stations, the calculation of a spatiotemporal spectrum at f 0 frequency was carried out
using the following formula:
Eðk x , k y , f 0 Þ = 2 ∑
n − 1
i = 1
∑
n
j = i + 1
½P ij ðf 0 Þ cos 2πðk x x ij + k y y ij Þ − Q ij ðf 0 Þ sin 2πðk x x ij + k y y ij Þ,
where k
2
x + k
2
y = k
2 is the spatial wave number, while the wavelength L is: L = 1 ̸ k; i,
j are the sequential numbers of the sensors, n is the total number of the sensors; P ij
and Q ij are the real and imaginary parts of the cross spectrum between the sensors
with numbers i and j; x ij = X i − X j and y ij = Y i − Y j are the projections of the distances between the sensors on the horizontal axes x and y.
Usually, the number of sensors is small. Each sensor is installed on a mooring.
The number of moorings deployed in the study sites rarely exceeds 10. Hence, the
shape of the spectral peak is not a delta-function but has a finite width. Usually, the
spatiotemporal spectra of internal tides with semidiurnal frequency (or possibly,
other frequencies) are presented as contour lines of percentage normalized by the
maximum value.
Analysis
We studied internal tides in the region west of the Iberian Peninsula on the basis of
moored temperature and velocity measurements. The moorings deployed in the
region allowed us to analyze the properties of internal tides.
Two lines of WOCE moorings in 1993–1994 on the continental slope of the
Iberian Peninsula extending to the deep basin along 42° 16′ N and along 41° 00′ N
allowed us to determine the decay of internal tide amplitude with the distance from
the continental slope. A scheme of the region, bottom topography, and locations of
moorings along the line normal to the continental slope are shown in Fig. 1.
Locations of the instruments related to the continental slope are shown in Fig. 2.
The eastern mooring of the ACM 28 line was located at a distance of 60 km
from the shore on the continental slope at a depth of 1300 m. The line of moorings
extended to the depths of 4200 m. The length of the line of moorings was 150 km.
All moorings returned the temperature data at 700–800 m. Intense internal tides
were recorded on all of the moorings. The mean peak to peak temperature variations
on different moorings were 0.25–0.50 °C, which corresponds to the amplitude of
internal tides within 38–78 m. The amplitudes of semidiurnal internal tides were
decreasing from 78 m over the continental slope to 38 m in the deep basin over a
distance of 150 km. A graph of the variations of internal tide amplitudes at 700–
800 m is shown in Fig. 2.
The locations of instruments over the background of depth are shown in the top
panel of Fig. 2. The amplitudes of internal tides are shown in the bottom panel. One
can see a decrease in the amplitudes up to the depths of 4200 m as the distance from
Internal Tides West of the Iberian Peninsula
187
using the following formula:
Eðk x , k y , f 0 Þ = 2 ∑
n − 1
i = 1
∑
n
j = i + 1
½P ij ðf 0 Þ cos 2πðk x x ij + k y y ij Þ − Q ij ðf 0 Þ sin 2πðk x x ij + k y y ij Þ,
where k
2
x + k
2
y = k
2 is the spatial wave number, while the wavelength L is: L = 1 ̸ k; i,
j are the sequential numbers of the sensors, n is the total number of the sensors; P ij
and Q ij are the real and imaginary parts of the cross spectrum between the sensors
with numbers i and j; x ij = X i − X j and y ij = Y i − Y j are the projections of the distances between the sensors on the horizontal axes x and y.
Usually, the number of sensors is small. Each sensor is installed on a mooring.
The number of moorings deployed in the study sites rarely exceeds 10. Hence, the
shape of the spectral peak is not a delta-function but has a finite width. Usually, the
spatiotemporal spectra of internal tides with semidiurnal frequency (or possibly,
other frequencies) are presented as contour lines of percentage normalized by the
maximum value.
Analysis
We studied internal tides in the region west of the Iberian Peninsula on the basis of
moored temperature and velocity measurements. The moorings deployed in the
region allowed us to analyze the properties of internal tides.
Two lines of WOCE moorings in 1993–1994 on the continental slope of the
Iberian Peninsula extending to the deep basin along 42° 16′ N and along 41° 00′ N
allowed us to determine the decay of internal tide amplitude with the distance from
the continental slope. A scheme of the region, bottom topography, and locations of
moorings along the line normal to the continental slope are shown in Fig. 1.
Locations of the instruments related to the continental slope are shown in Fig. 2.
The eastern mooring of the ACM 28 line was located at a distance of 60 km
from the shore on the continental slope at a depth of 1300 m. The line of moorings
extended to the depths of 4200 m. The length of the line of moorings was 150 km.
All moorings returned the temperature data at 700–800 m. Intense internal tides
were recorded on all of the moorings. The mean peak to peak temperature variations
on different moorings were 0.25–0.50 °C, which corresponds to the amplitude of
internal tides within 38–78 m. The amplitudes of semidiurnal internal tides were
decreasing from 78 m over the continental slope to 38 m in the deep basin over a
distance of 150 km. A graph of the variations of internal tide amplitudes at 700–
800 m is shown in Fig. 2.
The locations of instruments over the background of depth are shown in the top
panel of Fig. 2. The amplitudes of internal tides are shown in the bottom panel. One
can see a decrease in the amplitudes up to the depths of 4200 m as the distance from
Internal Tides West of the Iberian Peninsula
187