Kochin function
In the far field, the velocity potential
φ%XX ( M )
for the problem with number XX may be approximated :
φ%XX ( M ) ≅ f 0 ( z )
k
2π r
e
(
i kr −π
4
)H
XX
(θ )
(1)
With :
•
•
•
•
( r ,θ , z ) are the cylindrical coordinates of point M
f 0 ( z ) is the depth dependence. f 0 ( z ) = e kz in deep
cosh k ( z + h )
f0 ( z ) =
in finite water depth. h is the water depth.
water
whereas
cos kh
k is the wavenumber.
H XX (θ ) is the Kochin function calculated by the program for problem with number
XX. The Kochin functions are stored in files /Results/Kochin.XX.dat (ASCII files). First
column are the angles φ , second and third columns are the amplitude and phase of
the Kochin function (it is a complex coefficient).
Let consider a floating body with one degree of freedom responding to a regular wave of amplitude A,
circular frequency ω and propagating in direction β . Let number 1 be the radiation problem and
number 2 the diffraction problem. Let
X% ( ω ) be the RAO of the floating body. Then, the total velocity
potential in the far field is:


 %
k i( kr +π 4 )
k i( kr +π 4 )
ik ( x cos β + y sin β ) 
%
φ ( M ) = −iAf 0 ( z )  X (ω )
e
H1 (θ ) +
e
H 2 (θ ) + e14
4244
3
2
r
2
r
π
π
 14444244443 144424443 Incident wave potential 
Contribution from radiation
Contribution from diffraction


(2)

5-MeO-MiPT

David Jerison

玉入れゲーム ～シーソー式～