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*WAVJON

Data format:

A single line with up to 16 values

NWAGEN TETH HS TP TZ TM GAMMA HMHS IRAND TMIN TMAX IOSP EXPONENT NB_DIR DELTA IOP

Status :

Optional (dynamics)

Purpose :

To define a JONSWAP (or PIERSON MOSKOWITZ) wave spectrum divided into N frequency components

Restrictions :

  • One period only must be non-zero. The two others must be 0.

  • The number of wave components (including those separately defined with keyword *WAVE) is limited to MAXWAV.

  • If WAVJON is selected , DEPTH is required .

Details :

Parameter Description
NWAGEN Number of sinusoidal wave components to be generated
TETH Direction of propagation (degrees from the positive X axis)
HS Significant height
TP Peak period
TZ Zero up-crossing period
TM Mean period
GAMMA Jonswap spectrum shape coefficient (Default = 3.3). Pierson Moskowitz spectrum is obtained with GAMMA = 1.
HMHS The target maximum wave height over significant wave height ratio. A maximum wave height at least equal to HMHS x HS will be encountered during the simulation. If HMHS = 0, no maximum wave height is looked for.
IRAND Arbitrary positive integer odd number used to trigger the phase random series generation. Two runs using the same IRAND value will generate the same phase series. (Def =12345). A integer I5 is recommended.
TMIN Minimum period for the waves generation (Default = 0.4*Tp).
TMAX Maximum period for the waves generation (Default = 2*Tp).
IOSP = 1 : equal angle between spreading direction
= 2 : spreading direction chosen such by constant energy
EXPONENT Spreading function exponent
NBDIR number of spreading directions
DELTA maximum angle in degree of spreading from reference wave direction
IOP =0 : unchanged
=1 modification of the Jonswap spectrum to obtain A TMA spectrum (for water in finite depth)
\(S_{TMA}(\omega, d) = S_{JONSWAP}(\omega) \Phi(\omega^*, d)\)
\(\Phi(\omega^*, d) = \frac{1}{\Bigl[f(\omega^*)\Bigr]^{\frac{1}{2}}} \Bigl[1 + \frac{K}{\sinh K}\Bigr]^{-1}\)
\(\omega^* = \omega \sqrt{\frac{d}{g}}\)
\(f(\omega^*) = \tanh^{-1} [k(\omega^*)d]\)
\(K = 2\omega^{*2} f(w^*)\)

Note

1) A Jonswap spectrum is defined by the following equation :

\[ S(f) = B_1 \Bigl(\frac{H_5}{4}\Bigr)^2 \ldotp \Bigl(\frac{1}{f} \Bigr)^5 \ldotp \exp \Bigl[ -\frac{5}{4} \Bigl(\frac{f}{f_0}\Bigr)^{-4} \Bigr] \exp \Bigl[\ln(gama) \ldotp \exp \Bigl( - \frac{(\frac{f}{f_0 - 1})^2}{2s^2} \Bigr) \Bigr] \]

where
\(s\) = 0.07 if f < fo (fo=1/TP)
\(s\) = 0.09 if f > fo

\(B_1\) is a constant determined by the program.

2) The maximum wave height will have just occurred at t = 2.TP + 3(TFIN-2.Tp)/4 (see DYNAMIC for TFIN).

Examples :

*WAVJON
50 180. 11.5 0. 11.5 0. 3.3 1.7

This defines an irregular wave of 50 components, heading towards the negative X-direction. The significant height is 11.5 m and the Zero up-crossing period is 11.5 seconds. A Jonswap spectrum is selected and we ask for the ratio of the maximum wave height to the significant height to be 1.7.

*WAVJON
50 180. 11.5 0. 11.5 0. 1.

The only difference with the previous example is that a Pierson-Moskowitz spectrum is now selected.