196
6 Internal Waves
For example, for the case of the Earth's rotation, a more complex relationship
for the wave number, given by Eq. (6.25) has to be used in place of Eq. (6.26).
The multimodal vertical structure of internal waves suggests that, similarly
to surface waves, internal waves can be described in terms of energy spectra.
The shift from the description of internal waves as an analytic solution of the
vertical velocity equations, as done above, to the description of internal waves in
terms of their spectra, was largely emphasized by the Garrett and Munk (1972,
1975) formulation of wave number frequency spectrum, based on observations
available at that time. For example, the spectrum proposed in 1975 takes the
form:
( - _)
2
EJ
A (k/f.)
S k w = - --;:::=::.== ----'-,:;---",
7rwJw2_J2 k.
(6.28)
where k is the dimensionless horizontal wave number, w = w / it is the dimensionless frequency with it = 3 cycle per hour, J = f / it is the dimensionless inertial frequency, kx = 67rJw 2 - J2 is the horizontal wave-number scale,
E = 6.3 X 10- 5 , and A(>') = (t-1)(1 + >')-\ where t = 2.5, and>. = k/k •. Formula (6.28) is valid under the assumption of horizontal isotropy of the internal
wave field.
6.4.2 Topographic Effects
Observations, as well as numerical simulations, help to develop some understanding of the complexity of internal waves. As mentioned in Sect. 6.1,
the interaction of semi diurnal tides with shelf topography may be one of the
sources of internal waves. They have wavelengths of a tens of kilometres and
may propagate out of the generation area. During measurement program in
the Andaman Sea near northern Sumatra, large-amplitude, long internal waves
with currents as high as 1.8 m/s were observed (Osborne and Burch, 1980).
Photographs of the Andaman Sea's surface by LANDSAT satellite, as well as
photographs taken during the Apollo-Soyuz mission, showed that the shallow
waters around the Andaman Islands and near the southernmost point of Nicobar Islands, or close to northern Sumatra are potential sources of the observed
internal waves. A set of current metres and thermistors was placed at approximate depths of 53, 87, 116, 164 and 254 metres, in the ocean with 1100 m
water depth. In Fig. 6.10, a typical temperature signal of an internal wave,
recorded at the depth of 164 m, is shown. The wave pattern is similar to the
solitary shape described in Sect. 4.2.3, suggesting a soliton interpretation of the
signal (see also Massel, 1989). The leftmost soliton in Fig. 6.10 is the largest
and leads the packet. Similar packets occur, on average, every 12 hour and 26
minutes, which suggests a link between soliton generation and the semidiurnal
tide. The average number of observed solitons is six or seven.
6 Internal Waves
For example, for the case of the Earth's rotation, a more complex relationship
for the wave number, given by Eq. (6.25) has to be used in place of Eq. (6.26).
The multimodal vertical structure of internal waves suggests that, similarly
to surface waves, internal waves can be described in terms of energy spectra.
The shift from the description of internal waves as an analytic solution of the
vertical velocity equations, as done above, to the description of internal waves in
terms of their spectra, was largely emphasized by the Garrett and Munk (1972,
1975) formulation of wave number frequency spectrum, based on observations
available at that time. For example, the spectrum proposed in 1975 takes the
form:
( - _)
2
EJ
A (k/f.)
S k w = - --;:::=::.== ----'-,:;---",
7rwJw2_J2 k.
(6.28)
where k is the dimensionless horizontal wave number, w = w / it is the dimensionless frequency with it = 3 cycle per hour, J = f / it is the dimensionless inertial frequency, kx = 67rJw 2 - J2 is the horizontal wave-number scale,
E = 6.3 X 10- 5 , and A(>') = (t-1)(1 + >')-\ where t = 2.5, and>. = k/k •. Formula (6.28) is valid under the assumption of horizontal isotropy of the internal
wave field.
6.4.2 Topographic Effects
Observations, as well as numerical simulations, help to develop some understanding of the complexity of internal waves. As mentioned in Sect. 6.1,
the interaction of semi diurnal tides with shelf topography may be one of the
sources of internal waves. They have wavelengths of a tens of kilometres and
may propagate out of the generation area. During measurement program in
the Andaman Sea near northern Sumatra, large-amplitude, long internal waves
with currents as high as 1.8 m/s were observed (Osborne and Burch, 1980).
Photographs of the Andaman Sea's surface by LANDSAT satellite, as well as
photographs taken during the Apollo-Soyuz mission, showed that the shallow
waters around the Andaman Islands and near the southernmost point of Nicobar Islands, or close to northern Sumatra are potential sources of the observed
internal waves. A set of current metres and thermistors was placed at approximate depths of 53, 87, 116, 164 and 254 metres, in the ocean with 1100 m
water depth. In Fig. 6.10, a typical temperature signal of an internal wave,
recorded at the depth of 164 m, is shown. The wave pattern is similar to the
solitary shape described in Sect. 4.2.3, suggesting a soliton interpretation of the
signal (see also Massel, 1989). The leftmost soliton in Fig. 6.10 is the largest
and leads the packet. Similar packets occur, on average, every 12 hour and 26
minutes, which suggests a link between soliton generation and the semidiurnal
tide. The average number of observed solitons is six or seven.