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4.2
Internal waves
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Internal waves are a feature of stratified fluids. They have many properties in
common with surface waves but they are more diverse in character and have the
reputation of being fiendishly difficult to fully comprehend. We cannot, however,
ignore them as they are major players in the shelf sea system. Like surface waves, they
transmit energy and provide a source of power for stirring but, unlike surface waves,
internal waves can involve energetic motions in the interior of a fluid well away from
the surface boundary and deliver power for internal mixing where there are no other
available sources.
Here we shall develop a basic theory of internal waves for the relatively simple case
of an ocean with two homogeneous layers. We shall make use of a similar approach
to that which we applied to surface waves in order to illustrate the principal proper-
ties of this class of waves.
4.2.1
Velocity potential for waves on the interface between two layers
We will assume again that the motion is irrotational so that the velocity potential
method can be applied. This assumption is valid in each of the two layers, although
not in the interface between the two layers which is assumed to be very thin.
We will use the system illustrated in Fig. 4.6 . The upper layer has a depth h 1 and
density r while the corresponding values for the lower layer are h 2 and r
r.Ifz is
the vertical displacement of the interface, a sinusoidal progressive wave travelling
þ D
Figure 4.6 Definition of parameters for
an internal wave.
z
x
z =0
Density ρ
h 1
ζ
c
λ
h 2
Density ρ+Δρ
z =- h
 
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