A solitary wave is a shallow water wave
that consists of a single displacement of water above the mean water
level. John Scott Russell (1808-1882) was the first to report on the wave, caused by the stopping of a barge in a canal. It has been used by Munk as a model for waves in the surf
zone. It also is a reasonable description for the leading wave of a
tsunami.
where H
is the maximum wave height (which occurs at x=0
when t=0),
C is the wave celerity (speed) and sech ( ) is the hyperbolic secant.
is defined by
The length of a solitary wave is theoretically infinite. However,
for practical purposes, the water surface elevation (in the first
equation) decays to zero reasonably fast with x.
So, in much the same way as for other types of waves,
we can (arbitrarily) define a wave length, L,
as
At
a distance of x =
L/2
away
from the crest, the water surface displacement is reduced to 0.74% of
its maximum value. This is the definition used in the applet.
Alternatively,
the wave length can be defined such that, at x
=L/2,
h/H =
0.01, say. This gives
The speed of a solitary wave is
Question: How does the height of the wave affect its length? Comments: Robert Dalrymple
The wave form of a solitary wave is
given as a function of distance x
and time t by
The parameter k
.
To use the applet, you need to enter the maximum wave height H
and the water depth, h.
.
This wavelength is 95.3% (from
)
as long as the previous definition.
.
Thus an apparent wave period could be defined as T=L/C. The applet also gives the surface particle
velocity at the wave crest.