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Stratified non-diffusive flow over a horizontal flat plate

Published online by Cambridge University Press:  11 April 2006

S. K. Chaturvedi  and
G. S. Janowitz
S. K. Chaturvedi
Affiliation:
Department of Mechanics, Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago
G. S. Janowitz
Affiliation:
Department of Geosciences, North Carolina State University, Raleigh
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Abstract

The effects of inertia on the upstream-growing boundary layer over a finite horizontal flat plate of length b moving uniformly with speed U0 in a linearly stratified \[ [(dp/dy)_{-\infty}- = - \rho_0\beta)], \] viscous, non-diffusive fluid under the Boussinesq approximation are studied. The nonlinear inertia terms are linearized by the Oseen approximation, but no boundary-layer approximation is required. The flow is governed by two parameters, namely the internal Froude number Fr[= U0/(βgb2)½] and a parameter L3[= βgb3/U0ν], where $L^{\frac{3}{4}}$ is proportional to the ratio of boundary-layer thickness to plate length for the case Fr = 0. Large values of L3 and Fr2 = 0 correspond to the case of an upstream boundary layer. By increasing the Froude number gradually, a transition occurs from an upstream boundary layer accompanied by an upstream wake to a downstream boundary layer with a downstream wake. The upstream boundary layer and wake are characterized by a balance of viscous and buoyancy forces, whereas the downstream boundary layer and wake are characterized by a balance of inertia and viscous forces. In the so-called critical-boundary-layer case, Fr4L3 = O(1), inertia, viscous and buoyancy forces are all important and this boundary layer is accompanied by both upstream and downstream wakes. Complete transition occurs when Fr4L3 increases from 10·0 to 1000·0. The drag on the plate is also calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 465 - 480
Copyright
© 1977 Cambridge University Press

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References

Chaturvedi, S. K. & Janowitz, G. S. 1972 Stratified flow over a flat plate. Fluid, Thermal Aerospace Sci. Dept., Case Western Reserve Univ., Cleveland, Ohio Tech. Rep. TR-72–74.Google Scholar
Goldstein, S. 1930 Concerning some solutions of the boundary layer equations in hydrodynamics. Proc. Camb. Phil. Soc. 26, 1–30.Google Scholar
Janowitz, G. S. 1968 On wakes in stratified fluids. J. Fluid Mech. 33, 417.Google Scholar
Kelly, R. E. & Redekopp, L. G. 1970 The development of horizontal boundary layers in stratified flow. Part 1. Non-diffusive flows. J. Fluid Mech. 42, 497.Google Scholar
Long, R. R. 1959 The motion of fluids with density stratification. J. Geophys. Res. 64, 2151.Google Scholar
Martin, S. 1966 The slow motion of a finite flat plate through a viscous stratified fluid. Dept. Mech., Johns Hopkins Univ. Tech. Rep. ONR21.Google Scholar
Martin, S. & Long, R. R. 1968 The slow motion of a finite flat plate in a viscous stratified fluid. J. Fluid Mech. 31, 669.Google Scholar
Miyagi, T. 1964 Oseen flow past a flat plate inclined to the uniform stream. J. Phys. Soc. Japan 19, 6.Google Scholar
Pao, Y. H. 1968 Laminar flow of a stably stratified fluid past a plate. J. Fluid Mech. 34, 795.Google Scholar
Piercy, N. A. V. & Winny, H. F. 1933 Proc. Roy. Soc. A 140, SA3.
Stewartson, K. 1968 On inviscid flow of a rotating fluid past an axially symmetric body using Oseen's equation. Quart. J. Mech. Appl. Math. 21, 353.Google Scholar
Yih, C. S. 1959 Effect of density variation of fluid flow. J. Geophys. Res. 64, 2219.Google Scholar