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Periodic intrusions in a stratified fluid

  • OLIVER S. KERR (a1)


When a salt-stratified body of fluid is heated from the side a series of almost horizontal convective layers can develop with well-mixed interiors. These layers can propagate into the interior of the stratified fluid. This behaviour is also observed with intrusions at fronts between stratified bodies of fluid where their composition varies. We look at a simplified model of intrusion growth where the mechanism behind the creation of their well-mixed interiors is neglected, and look at how a stack of such intrusions will propagate away from the wall or front. We find that there is a transition from a regime where the propagation is essentially inviscid and the intrusion length is proportional to time, to one where viscosity is important and the propagation rate slows down, with the length being proportional to the square-root of time.



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Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Dover.
Chan, C. L., Chen, W.-Y. & Chen, C. F. 2002 Secondary motion in convection layers generated by lateral heating of a solute gradient (with an Appendix by O. S. Kerr). J. Fluid Mech. 455, 119.
Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Intl J. Heat Mass Transfer 14, 5765.
De Silva, I. P. D. & Fernando, H. J. S. 1998 Experiminets on collapsing turbulent regions in stratified fluids. J. Fluid Mech. 358, 2960.
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.
Imberger, J. 1972 Two-dimensional sink flow of a stratified fluid contained in a duct. J. Fluid Mech. 53, 329349.
Imberger, J. & Fandry, C. 1975 Withdrawal of a stratified fluid from a vertical two-dimensional duct. J. Fluid Mech. 70, 321332.
Imberger, J., Thompson, R. & Fandry, C. 1976 Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 78, 489512.
Jeevaraj, C. G. & Imberger, J. 1991 Experimental study of double-diffusive instability in sidewall heating. J. Fluid Mech. 222, 565586.
Malki-Epshtein, L., Phillips, O. M. & Huppert, H. E. 2004 The growth and structure of double-diffusive cells adjacent to a cooled side-wall in a salt-stratified environment. J. Fluid Mech. 518, 347362.
Manins, P. C. 1976 Intrusions into a stratified fluid. J. Fluid Mech. 74, 547560.
McEwan, A. D. & Baines, P. G. 1974 Shear fronts and and experimental stratified shear flow. J. Fluid Mech. 63, 257272.
Pao, H.-S. & Kao, T. W. 1974 Dynamics of establishment of selective withdrawal of a stratified fluid from a line sink. Part 1. Theory. J. Fluid Mech. 65, 657688.
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170177.
Ruddick, B. R. 2003 Laboratory studies of interleaving. Prog. Oceanogr. 56, 529547.
Ruddick, B. R., Phillips, O. M. & Turner, J. S. 1999 A laboratory and quantitative model of finite-amplitutde thermohaline intrusions. Dyn. Atmos. Oceans 30, 7199.
Ruddick, B. R. & Richards, K. 2003 Oceanic thermohaline intrusions: observations. Prog. Oceanogr. 56, 499527.
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions. Deep-Sea Res. 26, 903913.
Schladow, S. G., Thomas, E. & Koseff, J. R. 1992 The dynamics of intrusions into a thermohaline stratification. J. Fluid Mech. 236, 127165.
Suzukawa, Y. & Narusawa, U. 1982 Structure of growing double-diffusive convection cells. Trans. ASME: J. Heat Transfer 104, 248254.
Tanny, J. & Tsinober, A. B. 1988 The dynamics and structure of double-diffusive layers in sidewall-heating experiments. J. Fluid Mech. 196, 135156.
Tanny, J. & Tsinober, A. B. 1989 On the behaviour of a system of double diffusive layers during its evolution. Phys. Fluids A 1, 606609.
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effects of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375400.
Walsh, D. & Ruddick, B. 1995 Double-diffusive interleaving: the influence of non-constant diffusivities. J. Phys. Oceanogr. 25, 348358.
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Periodic intrusions in a stratified fluid

  • OLIVER S. KERR (a1)


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