Skip to main content
    • Aa
    • Aa

Equilibrium transport in double-diffusive convection

  • Timour Radko (a1) and D. Paul Smith (a1)

A theoretical model for the equilibrium double-diffusive transport is presented which emphasizes the role of secondary instabilities of salt fingers in saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for computing diffusivities of heat and salt as a function of the background property gradients and molecular parameters. The model predicts that the double-diffusive transport of heat and salt rapidly intensifies with decreasing density ratio. Fluxes are less sensitive to molecular characteristics, mildly increasing with Prandtl number and decreasing with diffusivity ratio . Theory is successfully tested by a series of direct numerical simulations which span a wide range of and .

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

5. V. M. Canuto , Y. Cheng & A. M. Howard 2008 A new model for Double Diffusion + Turbulence. Geophys. Res. Lett. 35, L02613.

6. C. Charbonnel & J. Zahn 2007 Thermohaline mixing: a physical mechanism governing the photospheric composition of low-mass giants. Astron. Astrophys. 467, L29L32.

7. A. E. Gargett & R. W. Schmitt 1982 Observations of salt fingers in the central waters of the eastern North Pacific. J. Geophys. Res. 87, 80178092.

9. T. Guillot 1999 Interiors of giant planets inside and outside the solar system. Science 286, 7277.

10. D. Hebert 1988 Estimates of salt-finger fluxes. Deep-Sea Res. 35, 18871901.

13. R. Inoue , E. Kunze , L. St Laurent , R. W. Schmitt & J. M. Toole 2008 Evaluating salt fingering theories. J. Mar. Res. 66, 413440.

14. S. Kimura & W. D. Smyth 2007 Direct numerical simulation of salt sheets and turbulence in a double-diffusive shear layer. Geophys. Res. Lett. 34, L21610.

18. E. Kunze 1987 Limits on growing, finite length salt fingers: a Richardson number constraint. J. Mar. Res. 45, 533556.

21. A. Manfroi & W. Young 1999 Slow evolution of zonal jets on the beta plane. J. Atmos. Sci. 56, 784800.

22. A. Manfroi & W. Young 2002 Stability of beta-plane Kolmogorov flow. Physica D 162, 208232.

30. T. Radko & M. E. Stern 1999 Salt fingers in three dimensions. J. Mar. Res. 57, 471502.

32. L. F. Richardson 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. A 97, 354373.

33. J. L. Robinson 1976 Theoretical analysis of convective instability of a growing horizontal thermal boundary layer. Phys. Fluids 19, 778791.

35. R. W. Schmitt 1983 The characteristics of salt fingers in a variety of fluid systems, including stellar interiors, liquid metals, oceans, and magmas. Phys. Fluids 26, 23732377.

36. R. W. Schmitt , J. R. Ledwell , E. T. Montgomery , K. L. Polzin & J. M. Toole 2005 Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science 308, 685688.

37. R. W. Schmitt , H. Perkins , J. D. Boyd & M. C. Stalcup 1987 C-SALT: an investigation of the thermohaline staircase in the western tropical North Atlantic. Deep-Sea Res. 34, 16971704.

38. C. Y. Shen 1995 Equilibrium salt-fingering convection. Phys. Fluids 7, 706717.

39. G. Sivashinsky 1985 Weak turbulence in periodic flows. Physica D 17, 243255.

40. R. Stancliffe , E. Glebbeek , R. Izzard & O. Pols 2007 Carbon-enhanced metal-poor stars and thermohaline mixing. Astron. Astrophys. 464, L57L60.

42. M. E. Stern 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12, 172175.

44. M. E. Stern , T. Radko & J. Simeonov 2001 Three-dimensional salt fingers in an unbounded thermocline with application to the central ocean. J. Mar. Res. 59, 355390.

48. L. St Laurent & R. W. Schmitt 1999 The contribution of salt fingers to vertical mixing in the North Atlantic tracer release experiment. J. Phys. Oceanogr. 29, 14041424.

49. S. Tait & C. Jaupart 1989 Compositional convection in viscous melts. Nature 338, 571574.

52. S. Vauclair 2004 Metallic fingers and metallicity excess in exoplanets’ host stars: the accretion hypothesis revisited. Astrophys. J. 605, 874879.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 55 *
Loading metrics...

Abstract views

Total abstract views: 121 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th May 2017. This data will be updated every 24 hours.