Physics for Geologists, Second edition

102 Sea waves
and
Solving for M : O = c (so density is not a component)
For L : l=a+b
For T : - 1 = -2a,
from which a = b = i, and the function is of the form
c = constant (g~)''~
For gravity waves, it turns out that the constant equals (2~)-'I2, so
There is a relationship between the period (T s), the velocity (cm s-l) and
the wavelength (h m):
A yacht hove-to in a storm can measure T quite accurately (it is more difficult
if moving at an irregular speed), and so X can be estimated. A period of 10 s,
for example, implies a wavelength of 156 m and a velocity of 15.6 m s-I
(56 km h-l, 30 knots).
Waves normally move in a group, each wave travelling at (g1/2n)'/~ m s-l.
The waves at the front of a group tend to die out because their energy is dis-
sipated, and new ones form at the back. The group as a whole travels more
slowly than the individual waves. The group velocity is important because
the energy of the waves depends on the group velocity, not the wave velocity.
The group velocity of gravity waves is half the wave velocity (see Note 4 on
page 141).
The waves are moving, but how is the water moving? Water is virtually
incompressible, so as a wave passes and the water level falls, water must be
displaced in one place as the wave becomes a trough, and replaced when it
becomes a crest again. An ideal wave that is not breaking is closely repre-
sented by circular motion around axes parallel to the crests (Figure 10.1).
Copyright 2002 by Richard E. Chapman