1084 
and defines the true convection. Therefore we shall take this equation 
for the vortex motion: 
Ow 
Br AM AV.) W iy Sela igh aad 
It is evident that for a small velocity U and a high value of » 
(2 therefore small) the vorticity will come everywhere by the 
diffusion. When, on the contrary, U is great and » small (R there- 
fore great) practically no eddies will diffuse against the current; 
all is drawn back. 
§ 3. Mlementary description of the flow for R not too small 
(fig. 1—4). 
I. When in a fluid originally at rest a body is suddenly set into 
motion, we may consider a surface 6, that surrounds the body at 
a very short distance e. Outside this surface we have, during the 
first moments, only to do with pressure forces and as these are 
continuous an irrotational motion (without vortices) will arise. Let 
us consider the flow at a moment Tr after the beginning of the 
motion of the body, then ¢« will be smaller as rt is smaller. The 
initial flow (because of the condition of continuity) must therefore be 
determined by the well-known boundary condition for the potential p : 
aot ee Ves Oy i ae ae ee 
where V, is the normal component of the velocity of the body at 
the point in question of the surface. Thus, the original flow is the 
irrotational motion of classic hydrodynamics (Pranptt1); this has been 
proved experimentally *). 
Between 6, and the body a thin vortex layer is formed, the 
intensity of which is defined by: 
op 
fom = ELAN HERE er lar «aioe pests | (0) 
1 L. PrANDTL, Verhandl. des III. internat. Mathematiker-Kongresses, Heidelberg 
1904, p. 484. 
H. Rusacu, Forschungsarbeiten herausgeg. v. Verein deutscher Ingenieure, 185. 
1916. 
Also in the limiting case of very great friction (R0) we find by the calcu- 
lation method of Srokes that the original motion is the ordinary potential flow. 
See A. B. Basset, Hydrodynamics Il (Cambridge 1888), p. 289 (Art. 505). 
See in connexion with this also the note of 8 7. 
