Hostname: page-component-68945f75b7-l9cl4 Total loading time: 0 Render date: 2024-08-05T19:05:38.449Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydraulic jumps at boundaries in rotating fluids

Published online by Cambridge University Press:  26 April 2006

Alexey V. Fedorov  and
W. Kendall Melville
Alexey V. Fedorov
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0213, USA
W. Kendall Melville
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0213, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider three-dimensional hydraulic jumps (shocks) propagating along boundaries in rotating fluids. This study is motivated by earlier work (Fedorov & Melville 1995), which dealt with the evolution to breaking of nonlinear Kelvin waves. We obtain the jump relations and derive an evolution equation for the jump as it propagates along the boundary. It is shown that after some initial adjustment the Kelvin-type jump assumes a permanent form and propagates with a constant velocity along the boundary or the coast. At some distance offshore the jump becomes oblique to the coastline, and the final shape of the jump and its speed depend only on the jump strength. The jump gives rise to a moderate mass transport offshore. The potential vorticity remains almost constant across the jump. The energy loss in the jump is proportional to the third power of the jump amplitude, which is similar to classical two-dimensional hydraulic jumps in non-rotating fluids. Jump properties are discussed for both weak and strong nonlinearity, and the role of a boundary layer region behind the leading edge of the jump is considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 324 , 10 October 1996 , pp. 55 - 82
Copyright
© 1996 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

Armi, L. 1986 The hydraulic of two flowing layers with different densities. J. Fluid Mech. 163, 27–58.Google Scholar
Armi, L. & Farmer, D. M. 1985 The internal hydraulics of the Strait of Gibraltar and associated sills and narrows. Oceanologica Acta 8, 37–46.Google Scholar
Baines, P. G. 1980 The dynamics of the southerly buster. Austral. Met. Mag. 28, 175–200.Google Scholar
Bannon, P. R. 1981 Synoptic scale forcing of coastal flows: forced double Kelvin waves in the atmosphere. Q. J. R. Met. Soc. 107, 313–327.Google Scholar
Beardsley, R. C., Dorman, C. E., Friehe, C. A., Rosenfeld, L. K. & Winant, C. D. 1987 Local atmospheric forcing during the CODE, 1, A description of the marine boundary layer and atmospheric conditions over a northern California upwelling region. J. Geophys. Res. 92, 1467–1488.Google Scholar
Bennet, J. R. 1973 A theory of large-amplitude Kelvin waves. J. Phys. Oceanogr. 3, 57–60.Google Scholar
Bennett, A. F. & Cummins, P. F. 1988 Tracking fronts in solutions to the shallow water equations. J. Geophys. Res. 93, 1293–1301.Google Scholar
Chow, V.-T. 1959 Open-Channel Hydraulics. McGraw-Hill.
Dorman, C. E. 1987 Possible role of gravity currents in northern California's summer wind reversals. J. Geophys., Res. 92, 1497–1505.Google Scholar
Fedorov, A. V. & Melville, W. K. 1995 On the propagation and breaking of nonlinear Kelvin waves. J. Phys. Oceanogr. 25, 2518–2531.Google Scholar
Fletcher, C. A. J. 1988 Computational Techniques for Fluid Dynamics. Springer.
Garvine, R. W. 1987 Estuary plumes and fronts in shelf waters: A layer model. J. Phys. Oceanogr. 17, 1877–1896.Google Scholar
Gill, A. E. 1977 Coastally trapped waves in the atmosphere. Q. J. R. Met. Soc. 103, 431–440.Google Scholar
Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
Hermann, A. J., Hickey, B. M., Mass, C. F. & Albright, M. D. 1990 Orographically trapped coastal wind events in the Pacific Northwest and their oceanic response. J. Geophys. Res. 95, 13169–13193.Google Scholar
Houghton, D. D. 1969 Effect of rotation on the formation of hydraulic jumps. J. Geophys. Res. 74, 1351–1360.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Mass, C. F. & Albright, M. D. 1987 Coastal southerlies and alongshore surges of the west coast of North America. Mon. Wealth. Rev. 115, 1707–1738.Google Scholar
Nof, D. 1984 Shock waves in currents and outflows. J. Phys. Oceanogr. 14, 1683–1702.Google Scholar
Nof, D. 1986 Geostrophic shock waves. J. Phys. Oceanogr. 16, 886–901.Google Scholar
O'Donnell, J. 1989 Transients in the nonlinear adjustment to geostrophy. In The Physical Oceanography of the Sea Straits (ed. L. J. Pratt), pp. 509–516. Kluwer.
Parret, C. A. & Cullen, M. J. P. 1984 Simulation of hydraulic jumps in the presence of rotation and mountains. Q. J. R. Met. Soc. 110, 147–165.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.
Pratt, L. J. 1983 On inertial flow over topography. Part 1. J. Fluid Mech. 131, 195–218.Google Scholar
Pratt, L. J. 1987 Rotating shocks in a separated laboratory channel flow. J. Phys. Oceanogr. 17, 483–491.Google Scholar
Renourard, D. P., Tomasson, G. G. & Melville, W. K. 1992 An experimental and numerical study of nonlinear internal waves. Phys. Fluids A 5, 1401–1411.Google Scholar
Stern, M. E. 1980 Geostrophic fronts, bores, breaking and blocking waves. J. Fluid Mech. 99, 687–703.Google Scholar
Stoker, J. J. 1957 Water Waves. Interscience.
Tomasson, G. G. 1991 Nonlinear waves in a channel:three-dimensional and rotational effects. Ph.D thesis, Dept of Civil Engineering, MIT.
Tomasson, G. G. & Melville, W. K. 1992 Geostrophic adjustment in a channel: Nonlinear and dispersive effects. J. Fluid Mech. 241, 23–57.Google Scholar
Welander, P. 1961 Numerical prediction of storm surges. Adv. Geophys. 8, 316–379.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.