## JMI2010A-4 Weakly nonlinear saturation of stationary resonance of a rotating flow in an elliptic cylinder (pp.27-37)

Author(s)： Yoichi Mie and Yasuhide Fukumoto

J. Math-for-Ind. **2A** (2010) 27-37.

- File： JMI2010A-4.pdf (394KB)

Abstract

We address weakly nonlinear stability of a uniformly rotating flow confined in a cylinder of elliptic cross-section to three-dimensional disturbances. A Lagrangian approach is developed to derive unambiguously the drift current induced by nonlinear interaction of isovortical disturbances. This approach rescues the insufficiency inherent in the Eulerian approach and provides a direct path to reach the amplitude equations in the Hamiltonian normal form. The nonlinear effect saturates the stationary instability mode, and asymptotic form of its saturation amplitude is gained, in a tidy form, in the short-wavelength regime.

Keyword(s). elliptical instability, weakly nonlinear stability, Lagrangian approach, mean flow