Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-29T06:33:10.953Z Has data issue: false hasContentIssue false
  • English
  • Français

Critical layers in accelerating two-layer flows

Published online by Cambridge University Press:  21 April 2006

Donald B. Altman
Donald B. Altman
Affiliation:
Institute for Naval Oceanography, Stennis Space Center, MS 39529, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A series of laboratory experiments on accelerating two-layer shear flows over topography is described. The mean flow reverses at the interface of the layers, forcing a critical layer to occur there. It is found that for a sufficiently thin interface, a slowly growing recirculating region, the ‘acceleration rotor’, develops on the interfacial wave at mean-flow Richardson numbers of O(0.5). This, in turn, can induce a secondary dynamical shear instability on the trailing edge of the wave. A single-mode, linear, two-layer numerical model reproduces many features of the acceleration rotor if mean-flow acceleration and bottom forcing are included. Velocity measurements are obtained from photographs using image processing software developed for the automated reading of particle-streak photographs. Typical results are shown.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 429 - 451
Copyright
© 1988 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.1978 Mixing in the deep ocean – the importance of boundaries. Oceanus 21, 14–19.Google Scholar
Broutman, D.1984 The focusing of short internal waves by an inertial wave. Geophys. Astrophys. Fluid Dyn. 30, 199–225.Google Scholar
Buckles, J., Hanratty, T. J. & Adrian, R. J.1984 Turbulent flow over large amplitude wavy surfaces. J. Fluid Mech. 140, 27–44.Google Scholar
Bulirsch, R. & Stöer, J.1966 Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math. 18, 1–13.Google Scholar
Chow, C.-Y. 1979 An Introduction to Computational Fluid Mechanics. Wiley Press.
Fritts, D. C.1982 The transient critical-level interaction in a Boussinesq fluid. J. Geophys. Res. 87C, 7997–8013.Google Scholar
Haury, L. R., Briscoe, M. G. & Orr, M. H.1979 Tidally generated internal wave packets in Massachusetts bay. Nature 278, 312–317.Google Scholar
Koop, C. G. & McGee, B.1983 Measurements of internal gravity waves in a stratified shear flow. Preprint – T. R. W. Space & Technology Group, Redondo Beach, CA 90278.
Miles, J. W. & Howard, L. N.1964 Note on a heterogeneous shear flow. J. Fluid Mech. 20, 331–336.Google Scholar
Stacey, M. W. & Zedel, L. J.1986 The time-dependent hydraulic flow and dissipation over the sill of observatory inlet. J. Phys. Oceanogr. 16, 1062–1076.Google Scholar
Thorpe, S. A.1968 A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 293–304.Google Scholar
Thorpe, S. A.1969 Experiments on the instability of stratified shear flows: immiscible fluids. J. Fluid Mech. 39, 25–48.Google Scholar
Thorpe, S. A.1973a Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–751.Google Scholar
Thorpe, S. A.1973b Turbulence in stably stratified fluids: a review of laboratory experiments. Boundary-Layer Met. 5, 95–119.Google Scholar
Thorpe, S. A.1978 On internal waves in an accelerating shear flow. J. Fluid Mech. 88, 623–639.Google Scholar
Thorpe, S. A.1981 An experimental study of critical layers. J. Fluid Mech. 103, 321–344.Google Scholar
Zilker, D. P. & Hanratty, T.1979 Influence of the amplitude of a solid wavy wall on a turbulent flow. J. Fluid Mech. 90, 257–271.Google Scholar