6.3 Internal Waves in Two-Layer Ocean
189
a z
Q x
b z
p
c z
o
sea sur ace
N
N=O
N=O
Fig. 6.5: Two-layer ocean model: a two layers of fluid of different densities, b vertical
density profile, c vertical profile of frequency
velocity of the internal wave Gi , can be found from the following dispersion
relation (Pond and Pickard, 1983):
(6.12)
and
W
Gi = k =
9
P2 - PI
k P2 coth( kh2) + PI coth(kh I ) ,
(6.13)
in which w = 27r/Ti and coth(x) = l/tanh(x).
For the deep water waves (hdLi and h2/Li are greater than 1/2), the phase
velocity (6.13) simplifies as follows:
Gi =
9 P2 - PI
- - - -
k PI + P2
(6.14)
Assuming, for example, that PI = 1020 kg/m 3 and P2 = 1023 kg/m 3 , Eq. (6.14)
gives:
Gi = 0.038/f = 0.038G,
(6.15)
where G is the phase velocity of the surface wave of this length (see Eq. 4.17).
Thus, the phase speeds of internal waves are much smaller than those of surface
gravity waves.
On the other hand, for long, shallow water waves, when Li/hl and Ldh2 > 20,
the phase velocity becomes:
Gi =
g(p2 - PI)h I h2
P2 h I + PI h2
(6.16)