Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T12:39:24.734Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave propagation in a stratified shear flow

Published online by Cambridge University Press:  29 March 2006

R. J. Hartman
R. J. Hartman
Affiliation:
Department of Physics, University of California, Santa Barbara
Get access Rights & Permissions [Opens in a new window]

Abstract

The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J > ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J > ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J [gsim ] ¼ conclusions of an earlier treatment by Booker & Bretherton.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 1 , 9 September 1975 , pp. 89 - 104
Copyright
© 1975 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

Abramowitz, M. & Stegun, I. 1970 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Booker, J. R. & Bretherton, F. P. 1967 J. Fluid Mech. 28, 545.
Bretherton, F. P. 1966 Quart. J. Roy. Met. Soc. 95, 213.
Case, K. M. 1960 Phys. Fluids, 3, 149.
Dyson, F. J. 1960 Phys. Fluids, 3, 155.
Eliassen, A., Hihiland, E. & Riis, E. 1953 Two-Dimensional Perturbation of a Flow with Constant Shear of a Stratified Fluid. Inst. for Weather & Climate Res., Norwegian Acad. Sci. & Lett., publ. no. 1.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, vol. 1. McGraw-Hill.
Hartman, R. J. 1973 Ph.D. dissertation, University of California, Santa Barbara.
Hazel, P. 1967 J. Fluid Mech. 30, 775.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.
Taylor, G. I. 1931 Proc. Roy. Soc. A 132, 499.