Stability of Conservative Flows and New Steady-Fluid Solutions from Bifurcation Diagrams Exploiting a Variational Argument

Paolo Luzzatto-Fegiz and Charles H. K. Williamson
Phys. Rev. Lett. 104, 044504 – Published 28 January 2010

Abstract

In this Letter, we address two issues affecting the use of a variational argument to determine stability of conservative fluid systems. We build on ideas from bifurcation theory, and thereby for families of steady flows, we link turning points in a velocity-impulse diagram to gains or losses of stability. We further introduce concepts from imperfection theory into these problems, enabling us to reveal hidden solution branches. Our approach applies to a wide range of flows. As an illustration involving a well-defined problem, we study a pair of counterrotating vortices. The approach results in stability boundaries in agreement with linear analysis, yet further enables us to discover a new family of steady vortices, which surprisingly do not exhibit any symmetry. All applications of our approach so far, using imperfect-velocity-impulse (IVI) diagrams, lead us to the discovery of lower-symmetry solutions.

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  • Received 20 July 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.044504

©2010 American Physical Society

Authors & Affiliations

Paolo Luzzatto-Fegiz and Charles H. K. Williamson

  • Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, New York 14853-7501, USA

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Issue

Vol. 104, Iss. 4 — 29 January 2010

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