Double-Diffusive Interleaving in the Presence of Turbulence: The Effect of a Nonconstant Flux Ratio

David Walsh International Arctic Research Center, University of Alaska, Fairbanks, Fairbanks, Alaska

Search for other papers by David Walsh in
Current site
Google Scholar
PubMed
Close
and
Barry Ruddick Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

Search for other papers by Barry Ruddick in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The influence of turbulent mixing on double-diffusively driven thermohaline interleaving is investigated. The problem is formulated using a turbulence-modified flux ratio to link the fluxes of T and S; the addition of turbulence changes the way in which the effective flux ratio varies with the density ratio Rρ. Formulation of the problem maps onto past interleaving studies, except that the flux ratio is a function of Rρ in the present work. Posing the problem in this way allows the effects of turbulence and intrinsic variations in the salt-finger flux ratio to be studied within the same theoretical framework.

Turbulence modifies the slope, wavelength, and growth rate of the fastest-growing intrusions, decreasing the range of slopes and wavenumbers that can grow. However, analysis shows that growing solutions exist for any finite value of the turbulent diffusivity Kt, suggesting that double-diffusively driven intrusions can exist in the ocean even when double-diffusive fluxes are much weaker than turbulent fluxes.

If the flux ratio is a decreasing function of Rρ (as suggested by some models of salt finger convection) a different instability occurs, which has unbounded growth rates in the high wavenumber limit (a “UV catastrophe”). In most cases, the instability can be suppressed by the addition of sufficiently strong turbulent mixing. The threshold for this instability depends upon variation of the T/S flux ratio with Rρ, and hence on the relative strengths of turbulent and double-diffusive mixing. The instability is shown to be nonintrusive in nature, as it does not rely upon lateral advection across a front; it is found to be closely related to the one-dimensional double-diffusive instability investigated by Huppert.

Corresponding author address: Dr. David Walsh, International Arctic Research Center, University of Alaska, Fairbanks, P.O. Box 757335, Fairbanks, AK 99775-7335.

dwalsh@iarc.uaf.edu

Abstract

The influence of turbulent mixing on double-diffusively driven thermohaline interleaving is investigated. The problem is formulated using a turbulence-modified flux ratio to link the fluxes of T and S; the addition of turbulence changes the way in which the effective flux ratio varies with the density ratio Rρ. Formulation of the problem maps onto past interleaving studies, except that the flux ratio is a function of Rρ in the present work. Posing the problem in this way allows the effects of turbulence and intrinsic variations in the salt-finger flux ratio to be studied within the same theoretical framework.

Turbulence modifies the slope, wavelength, and growth rate of the fastest-growing intrusions, decreasing the range of slopes and wavenumbers that can grow. However, analysis shows that growing solutions exist for any finite value of the turbulent diffusivity Kt, suggesting that double-diffusively driven intrusions can exist in the ocean even when double-diffusive fluxes are much weaker than turbulent fluxes.

If the flux ratio is a decreasing function of Rρ (as suggested by some models of salt finger convection) a different instability occurs, which has unbounded growth rates in the high wavenumber limit (a “UV catastrophe”). In most cases, the instability can be suppressed by the addition of sufficiently strong turbulent mixing. The threshold for this instability depends upon variation of the T/S flux ratio with Rρ, and hence on the relative strengths of turbulent and double-diffusive mixing. The instability is shown to be nonintrusive in nature, as it does not rely upon lateral advection across a front; it is found to be closely related to the one-dimensional double-diffusive instability investigated by Huppert.

Corresponding author address: Dr. David Walsh, International Arctic Research Center, University of Alaska, Fairbanks, P.O. Box 757335, Fairbanks, AK 99775-7335.

dwalsh@iarc.uaf.edu

Save
  • Barton, E. D., and P. Hughes, 1982: Variability of water mass interleaving off N.W. Africa. J. Mar. Res.,40, 963–984.

  • Carmack, E. C., K. Aagaard, J. H. Swift, R. G. Perkin, F. A. McLaughlin, R. W. Macdonald, and E. P. Jones, 1998: Thermohaline transitions. Physical Processes in Lakes and Oceans, J. Imberger, Ed., Vol. 54, Coastal and Estuarine Studies, Amer. Geophys. Union, 179–186.

  • Crapper, P. F., 1976: The transport across a density interface in the presence of externally imposed turbulence. J. Phys. Oceanogr.,6, 982–984.

  • Hamon, B. V., 1967: Medium-scale temperature and salinity structure in the upper 1500 m in the Indian Ocean. Deep-Sea Res.,14, 169–181.

  • Hebert, D., 1999: Intrusions: What drives them? J. Phys. Oceanogr.,29, 1382–1391.

  • Holyer, J. Y., 1983: Double-diffusive interleaving due to horizontal gradients. J. Fluid Mech.,137, 347–362.

  • Horne, E. P. W., 1978: Interleaving at the subsurface front in the slope water off Nova Scotia. J. Geophys. Res.,83, 3659–3671.

  • Huppert, H. E., 1971: On the stability of a series of double-diffusive layers. Deep-Sea Res.,18, 1005–1021.

  • Kelley, D., 1984: Effective diffusivities within oceanic thermohaline staircases. J. Geophys. Res.,89, 10484–10488.

  • Kunze, E., 1987: Limits on growing, finite-length salt fingers: A Richardson number constraint. J. Mar. Res.,45, 533–556.

  • ——, 1994: A proposed flux constraint for salt fingers in shear. J. Mar. Res.,52, 999–1016.

  • Kuz’mina, N. P., and V. B. Rodionov, 1992: Influence of baroclinicity on formation of thermohaline intrusions in ocean frontal zones. Izv. Atmos. Oceanic Phys.,28 (10–11), 804–810.

  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1993: Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature,364, 701–703.

  • Linden, P., 1971: Salt-fingers in the presence of grid-generated turbulence. J. Fluid Mech.,49, 611–624.

  • May, B. D., and D. E. Kelley, 1997: Effect of baroclinicity on double-diffusive interleaving. J. Phys. Oceanogr.,27, 1997–2008.

  • McDougall, T. J., 1985a: Double-diffusive interleaving. Part I: Linear stability analysis. J. Phys. Oceanogr.,15, 1532–1541.

  • ——, 1985b: Double-diffusive interleaving. Part II: Finite amplitude, steady state interleaving. J. Phys. Oceanogr.,15, 1542–1556.

  • ——, and B. R. Ruddick, 1992: The use of ocean microstructure to quantify both turbulent mixing and salt fingering. Deep-Sea Res.,39, 1931–1952.

  • Merryfield, W. J., 2000: Origin of thermohaline staircases. J. Phys. Oceanogr.,30, 1046–1068.

  • Osborne, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn.,3, 321–345.

  • Perkin, R. G., and E. L. Lewis, 1984: Mixing in the West Spitsbergen Current. J. Phys. Oceanogr.,14, 1315–1325.

  • Phillips, O. M., 1972: Turbulence in a strongly stratified fluid—Is it unstable? Deep-Sea Res.,19, 79–81.

  • Richards, K. J., and R. T. Pollard, 1991: Structure of the upper ocean in the western equatorial Pacific. Nature,350, 48–50.

  • Ruddick, B. R., 1992: Intrusive mixing in a Mediterranean salt lens— Intrusion slopes and dynamical mechanism. J. Phys. Oceanogr.,22, 1274–1285.

  • ——, D. Walsh, and N. Oakey, 1997: Variations in apparent mixing efficiency in the North Atlantic central water. J. Phys. Oceanogr.,27, 2589–2605.

  • Schmitt, R. W., 1979a: The growth rate of super-critical salt fingers. Deep-Sea Res.,26A, 23–40.

  • ——, 1979b: Flux measurements on salt fingers at an interface. J. Mar. Res.,37, 419–436.

  • ——, 1981: Form of the temperature–salinity relationship in the central water: Evidence for double-diffusive mixing. J. Phys. Oceanogr.,11, 1015–1026.

  • ——, H. Perkins, J. D. Boyd, and M. C. Stalcup, 1987: An investigation of the thermohaline staircase in the western tropical North Atlantic. Deep-Sea Res.,34, 1655–1666.

  • Stern, M. E., 1967: Lateral mixing of water masses. Deep-Sea Res.,14, 747–753.

  • ——, 1969: Collective instability of salt fingers. J. Fluid Mech.,35, 209–218.

  • ——, 1975: Ocean Circulation Physics. Academic Press, 246 pp.

  • St. Laurent, L., and R. W. Schmitt, 1999: The contribution of salt fingers to vertical mixing in the North Atlantic Tracer Release Experiment. J. Phys. Oceanogr.,29, 1404–1424.

  • Stommel, H., and N. K. Fedorov, 1967: Small scale structure in temperature and salinity near Timor and Mindinao. Tellus,19, 306– 325.

  • Toole, J. M., 1981: Intrusion characteristics in the Antarctic polar front. J. Phys. Oceanogr.,11, 780–793.

  • ——, and D. T. Georgi, 1981: On the dynamics and effects of double-diffusively driven intrusions. Progress in Oceanography, Vol. 10, Pergamon, 121–145.

  • Turner, J. S., 1965: The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass. Transfer,8, 759–767.

  • ——, 1973: Buoyancy Effects in Fluids. Cambridge University Press, 368 pp.

  • Walsh, D., and B. R. Ruddick, 1995a: Double-diffusive interleaving:The influence of non-constant diffusivities. J. Phys. Oceanogr.,25, 348–358.

  • ——, and ——, 1995b: An investigation of Kunze’s salt finger flux laws—Are they stable? Double-Diffusive Convection, Geophys. Monogr., No. 94, Amer. Geophys. Union, 334 pp.

  • ——, and ——, 1998: Nonlinear equilibration of thermohaline intrusions. J. Phys. Oceanogr.,28, 1043–1070.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 299 68 3
PDF Downloads 94 24 3