1085 
(s indicates here a tangential direction at a point of the surface) '). 
Fig. 1 illustrates the “relative” flow for the two-dimensional case, 
the body being a circular cylinder. 
Il. The above mentioned vortex layer flows out by the diffusion, 
becomes thicker; the vorticity comes into the current and is carried 
along to the back of the body. See fig. 2 (the dotted circle in 
the vortex region gives the direction of rotation). When the vorticity 
behind the body has got a definite intensity, a part of the fluid 
there begins to rotate as a whole or to flow in closed orbits 
i.o.w. behind the body at both sides of the axis of symmetry 
there are formed circular currents (see fig. 3) *). Behind the body 
we therefore have a current towards the left; in front of it the 
current remains as it was to the right. Therefore we must have at 
both sides a point S, where the current leaves the surface (for solids 
of revolution this will take place along a parallel circle). 
At the back of the body a vortex layer is now formed the rotation 
of which is opposite to that at the front (in the tigure indicated by 
dotted, horizontal hatching). 
III. After some time we might expect a stationary state to be 
created, in the way as has been sketched in fig. 4, where the 
diffusion and the convection neutralize each other. In reality 
this is not the case. After passing a state as is represented by fig. 3. 
the flow begins to fluctuate; it becomes more or less “turbulent”. 
In stead of the regular vortex distribution a more or less irregular 
one is formed; the vortices “coagulate” so to say, so that regions 
with strong vortex motions (vortex cores) are formed, dispersed in 
a mass with weaker vortex motion. 
A more detailed discussion of these phenomena will be omitted 
here *). 
1) The limit of e for t=O is determined by the sphere of action of the mole- 
cular forces at the surface of the body. As long as the fluid is treated as a conti- 
nuum this may be regarded as infinitely small. 
3) These considerations have of course the same purpose as those of PRANDTL 
(Le); the above form has been chosen to illustrate the propagation of the vortex motion. 
That the accumulation of vortices gives rise to circular currents in the fluid, 
will probably only be true for high values of # (when the vortex motion is not too 
diluted). Only in the limiting case of very great R it can be proved by means of 
the formulae (see below, § 7 and 8). 
On the photo's of RupacH le. we can see that the circular currents are 
formed on a small scale behind the cylinder at both sides of the point where the 
flow unites. Theoretically this has been investigated by BLAsius (see l.c. § 8). 
3) This fluctuating motion may also be described in another way. When Ris high, 
so that the velocity of diffusion of the vortex motion is small, then the vortex sheet 
