TY - GEN

T1 - Evolution of an elliptical flow in weakly nonlinear regime

AU - Hattori, Yuji

AU - Fukumoto, Yasuhide

AU - Fujimura, Kaoru

PY - 2008

Y1 - 2008

N2 - We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the weakly nonlinear evolution of helical modes is considered. Nonlinear selfinteraction of the two base Kelvin waves results in cubic nonlinear terms, which causes saturation of the elliptical instability. Next, the case of triad interaction is considered. Three Kelvin waves, one of which is a helical mode, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the numerical results on the secondary instability obtained by Kerswell (1999).

AB - We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the weakly nonlinear evolution of helical modes is considered. Nonlinear selfinteraction of the two base Kelvin waves results in cubic nonlinear terms, which causes saturation of the elliptical instability. Next, the case of triad interaction is considered. Three Kelvin waves, one of which is a helical mode, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the numerical results on the secondary instability obtained by Kerswell (1999).

KW - Amplitude equations

KW - Elliptical flow

KW - Elliptical instability

KW - Secondary instability

KW - Weakly nonlinear analysis

UR - http://www.scopus.com/inward/record.url?scp=84861146308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861146308&partnerID=8YFLogxK

U2 - 10.1007/978-1-4020-6472-2_66

DO - 10.1007/978-1-4020-6472-2_66

M3 - Conference contribution

AN - SCOPUS:84861146308

SN - 9781402064715

T3 - Solid Mechanics and its Applications

SP - 433

EP - 438

BT - IUTAM Symposium on Computational Physics and New Perspectives in Turbulence - Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence

T2 - IUTAM Symposium on Computational Physics and New Perspectives in Turbulence

Y2 - 11 September 2006 through 14 September 2006

ER -