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Two-dimensional instabilities of steady double-diffusive interleaving

Published online by Cambridge University Press:  26 April 2006

Oliver S. Kerr
Oliver S. Kerr
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

The stability of finite-amplitude double–diffusive interleaving driven by linear gradients of salinity and temperature is considered. We show that as the sinusoidal interleaving predicted by linear analysis grows to finite amplitude it is subject to instabilities centred along the lines of minimum vertical density gradient and maximum shear. These secondary instabilities could lead to the step-like density profiles observed in experiments. We show that these instabilities can occur for large Richardson numbers and hence are not driven by shear, but are driven, by double-diffusive effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 99 - 116
Copyright
© 1992 Cambridge University Press

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References

Booker, J. R. & Bretherton F, P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513–539.Google Scholar
Chen, C. F., Briggs, R. A. & Wirtz, D. G. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Intl J. Heat Mass Transfer 14, 57–65.Google Scholar
Chen, C. F., Paliwal, R. C. & Wong, S. B. 1976 Cellular convection in density stratified fluid: effect of inclination of the heated wall. Proc. 1976 Heat Transfer & Fluid Mech. Inst. 18–32. Stanford University Press.
Chen, C. F. & Skok, M. W. 1974 Cellular convection in a salinity gradient along a heated inclined wall. Intl J. Heat Mass Transfer 17, 51–60.Google Scholar
Chen, C. F. & Sandford, R. D. 1977 Stability of time-dependent double-diffusive convection in an inclined slot. J. Fluid Mech. 83, 83–95.Google Scholar
Hart, J. E. 1971 On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Hart, J. E. 1973 Finite amplitude sideways diffusive convection. J. Fluid Mech. 59, 47–64.Google Scholar
Holyer, J. Y. 1983 Double-diffusive interleaving due to horizontal gradients. J. Fluid Mech. 137, 347–362.Google Scholar
Holyer, J. Y. 1984 Stability of long, steady two-dimensional salt fingers. J. Fluid Mech. 147, 169–185.Google Scholar
Holyer, J. Y., Jones, T. J., Priestly, M. G. & Williams, N. C. 1987 The effect of vertical temperature and salinity gradients on double-diffusive interleaving. Deep-Sea Res. 34, 517–530.Google Scholar
Huppert, H. E. & Josberger, E. G. 1980 The melting of ice in cold stratified water. J. Phys. Oceanogr. 10, 953–960.Google Scholar
Huppert, H. E. & Turner, J. S. 1980 Ice blocks melting into a salinity gradient. J. Fluid Mech. 100, 367–384.Google Scholar
Kerr, O. S. 1989 Heating a salinity gradient from a vertical sidewall: linear theory. J. Fluid Mech. 207, 323–352.Google Scholar
Kerr, O. S. 1990 Heating a salinity gradient from a vertical sidewall: nonlinear theory. J. Fluid Mech. 217, 529–546.Google Scholar
Kerr, O. S. 1991 Double-diffusive instabilities at a sloping boundary. J. Fluid Mech. 225, 333–354.Google Scholar
Klostermeyer, J. 1983 Parametric instabilities of internal gravity waves in Boussinesq fluids with large Reynolds numbers. Geophys. Astrophys. Fluid Dyn. 26, 85–105.Google Scholar
Linden, P. F. & Weber, J. E. 1977 The formation of layers in a double-diffusive system with a sloping boundary. J. Fluid Mech. 81, 757–773.Google Scholar
Mcdougall, T. J. 1985 Double-diffusive interleaving I. J. Phys. Oceanogr. 15, 1532–1541.Google Scholar
Mied, R. P. 1976 The occurrence of parametric instabilities in finite-amplitude internal gravity waves. J. Fluid Mech. 78, 763–784.Google Scholar
Narusawa, U. & Suzukawa, Y. 1981 Experimental study of double-diffusive cellular convection due to a uniform lateral heat flux. J. Fluid Mech. 113, 387–405.Google Scholar
Paliwal, R. C. & Chen, C. F. 1980a Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation. J. Fluid Mech. 98, 755–768.Google Scholar
Paliwal, R. C. & Chen, C. F. 1980b Double-diffusive instability in an inclined fluid layer. Part 2. Stability analysis. J. Fluid Mech. 98, 769–785.Google Scholar
Posmentier, E. S. & Hibbard, C. B. 1982 The role of tilt in double-diffusive interleaving. J. Geophys. Res. 87, 518–524.Google Scholar
Proctor, M. R. E. 1981 Steady subcritical thermohaline convection. J. Fluid Mech. 105, 507–521.Google Scholar
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions. Deep-Sea Res. 26, 903–913.Google Scholar
Stern, M. E. 1960 The ‘salt fountain’ and thermohaline convection. Tellus 12, 172–175.Google Scholar
Stern, M. E. 1967 Lateral mixing of water masses. Deep-Sea Res. 14, 747–753.Google Scholar
Tanny, J. & Tsinober, A. B. 1988 The dynamics and structure of double-diffusive layers in sidewall-heating experiments. J. Fluid Mech. 196, 135–156.Google Scholar
Thangam, S., Zebib, A. & Chen, C. F. 1982 Double-diffusive convection in an inclined fluid layer. J. Fluid Mech. 116, 363–378.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effects of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Toole, J. M. & Georgi, D. T. 1981 On the dynamics and effects of double-diffusively driven intrusions. Prog. Oceanogr. 10, 123–145.Google Scholar
Tsinober, A. B., Yahalom, Y. & Shlien, D. J. 1983 A point source of heat in a stable salinity gradient. J. Fluid Mech. 135, 199–217.Google Scholar
Wirtz, R. A., Briggs, D. G. & Chen, C. F. 1972 Physical and numerical experiments on layered convection in a density-stratified fluid. Geophys. Fluid Dyn. 3, 265–288.Google Scholar