TY - JOUR

T1 - Dynamics Near an Unstable Kirchhoff Ellipse

AU - Guo, Yan

AU - Hallstrom, Chris

AU - Spirn, Daniel

PY - 2004/3/1

Y1 - 2004/3/1

N2 - We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general initial perturbation of the Kirchhoff ellipse are determined by the fastest growing mode for the corresponding linearized equation, on a time scale when the nonlinear instability occurs. In particular, we resolve a question suggested by Love's results and prove that such elliptical patches are indeed unstable in the full nonlinear sense.

AB - We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general initial perturbation of the Kirchhoff ellipse are determined by the fastest growing mode for the corresponding linearized equation, on a time scale when the nonlinear instability occurs. In particular, we resolve a question suggested by Love's results and prove that such elliptical patches are indeed unstable in the full nonlinear sense.

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U2 - 10.1007/s00220-003-1017-z

DO - 10.1007/s00220-003-1017-z

M3 - Article

AN - SCOPUS:1642323672

VL - 245

SP - 297

EP - 354

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -