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Finite-amplitude steady waves in plane viscous shear flows

Milinazzo, F. A. and Saffman, P. G. (1985) Finite-amplitude steady waves in plane viscous shear flows. Journal of Fluid Mechanics, 160 (11). pp. 281-295. ISSN 0022-1120. doi:10.1017/S0022112085003482.

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Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

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Additional Information:© 1985 Cambridge University Press. Received 7 January 1985 and in revised form 14 May 1985. This work was supported by NASA Lewis (NAG3-179), the Department of Energy, Office of Basic Energy Sciences (DE-AT03-76ER72012), and the Office of Naval Research (N00014-85-K-0205).
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Department of Energy (DOE)DE-AT03-76ER72012
Office of Naval Research (ONR)N00014-85-K-0205
Issue or Number:11
Record Number:CaltechAUTHORS:20120629-072147863
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Official Citation: F. A. Milinazzo and P. G. Saffman (1985). Finite-amplitude steady waves in plane viscous shear flows. Journal of Fluid Mechanics, 160 , pp 281-295 doi:10.1017/S0022112085003482
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32182
Deposited By: Ruth Sustaita
Deposited On:02 Jul 2012 16:31
Last Modified:09 Nov 2021 21:25

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