Page 103 - Introduction to Naval Architecture

90 THE ENVIRONMENT

In this equation ^ris termed the wave number and a) = 2n/Tis known as
the wave frequency. Tis the wave period. The principal characteristics of
the wave, including the wave velocity, C, are:

As with trochoidal waves water particles in the wave move in circular
orbits, the radii of which decrease with depth in accordance with:

From this it is seen that for depth A/2 the orbit radius is only 0.02//
which can normally be ignored.
The average total energy per unit area of wave system ispgH*/8, the
potential and kinetic energies each being half of this figure. The energy
of the wave system is transmitted at half the speed of advance of the
waves. The front of the wave system moves at the speed of energy
transmission so the component waves, travelling at twice this speed, will
'disappear' through the wave front.
For more information on sinusoidal waves, including proofs of the
2 3
above relationships, the reader should refer to a standard text '

Irregular wave systems
The irregular wave surface can be regarded as the compound of a large
number of small waves. Each component wave will have its own length
and height. If they were all travelling in the same direction the irregular
pattern would be constant across the breadth of the wave, extending to
infinity in each direction. Such a sea is said to be a long crested irregular
system and is referred to as one-dimensional, the one dimension being
frequency. In the more general case the component waves will each be
travelling in a different direction. In that case the sea surface resembles
a series of humps and hollows with any apparent crests being of short
length. Such a system is said to be a short crested irregular wave system or