Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-05T06:10:22.368Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar flow of a stably stratified fluid past a flat plate

Published online by Cambridge University Press:  28 March 2006

Yih-Ho Pao
Yih-Ho Pao
Affiliation:
Boeing Scientific Research Laboratories, Seattle, Washington
Get access Rights & Permissions [Opens in a new window]

Abstract

Laminar flow of a stably stratified fluid with uniform upstream velocity and density gradient past a flat plate is investigated experimentally and theoretically. In the experimental study, the flat plate, parallel to the direction of motion, is towed horizontally at uniform speeds in a tank of stratified salt water at uniform density gradients. The horizontal velocity in front of, above, and behind the flat plate is measured with a flow visualization technique. One of the striking phenomena is the strong upstream influence (the upstream wake) of an obstacle in a flow of stably stratified fluid when the gravity effect is comparable to, or more than the inertial effect. The velocity profiles of the upstream wake and boundary layer above the flat plate are wavy and found to be governed by the ratio of Reynolds number Be to Richardson number Ri. The problem is also analysed theoretically with Boussinesq's approximation and two-parameter perturbation expansions for the upstream wake and the boundary layer. The solutions for the upstream wake and for the boundary layer are compared with measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 4 , 23 December 1968 , pp. 795 - 808
Copyright
© 1968 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

Boussinesq, J. 1903 Theorie analytique de la chaleur, 2, 172. Paris: Gauthier-Villars.
Childress, S. 1963 The effect of a strong magnetic field on two-dimensional flows of a eonducting fluid J. Fluid Mech. 15, 429–41.Google Scholar
Gibson, C. H. & Schwarz, W. H. 1963 Detection of conductivity fluctuations in a turbulent flow field J. Fluid Mech. 16, 357–64.Google Scholar
Janowitz, G. S. 1967 On wakes in stratified fluids. Ph.D. Thesis, Department of Mechanics, The Johns Hopkins University.
Long, R. R. 1959 The motion of fluids with density stratification J. Geophys. Res. 64, 2151–63.Google Scholar
Long, R. R. 1962 Velocity concentrations in stratified fluids Proc. Am. Soc. Civil Engr., J. Hydraulics Div. 1, 9–26.Google Scholar
Martin, S. 1966 The slow motion of a finite flat plate through a viscous stratified fluid. Ph.D. Thesis, Department of Mechanics, The Johns Hopkins University.
Pao, Y. H. 1965 Laminar flow of stratified fluid past a flat plate. Bull. Am. Phys. Soc. Series 11, 8, 426.Google Scholar
Pao, Y. H. 1967a Turbulence in stratified fluids. Proc. IUGG and IUTAM symposium on boundary layer and turbulence including geophysical applications. Phys. Fluids, 10, S 311.Google Scholar
Pao, Y. H. 1967b Laminar flow of a stably stratified fluid past a flat plate. Boeing Document, D1-82-0488.Google Scholar
Pao, Y. H. 1967c Inviscid flows of stably stratified fluids over barriers. Boeing Document, D1-82-0646.Google Scholar
Pao, Y. H. & Timm, G. K. 1966 Flow of a stratified fluid past a circular cylinder. Bull. Am. Phys. Soc. (Series 11) 11, (5), 721.Google Scholar
Timm, G. K. & Pao, Y. H. 1966 Laboratory simulation of mountain waves. Bull. Am. Phys. Soc. (Series 11) 11 (5), 721.Google Scholar