Skip to main content Accessibility help
×
Home

Two-dimensional sink flow of a stratified fluid contained in a duct

  • Jorg Imberger (a1) (a2)

Abstract

A reservoir is assumed to be filled with water which has a linear variation of density with depth. The geometry of the boundaries is simplified to a parallel walled duct with the line sink at the centre of the fluid. The primary focus is on partitioning the flow into distinct flow regimes and predicting the withdrawal-layer thickness as a function of the distance from the sink; the predictions are verified experimentally.

For fluids with a Schmidt number of order unity, the withdrawal layer is shown to be composed of distinct regions in each of which a definite force balance prevails. The outer flow, where inertia forces are neglected, changes from a parallel uniform flow upstream to a symmetric self-similar withdrawal layer near the sink. For distances from the sink smaller than a critical distance, dependent on the flow parameters, inertia forces become of equal importance to buoyancy and viscous forces. The equations valid in this inner region are derived. Using the inner limit of the outer flow as the upstream boundary condition, these inner equations are solved approximately for the withdrawal-layer thickness by an integral method. The inner and outer variations of δ, the withdrawal-layer thickness, are combined to yield a composite solution and it is seen that the inclusion of inertia forces yields layers thicker than those obtained from a strict buoyancy-viscous force balance. In terms of the inner variables the only parameter remaining is the Schmidt number.

Laboratory experiments were carried out to verify the theoretical conclusions. The observed withdrawal-layer thicknesses were shown to be closely predicted by the integral solution. Furthermore, the data could be represented in terms of the inner variables by a single curve dependent only on the Schmidt number.

Copyright

References

Hide All
Bellman, R. 1953 Stability Theory of Differential Equations. McGraw-Hill.
Brooks, N. H. & KOH, R. C. Y. 1969 J. Hyd. Div. Proc. A.S.C.E. 95 (HY4), 13691400.
Clare, C. B., Stockhausen, P. J. & Kennedy, J. F. 1967 J. Ceophys. Res. 72, 13931395.
Debler, W. R. 1959 J. Eng. Mech. Div. Proc. A.S.C.E. 85, 673695.
Kao, T. W. 1965 J. Fluid Mech. 21, 535543.
Kao, T. W. 1970 Phys. Fluids, 13, 558564.
Koh, R. C. Y. 1966 J. Fluid Mech. 24, 555575.
Orlob, G. T. & Selna, L. G. 1970 J. Hyd. Div. Proc. A.X.C.E. 96 (HY2), 391410.
Schiff, L. L. 1966 Deep Sea Ree. 13, 621626.
Yih, C S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed