Velocity induced by a

distribution of vorticity

y-xr,)(r

4

1u(x)

3

dy

r

y

Simple paired vortex structure:

)('2

1,0)(

)sin()(

,2

11

1

22

kakJUkaJ

krJ

kflowEulerD

U

Volume and energy constraints, can be

satisfied by including filamentary structures.

O(r-3/4

)

O(r-5/2

)

2+1 dimensional model. Target

vortex is a planar curve. Cocoon

is

In 2D plane orthogonal to the

curve. Local radius of curvature

allowed to vary.