Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T22:12:57.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Upstream influence and Long's model in stratified flows

Published online by Cambridge University Press:  12 April 2006

P. G. Baines
P. G. Baines
Affiliation:
C.S.I.R.O. Division of Atmospheric Physics, Aspendale, Victoria, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes an experimental study of a stratified fluid which is flowing over a smooth two-dimensional obstacle which induces no flow separation and in which effects of viscosity and diffusion are not important. The results are restricted to fluid of finite depth. Various properties of the flow field, in particular the criterion for the onset of gravitational instability in the lee-wave field, are measured and compared with the theoretical predictions of Long's model. The agreement is found to be generally poor, and the consequent inapplicability of Long's model is explained by the failure of Long's hypothesis of no upstream influence, which is demonstrably invalid when stationary lee waves are possible. The obstacle generates upstream motions with fluid velocities which appear to be of first order in the obstacle height. These motions have some of the character of shear fronts or columnar disturbance modes and have the same vertical structure as the corresponding lee-wave modes generated downstream. They result in a reduced fluid velocity upstream below the level of the top of the obstacle, together with a jet of increased fluid velocity above this level which pours down the lee side of the obstacle. This phenomenon becomes more pronounced as the number of modes is increased.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 147 - 159
Copyright
© 1977 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

Baines, P. G. 1977 Inviscid stratified flow over finite two-dimensional obstacles in fluid of infinite depth. In preparation.
Barnard, B. J. S. & Pritchard, W. G. 1975 The motion generated by a body moving through a stratified fluid at large Richardson numbers. J. Fluid Mech. 71, 43.Google Scholar
Benjamin, T. B. 1970 Upstream influence. J. Fluid Mech. 40, 49.Google Scholar
Davis, R. E. 1969 The two-dimensional flow of a stratified fluid over an obstacle. J. Fluid Mech. 36, 127.Google Scholar
Drazin, P. G. & Moore, D. W. 1967 Steady two-dimensional flow of a fluid of variable density over an obstacle. J. Fluid Mech. 28, 353.Google Scholar
Droughton, J. V. & Chen, C. F. 1971 Channel flow of a density stratified fluid about immersed bodies. J. Basic Engng 94, 122.Google Scholar
Grimshaw, R. 1968 A note on the steady two-dimensional flow of a stratified fluid over an obstacle. J. Fluid Mech. 33, 293.Google Scholar
Huppert, H. E. & Miles, J. W. 1969 Lee waves in a stratified flow. Part 3. Semi-elliptical obstacle. J. Fluid Mech. 55, 481.Google Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids. III. Continuous density gradients. Tellus 7, 343.Google Scholar
Mcewan, A. D. & Baines, P. G. 1974 Shear fronts and an experimental stratified shear flow. J. Fluid Mech. 63, 257.Google Scholar
Mcintyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52, 209.Google Scholar
Maxworthy, T. 1970 The flow created by a sphere moving along the axis of a rotating slightly viscous fluid. J. Fluid Mech. 40, 453.Google Scholar
Miles, J. W. 1968a Lee waves in a stratified flow. Part 1. Thin barrier. J. Fluid Mech. 32, 549.Google Scholar
Miles, J. W. 1968b Lee waves in a stratified flow. Part 2. Semi-circular obstacle. J. Fluid Mech. 33, 803.Google Scholar
Miles, J. W. 1972 Axisymmetric rotating flow past a circular disk. J. Fluid Mech. 53, 689.Google Scholar
Miles, J. W. 1975 Axisymmetric rotating flow past a prolate spheroid. J. Fluid Mech. 72, 363.Google Scholar
Miles, J. W. & Huppert, H. E. 1969 Lee waves in a stratified flow. Part 4. Perturbation approximations. J. Fluid Mech. 35, 497.Google Scholar
Pao, Y.-H. 1969 Inviscid flows of stably stratified fluids over barriers. Quart. J. Roy. Met. Soc. 95, 104.Google Scholar
Pekelis, Y. M. 1972 Solution of the problem of flow past an obstacle. USSR Gidromet. Nauch-Issl. Trentr. SSSR, Leningrad, Trudy 99, 63.Google Scholar
Pritchard, W. G. 1969 The motion generated by a body moving along the axis of a uniformly rotating fluid. J. Fluid Mech. 39, 443.Google Scholar
Segur, H. 1971 A limitation on Long's model in stratified flows. J. Fluid Mech. 48, 161.Google Scholar
Trustrum, K. 1964 Rotating and stratified fluid flow. J. Fluid Mech. 19, 415.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Wei, S. N., Kao, T. W. & Pao, H.-P. 1975 Experimental study of upstream influence in the two-dimensional flow of a stratified fluid over an obstacle. Geophys. Fluid Dyn. 6, 315.Google Scholar
Wong, K. K. & Kao, T. W. 1970 Stratified flow over extended obstacles and its application to topographical effect on ambient wind shear. J. Atmos. Sci. 27, 884.Google Scholar
Yih, C.-S. 1960 Exact solutions for steady two-dimensional flow of a stratified fluid. J. Fluid Mech. 9, 161.Google Scholar