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The double-diffusive modon

Published online by Cambridge University Press:  31 July 2008

TIMOUR RADKO
TIMOUR RADKO*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA tradko@nps.edu
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Abstract

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Fully developed two-dimensional salt-finger convection is characterized by the appearance of coherent dipolar eddies which carry relatively fresh and cold fluid upward and salty and warm fluid downward. Such structures – the double-diffusive modons – are prevalent in the regime in which density stratification is close to neutral and the salt-finger instability is extremely vigorous. The structure and translation velocities of modons are discussed in terms of the asymptotic expansion in which the background density ratio approaches unity. It is argued that the vertical salt flux is driven primarily by double-diffusive modons, which makes it possible to derive explicit expressions for the mixing rates of temperature and salinity as a function of their background gradients. Predictions of the proposed mixing model are successfully tested by direct numerical simulations.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008, pp. 59 - 85
Copyright
Copyright © Cambridge University Press 2008

References

REFERENCES

Balmforth, N. J., Ghadge, S. A., Kettapun, A. & Mandre, S. D. 2006 Bounds on double-diffusive convection. J. Fluid Mech. 569, 29–50.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, 113–133.Google Scholar
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids (Suppl. 2) 12, 233–238.Google Scholar
Kunze, E. 2003 A review of salt fingering theory. Prog. Oceanogr. 56, 399–417.CrossRefGoogle Scholar
Lamb, H. 1895 Hydrodynamics. Cambridge University Press.Google Scholar
Larichev, V. D. & Reznik, G. M. 1976 Two-dimensional Rossby soliton: An exact solution. Rep. USSR Acad. Sci. 231, 1077–1079.Google Scholar
Lueck, R. G. 1987 Microstructure measurements in a thermohaline staircase. Deep-Sea Res. 34, 1677–1688.Google Scholar
Malkus, W. V. R. & Veronis, G. 1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.Google Scholar
Merryfield, W. J. & Grinder, M. 1999 Salt fingering fluxes from numerical simulations (unpublished manuscript).Google Scholar
Monin, A. S. & Ozmidov, R. V. 1985 Turbulence in the Ocean. D. Reidel.Google Scholar
Radko, T. 2003 A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech. 497, 365–380.Google Scholar
Radko, T. 2005 What determines the thickness of layers in a thermohaline staircase? J. Fluid Mech. 523, 79–98.Google Scholar
Radko, T. & Stern, M. E. 1999 Salt fingers in three dimensions. J. Mar. Res. 57, 471–502.Google Scholar
Radko, T. & Stern, M. E. 2000 Finite amplitude salt fingers in a vertically bounded layer. J. Fluid Mech. 425, 133–160.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory. Springer.Google Scholar
Schmitt, R. W. 1979 The growth rate of supercritical salt fingers. Deep-Sea Res. 26A, 23–44.CrossRefGoogle Scholar
Schmitt, R. W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26, 255–285.Google Scholar
Schmitt, R. W. 2003 Observational and laboratory insights into salt finger convection. Prog. Oceanogr. 56, 419–433.Google Scholar
Shen, C. Y. & Veronis, G. 1997 Numerical simulation of two-dimensional salt fingers. J. Geophys. Res. 102, 23131–23143.CrossRefGoogle Scholar
Stern, M. E. 1960 The “salt-fountain” and thermohaline convection. Tellus 12, 172–175.Google Scholar
Stern, M. E. 1975 a Minimal properties of planetary eddies. J. Mar. Res. 33, 1–13.Google Scholar
Stern, M. E. 1975 b Ocean Circulation Physics. Academic.Google Scholar
Stern, M. E. & Radko, T. 1998 The salt finger amplitude in unbounded T-S gradient layers. J. Mar. Res. 56, 157–196.CrossRefGoogle Scholar
Stern, M. E., Radko, T. & Simeonov, J. 2001 3D salt fingers in an unbounded thermocline with application to the Central Ocean. J. Mar. Res. 59, 355–390.Google Scholar
Stern, M. E. & Simeonov, J. 2005 The secondary instability of salt fingers. J. Fluid Mech. 533, 361–380.CrossRefGoogle Scholar
Taylor, J. 1993 Anisotropy of salt fingers. J. Phys. Oceanogr. 23, 554–565.2.0.CO;2>CrossRefGoogle Scholar