Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-04T18:33:07.920Z Has data issue: false hasContentIssue false
  • English
  • Français

Planform selection in salt fingers

Published online by Cambridge University Press:  21 April 2006

Michael R. E. Proctor  and
Judith Y. Holyer
Michael R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
Judith Y. Holyer
Affiliation:
School of Mathematics, University of Bristol, Bristol B58 1TW
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of small-aspect-ratio thermohaline convection is discussed in conditions appropriate to the salt-finger regime. Two-scale methods are employed to produce nonlinear coupled evolution equations for an arbitrary number of interacting roll solutions. These are solved in simple cases and it is shown that roll-type planforms are preferred over square cells throughout the range of validity of the analysis. The methods can be generalized to other double-diffusive convection problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 241 - 253
Copyright
© 1986 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

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306.Google Scholar
Chapman, C. J. & Proctor M. R. E.1980 Nonlinear Rayleigh-Bénard convection with poorly conducting boundaries. J. Fluid Mech. 101, 759–782.Google Scholar
Da Costa, L., Knobloch, E. & Weiss, N. O. 1981 Oscillatory and steady convection in a magnetic field. J. Fluid Mech. 109, 25–43.Google Scholar
Holyer J. Y.1981 On the collective instability of salt fingers. J. Fluid Mech. 110, 195–207.Google Scholar
Howard L. N.1965 Boundary layer treatment of the mean field equations. Woods Hole Oceanographic Inst. Rep. WHOI-65–51, pp. 124–125.Google Scholar
Howard, L. N. & Veronis G.1984 The salt finger zone. Woods Hole Oceanographic Inst. Rep. WHOI-84–44, pp. 85–89.Google Scholar
Huppert, H. E. & Moore D. R.1976 Nonlinear double-diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Jenkins, D. R. & Proctor M. R. E.1984 The transition from roll to square cell solutions in Rayleigh-Bénard convection. J. Fluid Mech. 131, 461–471.Google Scholar
Knobloch, E. & Proctor M. R. E.1981 Nonlinear periodic convection in double-diffusive systems. J. Fluid Mech. 108, 291–316.Google Scholar
Normand C.1984 Nonlinear convection in high vertical channels. J. Fluid Mech. 143, 223–242.Google Scholar
Proctor, M. R. E. & Weiss N. O.1982 Magnetoconvection. Rep. Prog. Phys. 45, 1317–1379.Google Scholar
Proctor M. R. E.1986 Columnat convection in double-diffusive systems. Cont. Maths (in press).Google Scholar
Schmitt R. W.1983 The characteristics of salt fingers in a variety of fluid systems: including stellar interiors, liquid metals, oceans and magmas. Phys. Fluids 6, 2373–2377.Google Scholar
Shirtcliffe, T. G. L. & Turner J. S.1970 Observations of the cell structure of salt fingers. J. Fluid Mech. 41, 707–719.Google Scholar
Soward A. M.1974 A convection driven dynamo. I. The weak field case Phil. Trans. R. Soc. Lond. A 275, 611–651.Google Scholar
Stern M. E.1960 The ‘salt fountain’ and thermohaline convection. Tellus 12, 172–175.Google Scholar
Straus J. M.1972 Finite amplitude doubly-diffusive convection. J. Fluid Mech. 56, 353–374.Google Scholar
Swift J. W.1984 Ph.D. Thesis, University of Berkeley.
Turner J. S.1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner J. S.1985 Multicomponent convection. Ann. Rev. Fluid Mech. 17, 11–44.Google Scholar