle Scholar
Stevens, R. J. A. M., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495–507.CrossRefGoogle Scholar
Taylor, J. & Bucens, P. 1989 Laboratory experiments on the structure of salt fingers. Deep-Sea Res. A 36 (11), 1675–1704.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. Deep-Sea Res. 14 (5), 599–611.Google Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6, 37–57.CrossRefGoogle Scholar
Turner, J. S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17 (1), 11–44.CrossRefGoogle Scholar
Verzicco, R. & Camussi, R. 1999 Prandtl number effects in convective turbulence. J. Fluid Mech. 383, 55–73.CrossRefGoogle Scholar
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19–49.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402–413.CrossRefGoogle Scholar
Wood, T. S., Garaud, P. & Stellmach, S. 2013 A new model for mixing by double-diffusive convection (semi-convection). II. The transport of heat and composition through layers. Astrophys. J. 768 (2), 157.CrossRefGoogle Scholar
Yoshida, J. & Nagashima, H. 2003 Numerical experiments on salt-finger convection. Prog. Oceanogr. 56 (34), 435–459.CrossRefGoogle Scholar