VORTEX THEORY 
FOR 
BODIES MOVING IN WATER 
Roger BRARD 
Basstn d'Essats des Carénes 
Parts, France 
ABSTRACT 
This paper presents in a synthesized form old and 
new results about the vortex theory for bodies mo- 
ving in water. It is shown that the hydrodynamic 
forces exerted on such a body can be derived from 
the knowledge of a vortex distribution kinematical- 
ly equivalent to the body. A method is proposed for 
determining both the bound vortices and the free 
vortices when the bound vortex distribution is cho- 
sen to be adherent to the hull surface. The total 
vortex distribution is divided into two parts. The 
first one consists of a volume distribution inside 
the hull and of a vortex sheet on the hull surface. 
The volume distribution is identical with the vor- 
tex distribution due to the angular velocity of the 
body. The sheet is determined by the condition that 
this first part of the total distribution induces out- 
side the hull a velocity null everywhere at every 
time. This first part may be calculated once for 
all. The second part consists of the free vortex 
sheets shed by the body and ofa bound vortex sheet 
on the hull. It is equivalent to a normal dipole dis- 
tribution whose density is the solution ofa Volterra 
equation. The determination of the hydrodynamic 
forces exerted on the body is derived from the dy- 
namical equilibrium of the fluid outside the body, 
of the fluid inside the body and of the total bound 
vortex on the hull. This system can be subdivided 
into three systems: the quasi-steady system, the 
system due tothe added masses and the system de- 
pending on the history of the motion. 
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