Specifications

46
Wave direction
),(arctan
0 nvwv
QQD −==
θ
(5.6.24)
Directional spread
1
22 mS −= (5.6.25)
Wave ellipticity or 1/K where K is the check factor
wwnn
vv
CC
C
K
+
==
/1 ε
(5.6.26)
Power Spectral Density
vv
CPSD = (5.6.27)
In the present context parameters a
i
and b
i
are just helpful intermediate variables. In terms of
this more intricate Fourier analysis we again arrive at the power spectral density. Its value and
meaning already have been mentioned.
Wave ellipticity indicates the shape of the wave. For wavelengths much smaller than the
depth, waves describe circular orbits and the ellipticity is near 1. However, if the wavelength
becomes comparable to or larger than the depth, the vertical displacements are smaller than the
horizontal ones and the ellipticity is smaller than 1. The variation of the ellipticity with wave
frequency is indicative of the local depth. Historically, Datawell refers to its reciprocal as check
factor. When testing the buoy in a Ferris wheel the ‘wave ellipticity’ should yield 1 of course. In
the case of stabilized platform accelerometer-based motion sensors, however, the ellipticity is
seen to deviate by a small factor at the lower frequencies. This serves as a check on platform
stability and the parameter, the reciprocal of the wave ellipticity is named accordingly.
Wave direction and spread speak for themselves. By a close look at the simultaneous
north and west motion the wave direction can be determined. For clarity the Datawell wave
direction is the direction from which the waves arrive. Both are expressed in radians.
In this analysis we have followed the analysis in [Long63].