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.

The wave form of a solitary wave is
given as a function of distance ** x**
and time

where ** H**
is the maximum wave height (which occurs at

The parameter

is defined by
.
To use the applet, you need to enter the maximum wave height ** H**
and the water depth,

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,

**
**

At
a distance of ** x **=

Alternatively,
the wave length can be defined such that, at ** x**
=

. This wavelength is 95.3% (from ) as long as the previous definition.

The speed of a solitary wave is . Thus an apparent wave period could be defined as T=L/C. The applet also gives the surface particle velocity at the wave crest.

**Question**: How does the height of the wave affect its length?

Comments: Robert Dalrymple