Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T00:00:18.255Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydraulic jumps in an incompressible stratified fluid

Published online by Cambridge University Press:  29 March 2006

C. H. Su
C. H. Su
Affiliation:
Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado 80303 Permanent address: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912.
Get access Rights & Permissions [Opens in a new window]

Abstract

A multi-layer model is used to describe a ‘two-dimensional’ continuously stratified fluid. We use a momentum theorem in each layer to derive an ordinary differential equation describing the vertical structure behind a jump. This equation is compared with the corresponding equation for continuous flow. As one would expect from the classical one-layer theory, they are identical up to second order for weak disturbances. The energy change across a jump is also derived. By requiring that energy be lost through a jump, we calculate when a weak jump is possible in general. Algorithms for computing jumps of arbitrary strength are given. To ensure that the flow after the jump is stable and also for a numerical reason to be stated in § 8, we require that the Richardson number after the jump be equal to or greater than S¼S. Numerical examples are given to show the range of parameters within which jumps are possible; the velocity profiles related to different kinds of jumps also appear. Since hydraulic jumps in a continuously stratified fluid have not yet been observed in any laboratory, it should be of interest to verify these calculations experimentally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 1 , 13 January 1976 , pp. 33 - 47
Copyright
© 1976 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. 1966 J. Fluid Mech. 25, 241–270.
Benton, G. S. 1953 In Proc. 1st Symp. on Use of Models in Geophys. Fluid Dyn. (ed. R. R. Long), pp. 149-162.
Benton, G. S. 1954 J. Met. 11, 139–150.
Drazin, P., Lee, J. & Su, C. H. 1974 N.C.A.R. Rep. no. 101.
DRAZIN, P. & SU, C. H. 1975 J. Atmos. Sci. 32, 437.
Dubreil-Jacotin, M. L. 1937 J. Math. Pure Appl. 9 (16), 43-67.
Eliassen, A. & Palm, E. 1961 Geofys. Publ. 22, no. 3.
Houghton, D. D. & Isaacson, E. 1970 S.I.A.M. Stud. Numer. Anal. 2, 21–52.
Lee, J. & Su, C. H. 1976 Continuous stratified flows over an obstacle. Submitted to J. Fluid Mech.Google Scholar
Long, R. R. 1953 Tellus, 5, 42–57.
Long, R. R. 1972 Ann. Rev. Fluid Mech. 4, 69–92.
Mehrotra, S. C. & Kelly, R. E. 1973 Tellus, 25, 560–567.
Miles, J. W. 1961 J. Fluid Mech. 10, 496.
Yih, C.-S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.
Yih, C.-S. & Guha, C. R. 1955 Tellus, 7, 358–366.