Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-18T15:03:49.454Z Has data issue: false hasContentIssue false
  • English
  • Français

Observations of parametric instability and breaking waves in an oscillating tilted tube

Published online by Cambridge University Press:  26 April 2006

S. A. Thorpe
S. A. Thorpe
Affiliation:
Department of Oceanography, The University, Southampton SO9 5NH, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are described in which a rectangular tube filled with a stratified fluid and tilted at an angle α (about 12°) is rocked at the critical frequency of waves on a slope, σ = N sin α, where N is the uniform buoyancy frequency of the fluid in the central section of the tube. Localized overturns with axes transverse to the flow are observed with a scale comparable with the tube height, producing convective motions and mixing. The overturns have a periodic structure along the tube and, although occurring on each forcing cycle, they alternate in position, so that they reoccur at a given position only every two cycles, that is at the frequency of the first subharmonic of the forcing frequency. The wavelength and vertical structure of the disturbance are consistent with the presence of an internal wave mode with a frequency half that of the forcing, and this is indicative of a parametric instability. The parameters of the regions where static instability occurs show that, as observed, the fluid is more likely to be unstable to convective motions than in earlier experiments (Thorpe 1994b) on standing waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 33 - 45
Copyright
© 1994 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

Drazin, P. G. 1977 On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356, 411–432.Google Scholar
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479–500.Google Scholar
Klostermeyer, J. 1982 On parametric instabilities of finite-amplitude internal gravity waves. J. Fluid Mech. 119, 367–377.Google Scholar
Klostermeyer, J. 1983 Parametric instabilities of internal gravity waves in Boussinesq fluids with large Reynolds numbers. Geophys. Astrophys. Fluid Dyn. 26, 85–105.Google Scholar
Klostermeyer, J. 1984 Observations indicating parametric instabilities in internal gravity waves at thermospheric heights. Geophys. Astrophys. Fluid Dyn. 29, 117–138.Google Scholar
Klostermeyer, J. 1990 On the role of parametric instability of internal gravity waves in atmospheric radar observations. Radio Sci. 25, 983–995.Google Scholar
McEwan, A. D. 1971 Degeneration of resonantly excited standing internal gravity waves. J. Fluid Mech. 50, 431–448.Google Scholar
McEwan, A. D. 1973 Interactions between internal gravity waves and their traumatic effect on a continuous stratification. Boundary-Layer Met. 5, 159–175.Google Scholar
McEwan, A. D. & Robinson, R. M. 1975 Parametric instability of internal gravity waves. J. Fluid Mech. 67, 667–687.Google Scholar
Mied, R. P. 1976 The occurrence of parametric instability in finite-amplitude internal gravity waves. J. Fluid Mech. 78, 763–784.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Taylor, J. 1992 The energetics of breaking events in a resonantly forced internal wave field J. Fluid Mech. 239, 309–340.Google Scholar
Thorpe, S. A. 1978a On the shape and breaking of finite-amplitude internal gravity waves in a shear flow. J. Fluid Mech. 85, 7–31.Google Scholar
Thorpe, S. A. 1978b On internal gravity 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
Thorpe, S. A. 1987 On the reflection of a train of finite amplitude internal gravity waves from a uniform slope. J. Fluid Mech. 178, 185–196.Google Scholar
Thorpe, S. A. 1994a The stability of statically unstable layers. J. Fluid Mech. 260, 315–331.Google Scholar
Thorpe, S. A. 1994b Statically unstable layers produced by overturning internal gravity waves. J. Fluid Mech. 260, 333–350.Google Scholar