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

2.1 Contour Dynamics

Motion in two-dimensional nondivergent perfect fluid can be described using Lagrangian conservation law of vorticity:
where u( x,t ) is the velocity, and Q( x,t ) is the vertical component of the vorticity. The vorticity distribution is assumed to be
for regions Dj ( j=1,2, ... ,J ) ( Dj1ÇDj2 = j ) on an infinite plane. Each region is called vortex patch.

In this situation,

Such dynamics concerning time evolution of the vortex patch is called contour dynamics.



<<index <previous next>