Yajnik and Lieber 



Fig. 1 - Absence of closed streamlines ( ) near a point of 



maximum vorticity (lines of equal vorticity are shown by ) 



streamline at the point cannot be zero. Similar conclusions are valid for axi- 

 symmetric flows without tangential component. 



A precise and general definition of an eddy is given in terms of the angular 

 velocities and it is shown to be a region of positive discriminant of the charac- 

 teristic equation of the deviatoric part of velocity gradient vo - (V • u) 1/3. The 

 definition implies that an eddy in one inertial frame is also an eddy in any other 

 inertial frame. Although vorticity cannot be zero in an eddy, presence of vor- 

 ticity is not sufficient to make a region of fluid an eddy. Also, since the dis- 

 criminant is zero for a viscous fluid on a stationary solid surface, even thin 

 rods can cause a large interference with eddies. This conclusion is supported 

 by photographic evidence presented here. It is shown that if v^p is positive at 

 a point, in the flow of a Newtonian fluid of constant properties in absence of 

 body forces, the point is in an eddy. The converse is also true in plane flows. 

 Hence the characteristic feature of the stress field in plane eddies is superhar- 

 monic character of pressvure. It is also shown that the streamlines in plane 

 eddies are convex and that velocity can be zero at, at most, one point in a convex 



438 



