13.42 Spring 2005
13.42 Design Principles for Ocean Vehicles
Prof. A.H. Techet
Spring 2005
Froude Krylov Excitation Force
1. Radiation and Diffraction Potentials
The total potential is a linear superposition of the incident, diffraction, and radiation potentials,
ω
φ
=
(
+
)
e
.
(1)
I
+
D
R
it
The
radiation
potential is comprised of six components due to the motions in the six directions,
1
23456
th
j
where
j
=,
,
,
,
,
. Each function
j
is the potential resulting from a unit motion in
j
direction for a body floating in a quiescent fluid. The resulting body boundary condition follows
from lecture 15:
2
3
)
(2)
∂
j
=
in
j
;
(
j
=
,
,
∂
n
(
,
,
∂
j
=
ir
G
×
n
±
)
j
−
3
;
(
j
=
4
5
6
(3)
∂
n
G
r
=
(
x
y
z
)
(4)
,,
nn
j
(
j
,
±
=
3
=
(
n
,
n
y
,
n
)
(5)
x
z
In order to meet all the boundary conditions we must have waves that radiate away from the body.
ikx
Thus
j
∝
e
∓
as
x
→±∞
.
For the
diffraction
problem we know that the derivative of the total potential (here the incident
potential plus the diffraction potential without consideration of the radiation potential) normal to
the body surface is zero on the body:
∂
T
=
0 on
S
, where
=
φφ
.
∂
n
B
T
I
+
D
version 1.0
updated 3/29/2005
1
2005, aht
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∂
φ
I
∂
D
;
on S
(6)
∂
n
=−
∂
n
B
We have so far talked primarily about the incident potential. The formulation of the incident
potential is straight forward from the boundary value problem (BVP) setup in lecture 15. There
exist several viable forms of this potential function each are essentially a phase shifted version of
another. The diffraction potential can also be found in the same fashion using the BVP for the
diffraction potential with the appropriate boundary condition on the body. This potential can be
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 Spring '05
 AlexandraTechet

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