Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T16:47:26.874Z Has data issue: false hasContentIssue false
  • English
  • Français

On inertial flow over topography. Part 2. Rotating-channel flow near the critical speed

Published online by Cambridge University Press:  20 April 2006

L. J. Pratt
L. J. Pratt
Affiliation:
Graduate School of Oceanography, University of Rhode Island, Kingston, R.I. 02882-1197
Get access Rights & Permissions [Opens in a new window]

Abstract

A narrow flow passing over an obstacle in a rotating channel is analysed. When the upstream Froude number of the flow approaches unity and the obstacle height is sufficiently small, stationary Kelvin waves may appear in the channel. Under these conditions the usual nonlinear hydraulic theory (e.g. Gill 1977) must be replaced by a nonlinear dispersive theory. When the flow upstream of the obstacle is subcritical, the nonlinear dispersive theory produces three solutions, two of which resemble the solutions of hydraulic theory and a third which contains cnoidal lee waves. Upstream influence due to the obstacle becomes a function of obstacle shape as well as height. The ‘controlled’ solution is distinguished by the presence of a partial solitary wave in the lee of the obstacle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 95 - 110
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. R. Soc. Lond. A 224, 448–460.Google Scholar
Chow, V. T. 1959 Open Channel Hydraulics. McGraw-Hill..
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
Kyner, W. T. 1962 Steady flows near the critical speed. J. Fluid Mech. 14, 517–528.Google Scholar
Long, R. R., 1954 Some aspects of the flow of stratified fluids. II. Experiments with a two-fluid system. Tellus 6, 97–115.Google Scholar
Pratt, L. J. 1983a On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle. J. Fluid Mech. 131, 195–218.Google Scholar
Pratt, L. J. 1984 On nonlinear flow with multiple obstructions. J. Atmos. Sci. (in press).Google Scholar
Stern, M. E. 1980 Geostrophic fronts, bores, breaking and blocking waves. J. Fluid Mech. 99, 687–703.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
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.