On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully-developed flows
Abstract
There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmein-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poisseulle flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.
- Publication:
-
National Aeronautics and Space Administration Report
- Pub Date:
- November 1986
- Bibcode:
- 1986nasa.reptW....B
- Keywords:
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- Fluid Dynamics;
- Fluid Flow;
- Goertler Instability;
- Tollmien-Schlichting Waves;
- Vortices;
- Boundary Layer Transition;
- Laminar Flow;
- Reynolds Number;
- Three Dimensional Flow;
- Turbulence;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer