Stability of conservative flows and new steady-fluid solutions from bifurcation diagrams exploiting a variational argument

• Published in: Physical review letters Vol. 104; no. 4; p. 044504
• Main Authors: Luzzatto-Fegiz, Paolo, Williamson, Charles H K
• Format: Journal Article
• Language: English
• Published: United States 29.01.2010
• ISSN: 1079-7114
• DOI: 10.1103/physrevlett.104.044504

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.