Isochoric Circulation-Preserving Motions with Stream-Lines of a Potential Motion

Abstract

We consider the class of steady isochoric circulation-preserving motions. These motions are defined kinematically by the conditions

$$ curl\left( {\omega \times v} \right)\; = 0, $$

(I.1)

and

$$ div\;v = 0, $$

(I.2)

where

$$ \upsilon \;{\text{ = }}\;\upsilon {\text{s,}} $$

(I.3)

i s the velocity, s being the unit vector tangent to the stream-line, and where

$$ \omega = curl\,v $$

(I.4)

is the vorticity.