2.1 Contour Dynamics
2.2 Equations of Cotour Dynamics
2.3 Theory of an Elliptical Vortex
2.4 Finite-Time Lyapunov Analysis on Fluid Deformation
2.3 Theory of an Elliptical VortexIn two-dimentional nondivergent perfect fluid, an ellipse is assumed as
where λ is the ratio of the major axis to the minor axis, and the initial vorticity is given to be a constant q inside the ellipse and 0 outside.
Such a vortex rotates with a constant angular velocity g, depending on l and q ( Lamb,1932 ):
Love(1893) examined the stability of the vortex when the following small perturbation is added:
- When m = 1 , the perturbation is always neutral.
- When m = 2 , the perturbation is always neutral and does not change in time.
- When m = 3 , the perturbation grows in time and the vortex is unstable if l > 3 .
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