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On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle

Published online by Cambridge University Press:  20 April 2006

L. J. Pratt
L. J. Pratt
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 Present address: Graduate School of Oceanography, University of Rhode Island, Kingston, RI 02881.
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Abstract

The nonlinear time-dependent adjustment of a homogeneous rotating-channel flow to the sudden obtrusion of an obstacle is studied. Solutions are obtained using a Lax–Wendroff numerical scheme which allows rotating breaking bores and jumps to form and be maintained. The flow upstream of the obstacle is found to be completely blocked, partially blocked (and hydraulically controlled), or unobstructed depending upon the height of the obstacle. Partial blockage is accomplished through the excitation of a combination of nonlinear Kelvin waves, some of which steepen into interfacial shocks. Riemann invariants for the Kelvin waves are found, and jump conditions on mass, momentum and potential vorticity for the shocks are discussed. The shocks are surrounded by dispersive regions of Rossby deformation scale, and the potential vorticity of passing fluid is altered at a rate proportional to the differential rate of energy dissipation along the line of breakage. For the special case of initially uniform potential vorticity the asymptotic state is found as a function of the initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 131 , June 1983 , pp. 195 - 218
Copyright
© 1983 Cambridge University Press

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References

Baines, P. O. & Davies, P. A. 1980 Laboratory studies of topographic effects in rotating and/or stratified fluids. In Orographic Effects in Planetary Flows, GARP Publ. Ser. no. 23. World Met. Orgn.
Blumen, W. 1972 Geostrophic adjustment Rev. Geophys. 10, 485–528.Google Scholar
Dafermos, C. M. 1974 Quasilinear hyperbolic systems that result from conservation laws. In Nonlinear Waves (ed. S. Leibovich & A. R. Seebass), pp. 82–100. Cornell University Press.
Fjortoft, R. 1951 Stability properties of large scale atmospheric disturbances. In Meteorology, pp. 454–000. Am. Met. Soc.
Gill, A. E. 1976 Adjustment under gravity in a rotating channel J. Fluid Mech. 77, 603–621.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 a coastal inertial jet: applications to the Agulhas Current. J. Phys. Oceanogr. 9, 975–991.Google Scholar
Griffiths, R. W., Killworth, P. D. & Stern, M. E. 1982 Ageostrophic instability of ocean currents J. Fluid Mech. 117, 343–377.Google Scholar
Houghton, D. D. & Kasahara, A. 1968 Nonlinear shallow fluid flow over an isolated ridge Communs Pure Appl. Maths 21, 1–23.Google Scholar
Klemp, J. B. & Lilly, D. K. 1975 The dynamics of wave-induced downslope winds J. Atmos. Sci. 32, 320–339.Google Scholar
Lax, P. & Wendroff, B. 1960 Systems of conservation laws Communs Pure Appl. Maths 13, 217–237.Google Scholar
Long, R. R. 1954 Some aspects of the flow of stratified fluids II. Experiments with a two-fluid system Tellus 5, 42–58.Google Scholar
Long, R. R. 1970 Blocking effects in flow over obstacles Tellus 22, 471–480.Google Scholar
Orlanski, I. 1968 Instability of frontal waves J. Atmos. Sci. 25, 178–200.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Rayleigh, Lord 1914 On the theory of long waves and bores Proc. R. Soc. Lond. A90, 324–328.Google Scholar
Richtmyer, R. D. 1963 A survey of difference methods for nonsteady fluid dynamics. NCAR Tech 63–2, Boulder, Colorado.
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.
Rubin, E. L. & Burstein, S. Z. 1967 Difference methods for the invisicid and viscous equations of a compressible gas J. Comp. Phys. 2, 178–196.Google Scholar
Shen, C. Y. 1981 The rotating hydraulics of open-channel flow between two basins J. Fluid Mech. 112, 161–188.Google Scholar
Sielecki, A. & Wurtele, M. G. 1970 The numerical integration of the nonlinear shallow-water equations with sloping boundaries J. Comp. Phys. 6, 219–236.Google Scholar
Stern, M. E. 1974 Comment on rotating hydraulics Geophys. Fluid Dyn. 6, 127–130.Google Scholar
Stoker, J. J. 1957 Water Waves. Interscience.
Whitehead, J. A., Leetmaa, A. & Knox, R. A. 1974 Rotating hydraulics of strait and sill flows Geophys. Fluid Dyn. 6, 101–125.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Worthington, L. V. 1969 An attempt to measure the volume transport of Norwegian Sea overflow water through the Denmark Strait. Deep-Sea Res. 16 (Suppl.), 421–433.Google Scholar