Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-08T22:29:51.175Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of long, steady, two-dimensional salt fingers

Published online by Cambridge University Press:  20 April 2006

Judith Y. Holyer
Judith Y. Holyer
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TP
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the stability of long, steady, two-dimensional salt fingers. It is already known that salt fingers carrying a large enough density flux are unstable to long-wavelength internal-wave perturbations. Stern (1969) studied the mechanism of this, the collective instability, and it was studied in more detail by Holyer (1981). We extend the earlier work to include perturbations of all wavelengths, as well as long-wavelength perturbations. By applying the methods of Floquet theory to the periodic salt fingers, the growth rates of perturbations are found. For both heat-salt and salt-sugar systems the collective instability, which can be recognized by its frequency of oscillation, does not have the largest growth rate. There is a new, non-oscillatory instability, which, according to linear theory, grows faster than the collective instability. We study the instabilities that arise by using a combination of analytical and numerical methods. Further work will be necessary in order to assess the importance of these instabilities in different physical situations and to examine their development as their amplitude increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 169 - 185
Copyright
© 1984 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

Beaumont, D. N. 1981 The stability of spatially periodic flows. J. Fluid Mech. 108, 461.Google Scholar
Chen, C. F. & Johnson, D. H. 1984 Double-diffusive convection: A report on an Engineering Foundation Conference. J. Fluid Mech. 138, 405.Google Scholar
Drazin, P. G. 1977 On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356, 411.Google Scholar
Griffiths, R. W. & Ruddick, B. R. 1980 Accurate fluxes across a salt—sugar interface. J. Fluid Mech. 99, 85.Google Scholar
Holyer, J. Y. 1981 On the collective instability of salt fingers. J. Fluid Mech. 110, 195.Google Scholar
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299.Google Scholar
Lambert, R. B. & Demenkow, J. W. 1972 On the vertical transport due to fingers in double-diffusive convection. J. Fluid Mech. 54, 627.Google Scholar
Linden, P. F. 1973 On the structure of salt fingers. Deep-Sea Res. 20, 325.Google Scholar
Schmitt, R. W. 1979 Flux measurements on salt fingers at an interface. J. Mar. Res. 37, 419.Google Scholar
Schmitt, R. W. & Georgi, D. T. 1982 Finestructure and microstructure in the North Atlantic Current. J. Mar. Res. 40, 659.Google Scholar
Stern, M. E. 1960 The ‘salt’ fountain and thermohaline convection. Tellus 12, 172.Google Scholar
Stern, M. E. 1969 Collective instability of salt fingers. J. Fluid Mech. 35, 209.Google Scholar
Stern, M. E. & Turner, J. S. 1969 Salt fingers and convecting layers. Deep-Sea Res. 16, 497.Google Scholar
Stommel, H., Arons, A. & Blanchard, D. 1956 An oceanographic curiosity: the perpetual salt fountain. Deep-Sea Res. 3, 152.Google Scholar
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Williams, A. J. 1974 Salt fingers observed in the Mediterranean outflow. Science 185, 941.Google Scholar