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Mixed bottom-friction–Kelvin–Helmholtz destabilization of source-driven abyssal overflows in the ocean

Published online by Cambridge University Press:  10 May 2009

GORDON E. SWATERS
GORDON E. SWATERS*
Affiliation:
Applied Mathematics Institute, Department of Mathematical & Statistical Sciences and Institute for Geophysical Research, University of Alberta, Edmonton, AB T6G 2G1, Canada
*
†Email address for correspondence: gordon.swaters@ualberta.ca
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Abstract

Source-driven ocean currents that flow over topographic sills are important initiation sites for the abyssal component of the thermohaline circulation. These overflows exhibit vigorous space and time variability over many scales as they progress from a predominately gravity-driven downslope flow to a geostrophic along-slope current. Observations show that in the immediate vicinity of a sill, grounded abyssal ocean overflows can possess current speeds greater than the local long internal gravity wave speed with bottom friction and downslope gravitational acceleration dominating the flow evolution. It is shown that these dynamics lead to the mixed frictionally induced and Kelvin–Helmholtz instability of grounded abyssal overflows. Within the overflow, the linearized instabilities correspond to bottom-intensified baroclinic roll waves, and in the overlying water column amplifying internal gravity waves are generated. The stability characteristics are described as functions of the bottom drag coefficient and slope, Froude, bulk Richardson and Reynolds numbers associated with the overflow and the fractional thickness of the abyssal current compared to the mean depth of the overlying water column. The marginal stability boundary and the boundary separating the parameter regimes in which the most unstable mode has a finite or infinite wavenumber are determined. When it exists, the high-wavenumber cutoff is obtained. Conditions for the possible development of an ultraviolet catastrophe are determined. In the infinite-Reynolds-number limit, an exact solution is obtained which fully includes the effects of mean depth variations in the overlying water column associated with a sloping bottom. For parameter values characteristic of the Denmark Strait overflow, the most unstable mode has a wavelength of about 19 km, a geostationary period of about 14 hours, an e-folding amplification time of about 2 hours and a downslope phase speed of about 74 cm s−1.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 33 - 66
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions, 9th ed., Dover.Google Scholar
Baines, P. G. 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127–167.CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Balmforth, N. J. & Mandre, S. 2004 Dynamics of roll waves. J. Fluid Mech. 514, 1–33.CrossRefGoogle Scholar
Bruce, J. G. 1995 Eddies southwest of Denmark Strait. Deep-Sea Res. 42, 13–29.CrossRefGoogle Scholar
Cenedese, C., Whitehead, J. A., Ascarelli, T. A. & Ohiwa, M. 2004 A dense current flowing down a sloping bottom in a rotating fluid. J. Phys. Oceanogr. 34, 188–203.2.0.CO;2>CrossRefGoogle Scholar
Dewar, W. K. 1987 Ventilating warm rings. J. Phys. Oceanogr. 17, 2219–2231.2.0.CO;2>CrossRefGoogle Scholar
Dickson, R. R. & Brown, J. 1994 The production of North Atlantic deep water: sources, rates, and pathways. J. Geophys. Res. 99, 12319–12341.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Emms, P. W. 1998 A streamtube model of rotating turbidity currents. J. Mar. Res. 56, 41–74.CrossRefGoogle Scholar
Girton, J. B. & Sanford, T. B. 2001 Synoptic sections of the Denmark Strait overflow. Geophys. Res. Lett. 28, 1619–1622.CrossRefGoogle Scholar
Girton, J. B. & Sanford, T. B. 2003 Descent and modification of the Denmark Strait overflow. J. Phys. Oceanogr. 33, 1351–1364.2.0.CO;2>CrossRefGoogle Scholar
Houghton, R. W., Schlitz, R., Beardsley, R. C., Butman, B. & Chamberlin, J. L. 1982 The middle Atlantic bight cold pool: evolution of the temperature structure during summer 1979. J. Phys. Oceanogr. 12, 1019–1029.2.0.CO;2>CrossRefGoogle Scholar
Jeffreys, H. 1925 The flow of water in an inclined channel of rectangular bottom. Phil. Mag. 49, 793–807.CrossRefGoogle Scholar
Jiang, L. & Garwood, R. W. 1996 Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1214–1233.2.0.CO;2>CrossRefGoogle Scholar
Jungclaus, J. H., Hauser, J. & Käse, R. H. 2001 Cyclogenesis in the Denmark Strait overflow plume. J. Phys. Oceanogr. 31, 3214–3228.2.0.CO;2>CrossRefGoogle Scholar
Karsten, R. H., Swaters, G. E. & Thomson, R. E. 1995 Stability characteristics of deep water replacement in the Strait of Georgia. J. Phys. Oceanogr. 25, 2391–2403.2.0.CO;2>CrossRefGoogle Scholar
Käse, R. H., Girton, J. B. & Sanford, T. B. 2003 Structure and variability of the Denmark Strait overflow: model and observations. J. Geophys. Res. 108 (C6), 10.1029/2002JC001548.CrossRefGoogle Scholar
Käse, R. H. & Oschlies, A. 2000 Flow through Denmark Strait. J. Geophys. Res. 105, 28527–28546.CrossRefGoogle Scholar
Killworth, P. D. 1977 Mixing on the Weddell Sea continental slope. Deep-Sea Res. 24, 427–448.CrossRefGoogle Scholar
Krauss, W. & Käse, R. H. 1998 Eddy formation in the Denmark Strait overflow. J. Geophys. Res. 103, 15523–15538.CrossRefGoogle Scholar
LeBlond, P. H., Ma, H., Doherty, F. & Pond, S. 1991 Deep and intermediate water replacement in the Strait of Georgia. Atmos.-Ocean 29, 288–312.CrossRefGoogle Scholar
LeBlond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.Google Scholar
Lyapidevskii, V. Yu. 2000 The structure of roll waves in two layer flows. J. Appl. Maths. Mech. 64, 937–943.CrossRefGoogle Scholar
Masson, D. 2002 Deep water renewal in the Strait of Georgia. Estuarine Coast. Shelf Sci. 54, 115–126.CrossRefGoogle Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Elsevier.CrossRefGoogle Scholar
Price, J. F. & Baringer, O. M. 1994 Outflows and deep water production by marginal seas. Progr. Oceanogr. 33, 161–200.CrossRefGoogle Scholar
Reszka, M. K., Swaters, G. E. & Sutherland, B. R. 2002 Instability of abyssal currents in a continuously stratified ocean with bottom topography. J. Phys. Oceanogr. 32, 3528–3550.2.0.CO;2>CrossRefGoogle Scholar
Smith, P. C. 1975 A streamtube model for bottom boundary currents in the ocean. Deep-Sea Res. 22, 853–873.Google Scholar
Spall, M. A. & Price, J. F. 1998 Mesoscale variability in Denmark Strait: the PV outflow hypothesis. J. Phys. Oceanogr. 28, 1598–1623.2.0.CO;2>CrossRefGoogle Scholar
Sutyrin, G. G. 2007 Ageostrophic instabilities in a horizontally uniform flow along a slope. J. Fluid Mech. 588, 463–473.CrossRefGoogle Scholar
Swaters, G. E. 1991 On the baroclinic instability of cold-core coupled density fronts on a sloping continental shelf. J. Fluid Mech. 224, 361–382.CrossRefGoogle Scholar
Swaters, G. E. 1998 Numerical simulations of the baroclinic dynamics of density-driven coupled fronts and eddies on a sloping bottom. J. Geophys. Res. 103, 2945–2961.CrossRefGoogle Scholar
Swaters, G. E. 2003 Baroclinic characteristics of frictionally destabilized abyssal overflows. J. Fluid Mech. 489, 349–379.CrossRefGoogle Scholar
Swaters, G. E. 2006 a On the frictional destabilization of abyssal overflows dynamically coupled to internal gravity waves. Geophys. Astrophys. Fluid Dyn. 100, 1–24.CrossRefGoogle Scholar
Swaters, G. E. 2006 b The meridional flow of source-driven abyssal currents in a stratified basin with topography. Part I. Model development and dynamical characteristics. J. Phys. Oceanogr. 36, 335–355.CrossRefGoogle Scholar
Swaters, G. E. 2006 c The meridional flow of source-driven abyssal currents in a stratified basin with topography. Part II. Numerical Simulation. J. Phys. Oceanogr. 36, 356–375.CrossRefGoogle Scholar
Swaters, G. E. & Flierl, G. R. 1991 Dynamics of ventilated coherent cold eddies on a sloping bottom. J. Fluid Mech. 223, 565–587.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Worthington, L. V. 1969 An attempt to measure the volume transport of Norwegian Sea overflow water through the Denmark Strait. Deep-Sea Res. 16, 421–432.Google Scholar
Worthington, L. V. & Wright, W. R. 1970 North Atlantic Ocean Atlas, vol. 2. The Woods Hole Oceanographic Institution.Google Scholar