access CMDAC database at the Oregon State University (CMDAC numbers are
acc00739–acc00747). Figure 1 shows the locations of moorings.
Other archived data were also used in our research. These experiments were also
aimed to study mesoscale eddies. Two moorings were deployed in 1978–1979 at
41° 00′ N, 24° W. The measurements were made at 2300, 3300, and 4000 m.
The CMDAC numbers are acc00705–acc00707. A mooring was deployed in 1980–
1981 at 41° 45′ N, 22° 00′ W. The measurements were made at 600, 1500, 3000,
and 3790 m. The CMDAC numbers are acc00522–acc00525.
We used the archived data of these measurements west of the Iberian Peninsula
to study the properties of internal tide whose spatial scales (100–200 km) are close
to the scales of mesoscale eddies (200–300 km). The available data with a time
sampling of one hour are quite applicable to study internal tides with periods of
12 h.
Spatiotemporal Spectrum
We used the method developed for seismological problems and applied by Barber to
the ocean waves to estimate the wavelength and direction of the internal tides [13].
We assume that the sensors are located randomly over the observational sites. The
method is based on the calculation of the cross spectra for each pair of the possible
combinations of sensors with further convolution at the frequency of the waves
under study. The spectra are calculated using the Fourier transformation of the
correlation function as described by Blackman and Tukey [14]. The amplitude
and phase cross-characteristics of the oscillation are used to calculate the spatiotemporal spectra at the wave frequency and estimate the components of the
horizontal wave number.
The method basically accounts for the statistical phase difference between each
pair of the wave sensors. In our case we used the temperature sensors, which
indicate the vertical motion induced by internal waves assuming that the vertical
gradients of temperature are significant. It is important that the distance between the
moorings should be comparable with the wavelength of the oscillations under
study. Otherwise uncertainty appears in the interpretation of the phase differences if
the distance between the sensors is too large. If the distance between the sensors is
two small and the span of the array of sensors is smaller than the wavelength due to
a limited number of sensors it is impossible to resolve the wavelength correctly.
If moored temperature measurements at the same depth at several points in the
ocean are available, we can calculate cross spectra of fluctuations P and
Q (co-spectrum and quadratic spectrum). Next, we perform a transformation at the
M 2 semidiurnal tidal frequency f 0 to determine the distribution of mutual spectral
energy at this frequency with respect to wavenumbers k x and k y .
So far we do not have a continuous spectrum of distances, but instead, we have a
finite set of definite distances corresponding to the distances between the moored
186
E. G. Morozov and M. G. Velarde
acc00739–acc00747). Figure 1 shows the locations of moorings.
Other archived data were also used in our research. These experiments were also
aimed to study mesoscale eddies. Two moorings were deployed in 1978–1979 at
41° 00′ N, 24° W. The measurements were made at 2300, 3300, and 4000 m.
The CMDAC numbers are acc00705–acc00707. A mooring was deployed in 1980–
1981 at 41° 45′ N, 22° 00′ W. The measurements were made at 600, 1500, 3000,
and 3790 m. The CMDAC numbers are acc00522–acc00525.
We used the archived data of these measurements west of the Iberian Peninsula
to study the properties of internal tide whose spatial scales (100–200 km) are close
to the scales of mesoscale eddies (200–300 km). The available data with a time
sampling of one hour are quite applicable to study internal tides with periods of
12 h.
Spatiotemporal Spectrum
We used the method developed for seismological problems and applied by Barber to
the ocean waves to estimate the wavelength and direction of the internal tides [13].
We assume that the sensors are located randomly over the observational sites. The
method is based on the calculation of the cross spectra for each pair of the possible
combinations of sensors with further convolution at the frequency of the waves
under study. The spectra are calculated using the Fourier transformation of the
correlation function as described by Blackman and Tukey [14]. The amplitude
and phase cross-characteristics of the oscillation are used to calculate the spatiotemporal spectra at the wave frequency and estimate the components of the
horizontal wave number.
The method basically accounts for the statistical phase difference between each
pair of the wave sensors. In our case we used the temperature sensors, which
indicate the vertical motion induced by internal waves assuming that the vertical
gradients of temperature are significant. It is important that the distance between the
moorings should be comparable with the wavelength of the oscillations under
study. Otherwise uncertainty appears in the interpretation of the phase differences if
the distance between the sensors is too large. If the distance between the sensors is
two small and the span of the array of sensors is smaller than the wavelength due to
a limited number of sensors it is impossible to resolve the wavelength correctly.
If moored temperature measurements at the same depth at several points in the
ocean are available, we can calculate cross spectra of fluctuations P and
Q (co-spectrum and quadratic spectrum). Next, we perform a transformation at the
M 2 semidiurnal tidal frequency f 0 to determine the distribution of mutual spectral
energy at this frequency with respect to wavenumbers k x and k y .
So far we do not have a continuous spectrum of distances, but instead, we have a
finite set of definite distances corresponding to the distances between the moored
186
E. G. Morozov and M. G. Velarde