Physics for Geologists, Second edition

Sea waves 103
Figure 10.1 Wave motion. A wave moves, but the motion within a wave in deep
water is in circular, or near-circular, orbits.
The diameter of the orbit is equal to the wave height at the surface, decreasing
rapidly with depth and becoming a lateral oscillation on the bottom:
2ndlX
X= He- , (10.3)
where x is the diameter of the orbit at depth d in a wave of height H and
wavelength h. At a depth of half a wavelength, the orbital diameter is about
1125th of the wave height - but this is still more than 80 mm at a depth of
125 m below a two-metre swell with 250 m wavelength. At the edge of the
continental shelf, at 200 m depth, the movement would be about a centime-
tre. Wave base is certainly not restricted to depths of about 10 m. A small
movement repeated frequently over a long period not only has the ability to
move particles but also to abrade them.
Once waves of stable dimensions have been generated by a storm (large h,
large velocity) they may achieve a velocity roughly 80 per cent of the wind's
velocity, and when the wind dies, the waves are propagated from the area.
The long-wavelength waves leave the short behind, and the short decay
quickly. Waves lose height by about 3 (i.e. to 3) after travelling a distance of
5h km. So waves that leave the storm with a height of 6 m and a wavelength
of 250 m, will only be reduced to 4 m after a passage of 1 250 km, 2.5 m after
2 500 km, and so on. Such waves, which are called swell when they have left
the storm that gave rise to them, can easily cross half an ocean. These waves
travel on great circle paths, and are unaffected by coriolis forces because the
water displacement is negligible.
Now, very large swell requires a long period of strong winds blowing
steadily in direction and force over a considerable fetch, say, three days over
500-800 km. This is one reason for the huge seas in the Southern Ocean,
where winds blow almost unobstructed from the west for much of the time.
Tropical cyclones, on the other hand, have very strong winds (commonly
exceeding 150 km h-I) but they blow in a pattern around a relatively lim-
ited area of about 200 km diameter. Waves therefore leave the cyclone in
all directions, the largest being in the quadrant where the winds are blow-
ing in the general direction of movement of the cyclone, the smallest (but
still very large) in the opposite quadrant. Again, the larger waves leave the
storm in all directions and become relatively harmless - and they indicate
the approximate direction of the storm. Within the area of the storm, the
seas are very dangerous mainly because of the confusion of wave trains with
different directions. Wave trains are additive, as we saw in Figure 1.1.
Copyright 2002 by Richard E. Chapman