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Rotating flows along indented coastlines

Published online by Cambridge University Press:  21 April 2006

Josef Chernia Wsky  and
Paul H. Leblond
Josef Chernia Wsky
Affiliation:
Department of Oceanography, University of British Columbia, 6270 University Boulevard, Vancouver, B.C., Canada V6T 1W5 Present address: G.A.Borstad Associates, 10474 Resthaven Drive, Sidney, B.C., Canada V8L 3H7.
Paul H. Leblond
Affiliation:
Department of Oceanography, University of British Columbia, 6270 University Boulevard, Vancouver, B.C., Canada V6T 1W5
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Abstract

We examine the problem of a steady, inviscid, reduced-gravity rotating flow in a wedge around a sharp corner. Solutions to nonlinear equations are obtained via a power-series expansion in a Rossby number, diffraction theory and Green's function method. The wedge of an angle $\frac{3}{2}\pi $ is used, as an example, to show details of the solution. The results exhibit the relative importance of the pressure gradient, centrifugal and Coriolis forces. For re-entrant corners, a centrifugal upwelling of the interface occurs very close to the apex and, hence, is not important if coastal radii of curvature are comparable to, or larger than, the Rossby radius; the flow is also supercritical within an arc, whose size depends upon the Rossby number and the angle of the wedge. Using two or more corner solutions, plausible flow streamlines can be generated in more complicated domains, as long as no two corners are closer than the Rossby radius of deformation. This procedure is illustrated with two examples: (i) circulation in a channel mouth; and (ii) flow around a square bump in a coastline.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 379 - 407
Copyright
© 1986 Cambridge University Press

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References

Bromwich, T. J. 1915 Diffraction of waves by a wedge. Proc. Lond. Math. Soc. 14, 450–463.Google Scholar
Buchwald, V. T. 1968 The diffraction of Kelvin waves at a corner. J. Fluid Mech. 31, 193–205.Google Scholar
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable: Theory and Technique. McGraw-Hill.
Carslaw, H. S. 1919 Diffraction of waves by a wedge of any angle. Proc. Lond. Math. Soc. 18, 291–306.Google Scholar
Charney, J. G. 1955 The Gulf Stream as an inertial boundary layer. Proc. Nat. Acad. Sci. 41, 731–740.Google Scholar
Cherniawsky, J. 1985 Rotating flows around sharp corners and in channel mouths. Ph.D. dissertation, University of British Columbia, Vancouver, B.C.
Cushman-Roisin, B. & O'Brien, J. J.1983 The influence of bottom topography on baroclinic transports. J. Phys. Oceanogr. 13, 1600–1611.Google Scholar
Drinkwater, K. F. 1985 On the mean and tidal currents in Hudson Strait. Atmosphere-Ocean (in press).
Fissel, D. B., Lemon, D. D. & Birch, J. R. 1982 Major features of the summer near-surface circulation of western Baffin Bay, 1978 and 1979. Arctic 35, 189–200.Google Scholar
Flierl, G. R. 1979 A simple model for the structure of warm and cold core rings. J. Geophys. Res. 84, 781–785.Google Scholar
Gill, A. E. 1977 The hydraulics of rotating-channel flow. J. Fluid Mech. 80, 641–671.Google Scholar
Gill, A. E. & Schumann, E. H. 1979 Topographically induced changes in the structure of an inertial coastal coastal jet: application to the Agulhas Current. J. Phys. Oceanogr. 9, 975–991.Google Scholar
Gutman, L. N. 1972 Introduction to the Nonlinear Theory of Mesoscale Meteorological Processe (translated from the Russian 1969 edn.). Israel Program for Scientific Translation, Jerusalem.
Hughes, R. L. 1981 A solution technique for deep baroclinic rotating flows. Dyn. Atmos. Oceans 5, 159–173.Google Scholar
Hughes, R. L. 1982 On a front between two rotating flows which application to the Flores Sea Dyn. Atmos. Oceans 6, 153–176.Google Scholar
Janowitz, G. S. & Pietrafesa, L. J. 1982 The effects of alongshore variation in botton topography on a boundary current - (topographically induced upwelling). Cont. Shelf Res. 1, 123–141.Google Scholar
Kawasaki, Y. & Sugimoto, T. 1984 Experimental studies on the formation and degeneration processes of the Tsugaru Warm Gyre. In Ocean Hydrodynamics of the Japan and East Chino. Seas (ed. T. Ichiye). Elsevier Ocenogr. Ser. No. 39, pp. 225–238. Elsevier.
Leblond, P. H. 1980 On the surface circulation in some channels of the Canadian Arcti archipelago. Arctic 33, 189–197.Google Scholar
Leblond, P. H., Osborn, T. R., Hodgins, D. O., Goodman, R. & Metge, M. 1981 Surface circulation in the western Labrador Sea. Deep-Sea Res. 28 A, 683–693.Google Scholar
Macdonald, H. M. 1915 A class of diffraction problems. Proc. Lond. Math. Soc. 14, 410–427.Google Scholar
Marko, J. R., Birch, J. R. & Wilson, M. A. 1982 A study of long-term satellite-tracked iceberg drifts in Baffin Bay and Davis Strait. Arctic 33, 234–240.Google Scholar
Merkine, L.-O. & Solan, A. 1979 The separation of flow past a cylinder in a rotating system, J. Fluid Mech. 92, 381–392.Google Scholar
Miles, J. W. 1972 Kelvin waves on oceanic boundaries. J. Fluid Mech. 55, 113–127.Google Scholar
Nof, D. 1978a On geostrophic adjustment in sea straits and wide estuaries: theory and laboratory experiments. Part I: One-layer system. J. Phys. Oceanogr. 8, 690–702.Google Scholar
Nof, D. 1978b On geostrophic adjustment in sea straits and wide estuaries: theory and laboratory experiments. Part II: Two-layer system. J. Phys. Oceanogr. 8, 861–872.Google Scholar
Nof, D. 1984 Shock waves in currents and outflows. J. Phys. Oceanogr. 14, 1683–1702.Google Scholar
Nof, D. & Olson, D. B. 1983 On the flow through broad gaps with application to the Windwarz Passage. J. Phys. Oceanogr. 30, 1940–1956.Google Scholar
Oberhettinger, F. 1954 Diffraction of waves a wedge. Commun. Pure Appl. Math. 7, 551–563.Google Scholar
Packham, B. A. & Williams, W. E. 1968 Diffraction of Kelvin waves at a sharp bend. J. Fluid Mech. 34, 517–530.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Roed, L. P. 1980 Curvature effects on hydraulically driven inertial boundary currents. J. Fluid Mech. 96, 395–412.Google Scholar
Roseau, M. 1967 Diffraction by a wedge in an anisotropic medium. Arch. Rat. Mech. Anal. 26, 188–218.Google Scholar
Sanderson, B. G. & LeBlond, P. H. 1984 The cross-channel flow at the entrance of Lancaster Sound. Atmosphere-Ocean 22, 484–497.Google Scholar
Sommerfeld, A. 1896 Mathematische theorie der diffraction. Math. Ann. 47, 317–341.Google Scholar
Sommerfeld, A. 1954 Optics. Academic.
Stakgold, I. 1968 Boundary Value Problems of Mathematical Physics, vols I and II. Macmillan.
Stommel, H. 1965 The Gulf Stream, 2nd edn. University of California Press.
Stommel, H. & Luyten, J. 1984 The density jump across Little Bahama Bank. J. Geophys. Res. 89, 2097–2100.Google Scholar
Whipple, F. J. W. 1916 Diffraction by a wedge and kindred problems. Proc. Lond. Math. Soc. 16, 94–111.Google Scholar
Whitehead, J. A. 1985 The deflection of a baroclinic jet by a wall in a rotating fluid. J. Fluid Mech. 157, 79–93.Google Scholar
Whitehead, J. A., Leetmaa, A. & Knox, R. A. 1974 Rotating hydraulics of strait and sill flows. Geophys. Fluid Dyn. 6, 101–125.Google Scholar
Whitehead, J. A. & Miller, A. R. 1979 Laboratory simulation of the gyre in the Alborán Sea. J. Geophys. Res. 84, 3733–3742.Google Scholar