Conventions and differences to other codes

Note

To be expanded.

Unlike most other codes, angles (such as the incoming wave direction) are given in radians in Capytaine.

With respect to WAMIT

In this section, the index \(W\) denotes a magnitude in WAMIT convention. Other magnitudes use Capytaine convention.

Time dependancy

In Capytaine, the complex-valued amplitudes (phasors) are defined with the convention

(3)\[x(t) = \Re ( X e^{-i \omega t}).\]

It is unlike WAMIT in which the following convention is used

(4)\[x(t) = \Re ( X_W e^{+ i \omega t})\]

Incoming potential

In deep water, the potential of the incoming undisturbed velocity field reads in Capytaine

(5)\[\Phi_0 = -i \frac{g}{\omega} e^{k z} e^{i k (x \cos \beta + y \sin \beta)},\]

whereas in WAMIT (equation 15.4 of WAMIT Manual v7.2), it reads

(6)\[\Phi_{0, W} = - \overline{\Phi_0} = i \frac{g}{\omega} e^{k z} e^{- i k (x \cos \beta + y \sin \beta)},\]

and similarly in finite depth.

It follows that the incoming velocity field from Capytaine \(u_0 = \nabla \Phi_0\) is related to the incoming velocity field from WAMIT \(u_{0, W} = \nabla \Phi_{0, W}\) as

(7)\[u_0 = \overline{u_{0, W}}.\]

Then the corresponding Froude-Krylov force and diffraction force (also called scattering force in WAMIT), as well as their sum the excitation force, are complex-conjugate between Capytaine and WAMIT:

(8)\[F_e = \overline{F_{e, W}}\]

With respect to Nemoh and Aquadyn

Capytaine mostly follows the same conventions as Nemoh, which are also the same as in Aquadyn. The main exception is the phase angle of the excitation force in Nemoh and Capytaine is the opposite of the one in Aquadyn.

With respect to HAMS

HAMS follows the same conventions (3) and (5) as Capytaine.