2. Theory

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 Vortex

In 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:

<<index <previous next>