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Maintenance of continental boundary-layer shear through counter-gradient vorticity flux in a barotropic model

Published online by Cambridge University Press:  26 April 2006

Jean-Raymond Bidlot  and
Melvin E. Stern
Jean-Raymond Bidlot
Affiliation:
Department of Oceanography, Florida State University, Tallahassee, FL 32306-3048, USA Present address: Management Unit of the Mathematical Models of the North Sea and Scheldt Estuary, 100 Gulledelle, B-1200 Brussels, Belgium.
Melvin E. Stern
Affiliation:
Department of Oceanography, Florida State University, Tallahassee, FL 32306-3048, USA
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Abstract

The use of a classical eddy parametrization in the analysis of continental boundary currents leads to the diffusion of momentum and relative vorticity and fails to recognize that the relevant eddies are dominated by the conservation of potential vorticity, which in turn may produce an increase in the mean relative vorticity. To illustrate this effect, we examine a non-inflected barotropic shear flow destabilized by the cross-steam variation in the bottom topògraphy of a continental slope. The finiteamplitude evolution of the waves is analysed in a simple model with a step-like bottom topography and with a piecewise-uniform potential vorticity distribution. The increase in maximum mean vorticity is computed for various values of the Rossby number and the topographic elevation, and it is suggested that a similar effect, taking into account the isopycnal topography as well as the isobaths, could maintain the large inshore shear of the Gulf Stream. Cross-shelf transport of different water ‘types’ (i.e. potential vorticity and passive tracers) are also computed and suggested to be pertinent to the more realistic oceanic problem involving baroclinic effects. The numerical calculation employs the well-known method of contour dynamics, and the Green's function appropriate for the step-like topography is derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 55 - 85
Copyright
© 1994 Cambridge University Press

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References

Bane, J. M. 1983 Initial observation of the subsurface and short-term variability of the seaward deflection of the Gulf Stream off Charleston, South Carolina. I. Geophys: Res. 88 (C8), 4673–4684.Google Scholar
Bidlot, J. R. 1993 Contour dynamical study of the barotropic instability of continental boundary currents. PhD dissertation, Florida State University.
Brooks, D. A., & Mooers, C. 1977 Free, stable continental shelf waves in a sheared, barotropic boundary current. J. Phys. Oceanogr. 7, 380–388.Google Scholar
Brooks, I. H. & Niiler, P. P. 1977 Energetics of the Florida current. J. Mar. Res. 35, 163–191.Google Scholar
Collings, S. I. & Grimshaw, R. 1980 The effect of topography on the stability of a barotropic coastal current. Dyn. Atmos. Oceans 5, 83–106.Google Scholar
Collings, S. I. & Grimshaw, R. 1984 Stable and unstable barotropic shelf waves in a coastal current. Geosphys. Astrophys. Fluid Dyn. 29, 179–220.Google Scholar
Dritschel, D. G. 1988 The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194, 511–547.Google Scholar
Ford, W. L., Longard, J. R. & Banks, R. E. 1952 On the nature, occurrence and origin of cold low salinity water along the edge of the Gulf Stream. J. Mar. Res. 11, 281–293.Google Scholar
Grimshaw, R. & Yi, Z. 1991 Evolution of a potential vorticity front over a topographic slope. J. Phys. Oceanogr. 21, 1240–1255.Google Scholar
Kozlov, V. F. 1983 The method of contour dynamics in model problems of ocean topographysical cyclogenesis. Izv. Atmos. Ocean. Phys. 635–640.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.
Lee, T. N. & Atkinson, L. P. 1983 Low frequency current and temperature variability from Gulf Stream frontal eddies and atmospheric forcing along the South East U.S. outer continental shelf. J. Geophys. Res. 88 (C8), 4541–4567.Google Scholar
Lee, T. N., Kourafalou, V., Wang, J. D., Ho, W. J., Blanton, J. O., Atkinson, L. P. & Pietrafesa, L. J. 1985 Shelf circulation from Cape Canaveral to Cape Fear during winter. In Oceanography of the Southeastern U.S. Continental Shelf, Coastal and Estuarine Science Series, vol. 2 (ed. L. P. Atkinson, D. W. Menzel & K. A. Bush), pp. 33–61. Washington DC: AGU.
Lee, T. N. & Mayer, D. A. 1977 Low-frequency current variability and spin-off eddies along the shelf off Southeast Florida. J. Mar. Res. 35, 193–220.Google Scholar
Lee, T. N., Yoder, J. A. & Atkinson, L. P. 1991 Gulf Stream frontal eddy influence on productivity of the Southeast U.S. continental shelf. J. Geophys. Res. 96, (C12), 22191–22205.Google Scholar
Meacham, S. P. 1991 Meander evolution on piecewise-uniform, quasi-geostrophic jets. J. Phys. Oceanogr. 21, 1139–1170.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics, 2nd edn. Springer.
Pozrikidis, C. & Higdon, J. J. 1985 Nonlinear Kelvin–Helmholtz instability of a finite vortex layer. J. Fluid Mech. 157, 225–263.Google Scholar
Pozrikidis, C. & Higdon, J. J. 1987 Instability of compound vortex layer and wakes. Phys. Fluids 30, 2965–2975.Google Scholar
Pratt, L. J. & Pedlosky, J. 1991 Linear and nonlinear instability of geostrophic shear layers. J. Fluid Mech. 224, 49–76.Google Scholar
Qiu, B., Toda, T. & Imosato, N. 1990 On Kuroshio front fluctuations in the East China Sea using satellite and in situ observational data. J. Geophys. Res. 95 (C10), 18191–18204.Google Scholar
Saffman, P. G. & Schatzman, J. C. 1982 Stability of a vortex street of finite vortices. J. Fluid Mech. 117, 171–185.Google Scholar
Send, U. 1989 Vorticity and instability during flow reversals on the continental shelf. J. Phys. Oceanogr. 19, 1620–1633.Google Scholar
Spitz, Y. H. & Nof, D. 1991 Separation of boundary currents due to bottom topography. Deep-Sea Res. 38, 1–20.Google Scholar
Stern, M. E. 1985 Lateral wave breaking and ‘shingle’ formation in large-scale shear flow. J. Phys. Oceanogr. 15, 1274–1283.Google Scholar
Stern, M. E. 1991a Countergradient vorticity flux generated in continental boundary currents. J. Phys. Oceanogr. 21, 1622–1630.Google Scholar
Stern, M. E. 1991b Entrainment of an eddy at the edge of a jet. J. Fluid Mech. 228, 343–360.Google Scholar
Stern, M. E. 1993 Topographic jetogenesis and transitions in straits and along continents. J. Phys. Oceanogr. 23, 843–854.Google Scholar
Stern, M. E. & Bidlot, J.-R. 1994 Lateral entrainment in baroclinic currents. J. Mar. Res. 52, 25–53.Google Scholar
Stern, M. E. & Pratt, L. J. 1985 Dynamics of vorticity fronts. J. Fluid Mech. 161, 513–532.Google Scholar
Sugimoto, T., Kimura, S. & Miyaji, K. 1988 Meander of the Kuroshio frontal variability in the East China Sea. J. Oceangr. Soc. Japan 44, 125–135.Google Scholar
Thompson, L. 1993 Two-layer quasi-geostrophic flow over finite isolated topography. J. Phys. Oceanogr. 23, 1297–1314.Google Scholar
Vukovich, F. M., Crissman, B. W., Bushnell, M. & King, W. J. 1979 Gulf Stream boundary eddies off the East Coast of Florida, J. Phys. Oceanogr. 9, 1214–1222.Google Scholar
Wang, X. 1992 Interaction of an eddy with a continental slope. PhD thesis, MIT/ WHOI Joint Program in Oceanography.
Zabusky, N. J., Hughes, M. H. & Roberts, K. V. 1979 Contour dynamics for the Euler equations in two dimensions. J. Comput. Phys. 30, 96–106.Google Scholar
Zantopp, R. J., Leaman, K. D. & Lee, T. N. 1987 Florida Current meanders: a close look in June–July 1984. J. Phys. Oceanogr. 17, 584–595.Google Scholar