R.J. Sobey, S.A. Hughes r Coastal Engineering 36 (1999) 1736
`Five', `Twenty' and `Hundred', have been defined, respectively, in wave shallow, wave
transitional and wave deep water. The details are listed in Table 1. The wave heights in
all three cases are moderately extreme for the depth. Note in particular the location of
both z P and z UV higher in the water column for waves `Twenty' and `Hundred'. The
significant attenuation in wave kinematics with depth is frequently mitigated by such a
practice. Global Fourier wave theory ZSobey, 1989., at truncation order 18 with 25 water
surface nodes from crest to trough, provides near-exact kinematics for these wave trains.
The PUV observational traces at the listed elevations were predicted at a time interval
of 0.5 s. LFI-PUVw3,3,0.1x predictions for wave `Twenty' are shown in Fig. 4. Part Za.
shows the `measured' pdZ t; z P . trace together with the `measured' u1Z t; z UV . and
u2Z t; z UV . traces. Part Zb. shows the h traces predicted by LFI-PUV Zmarkers. and by
the near-exact Fourier wave theory Zcontinuous line.. Compare this result to the
relatively poor prediction of h for wave `Twenty' using the locally linear method ZFig.
3.. Part Zc. shows all three velocity components at elevation z s yHr2 just below the
trough, and part Zd. all three acceleration components also at the same near trough
elevation. Again, the markers are LFI-PUV predictions and the continuous lines are
from the near-exact Fourier wave theory. Agreement throughout is almost perfect.
The excellent agreement is achieved at a relatively low order Z J s 3., and this is a
consistent strength of the LFI methodology. This success at such low order is achieved
by seeking separate solutions in each local window. The solution parameters,
v , ka , ka xa , A j,hn , will vary from window to window. The variation in the v , ka and
A j parameters, that would also be defined in a global solution, is not expected to be very
large. The local variation in these solution parameters for wave `Twenty' is shown in
Fig. 5. Note the double-width windows at the profile zero-crossings near t s "2 s.
Fig. 5. LFI-PUVw3,3,0.1x local solution parameters for wave `Twenty'.