Abstract
The inviscid instability of O(ε) two-dimensional periodic flows to spanwise-periodic longitudinal vortex modes in parallel O(1) shear flows is considered. In such cases, not only is the effect of fluctuations upon the mean state important but also the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Of specific interest is whether the spanwise distortion of the wave field feeds back to enhance or inhibit instability to longitudinal vortex form. Two cases are considered in detail: uniform shear between wavy walls and non-uniform shear beneath free-surface waves. In both cases wave distortion acts to inhibit, and in some circumstances curtail, instability for all but the shortest waves.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference20 articles.
1. Craik, A. D. D. 1970 A wave-interaction model for the generation of windrows J. Fluid Mech. 41,801–821.
2. Craik, A. D. D. 1985 Wave Interactions and Fluid Flows .Cambridge University Press.
3. Herbert, T. & Morkovin, M. V. 1980 In Laminar-Turbulent Transition (ed R. Eppler & H. Fasel ), pp47–72.Springer.
4. Abramowitz, M. & Stegun, I.A. 1965 Handbook of Mathematical Functions .Dover.
5. Benney, D. J. & Lin, C. C. 1960 A non-linear theory for oscillations in parallel flow.Phys. Fluids 3,656–657.
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