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Stability of steady vortices and new equilibrium flows from “Imperfect-Velocity-Impulse” diagrams

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Advances in Turbulence XII

Part of the book series: Springer Proceedings in Physics ((volume 132))

Abstract

In 1875, Lord Kelvin proposed an energy-based argument for determining the stability of steady inviscid flows [1]. While the key underpinnings of the method are well established, its practical use has been the subject of extensive debate. In this work, we draw on ideas from dynamical systems and imperfection theory to construct a methodology that represents a rigorous implementation of Kelvin’s argument. Besides yielding stability properties, which are found to be in precise agreement with the results of linear analysis, our approach also implicitly yields new bifurcated solutions branches, as we shall describe below.

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Correspondence to P. Luzzatto-Fegiz .

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Luzzatto-Fegiz, P., Williamson, C.H.K. (2009). Stability of steady vortices and new equilibrium flows from “Imperfect-Velocity-Impulse” diagrams. In: Eckhardt, B. (eds) Advances in Turbulence XII. Springer Proceedings in Physics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03085-7_74

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  • DOI: https://doi.org/10.1007/978-3-642-03085-7_74

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