Environmental Engineering Reference
In-Depth Information
Fig. 2.35 Vectors for the bar element [30]
The evaluation of the above vector products for the case of a planar flow field (u
x
¼
u;
u
y
¼
0; w) - at coordinates {x, z} - results in (in component notation):
v
N
;
x
¼
u
e
x
ð
e
x
u
þ
e
z
w
Þ;
v
N
;
x
¼
u
e
x
ð
e
x
u
e
z
w
Þ
v
N
;
y
¼
e
y
ð
e
x
u
þ
e
z
w
Þ;
v
N
;
y
¼
e
y
_
ð
e
x
_
u
þ
e
z
_
w
Þ
v
N
;
z
¼
w
e
z
ð
e
x
u
þ
e
z
w
Þ;
v
N
;
z
¼ _
_
w
e
z
ð
e
x
_
u
þ
e
z
_
w
Þ
One important issue is ascertaining the statistical distribution of the force acting on a
cylindrical component during the natural sea state. Assuming that the sea state function
z
(t)
is described by a Gaussian process with the following variance:
Z
1
2
z
¼
m
0
¼
s
S
z
ðÞ
d
v
0
then the velocity u and the acceleration
u are also described by Gaussian processes. For
_
details of this see [17].
2.6.3
linear motion behaviour
The velocity potential of the flow field caused by the presence of a body can be
formulated as follows:
Potential theory method
-
F
ð
x
;
y
;
z
;
t
Þ F
0
x
ð
;
y
;
z
;
t
Þ F
S
x
ð
;
y
;
z
;
t
Þ
where
F
0
undisturbed primary wave potential
F
S
perturbation potential
