23

Table 1

Sample theoretical waves

Wave

Five

3m

5m

10 s

y1.902

y0.618

y5.0 m

y5.0 m

Twenty

10 m

20 m

10 s

y0.951

y0.309

y10.0 m

y10.0 m

Hundred

20 m

100 m

10 s

y0.478

y0.155

y20.0 m

y20.0 m

The predicted water surface elevation and wave number components from the local

linear algorithm are shown in Fig. 3 as the markers, together with the near-exact

predictions from global Fourier wave theory as the solid lines. Solutions to Eq. Z14. at

required initial solution estimates that were almost exact. For this ` wave transitional'

situation, a solution was obtained throughout. It is smooth and visually convincing,

except when compared with the near-exact predictions. There is order of magnitude

agreement only. The crest elevation in particular is poorly predicted.

Some variations on the locally linear formulation may achieve a more acceptable and

perhaps also more robust local solution, but the indications are not encouraging.

Eliminating h between the *f*2 and both the *f*3 and *f*4 equations gives:

r *g *cosh *k*Z h q *z * P .

Z v y *k*a Ua . s Z uabs y *U*a . obs

o

tanh *kh*.

Z 16.

Fig. 3. Local linear theory Zmarkers. and global Fourier theory Zsolid lines. predictions for Record `Twenty'.