9.3 Results
As propagation of the sea currents direction is roughly the same with the wind and
the speed as an approximation of the momentum generator tangential speed, the
equations of motion
∂p
∂x
¼
∂p
∂y
¼ 0
are reduced to horizontal flow. For a circle with
a diameter D i ¼ 2 V/f, the final equations of inertial oscillations (or current) have
the form:
u ¼ V sin ft
v ¼ V cos ft
V ¼ u
2
þ v
2
and the inertial period (T i ): T i ¼
2π
f ¼
T sd
2 sin φ , where V is the component of the velocity
for the formula in the final equation of the equation of motion, the Coriolis parameter
f ¼ 2Ω sin φ, the sidereal day T sd ffi 23 h 56 min 4.1 s and φ is the latitude.
Based on the T i formula, the calculated inertial period for the analysed latitude
ranged from 16.5 to 17.5 h.
The progressive vector diagrams or integrated hodograph, together with the
vector component evolution indicated the presence of various wave events of
different nature, periods, intensities, and durations. Due to the short length of the
records, and taking into account the time scale of the identified motions, different
processing approaches were used. In all analysed data series, the integrated
hodograph revealed the presence of periodic motions (Table 9.1, Fig. 9.1). The
trends on the east and north directions of the sea current vector highlights oscillations with periods close to the inertial (17h10m) and gyratory motions with tens of
minutes’ periods. The time series were divided into two categories (Table 9.1): long
waves (periods of hours) and short waves, with periods of less than an hour.
For long waves, the use of the spectral method was inappropriate, because the
lunar semi-diurnal (M2) and diurnal (S1) tides are separated from the local inertial
period (17 h) by a frequency difference of about 0.02 cph, almost the same as Fast
Fourier Transform evolution (FFT) of the analysed time series. To this are considered the possible presence of transverse seiches on the western half of the Black Sea
(Fig. 9.2).
In the field of large frequency range, close to the cut-off Nyquist frequency,
numerical analysis process admits the interference processes between similar
frequencies. The exact frequency of the oscillations was achieved by calculating
the residual variation for different frequencies from the domain of interest (5 min
step) (Fig. 9.3).
For this reason, various methods have been adopted for the two categories of
phenomena. In both cases, the series were smoothed using sliding average method
on three terms (Fig. 9.3). This reduces the noise contribution in dispersion calculation. Prior spectral analysis indicated that there are no significant energies at very
high frequencies (~4 cph, corresponding to periods of less than 15 min).
9 Inertial Currents in Western Continental Black Sea Shelf
145
As propagation of the sea currents direction is roughly the same with the wind and
the speed as an approximation of the momentum generator tangential speed, the
equations of motion
∂p
∂x
¼
∂p
∂y
¼ 0
are reduced to horizontal flow. For a circle with
a diameter D i ¼ 2 V/f, the final equations of inertial oscillations (or current) have
the form:
u ¼ V sin ft
v ¼ V cos ft
V ¼ u
2
þ v
2
and the inertial period (T i ): T i ¼
2π
f ¼
T sd
2 sin φ , where V is the component of the velocity
for the formula in the final equation of the equation of motion, the Coriolis parameter
f ¼ 2Ω sin φ, the sidereal day T sd ffi 23 h 56 min 4.1 s and φ is the latitude.
Based on the T i formula, the calculated inertial period for the analysed latitude
ranged from 16.5 to 17.5 h.
The progressive vector diagrams or integrated hodograph, together with the
vector component evolution indicated the presence of various wave events of
different nature, periods, intensities, and durations. Due to the short length of the
records, and taking into account the time scale of the identified motions, different
processing approaches were used. In all analysed data series, the integrated
hodograph revealed the presence of periodic motions (Table 9.1, Fig. 9.1). The
trends on the east and north directions of the sea current vector highlights oscillations with periods close to the inertial (17h10m) and gyratory motions with tens of
minutes’ periods. The time series were divided into two categories (Table 9.1): long
waves (periods of hours) and short waves, with periods of less than an hour.
For long waves, the use of the spectral method was inappropriate, because the
lunar semi-diurnal (M2) and diurnal (S1) tides are separated from the local inertial
period (17 h) by a frequency difference of about 0.02 cph, almost the same as Fast
Fourier Transform evolution (FFT) of the analysed time series. To this are considered the possible presence of transverse seiches on the western half of the Black Sea
(Fig. 9.2).
In the field of large frequency range, close to the cut-off Nyquist frequency,
numerical analysis process admits the interference processes between similar
frequencies. The exact frequency of the oscillations was achieved by calculating
the residual variation for different frequencies from the domain of interest (5 min
step) (Fig. 9.3).
For this reason, various methods have been adopted for the two categories of
phenomena. In both cases, the series were smoothed using sliding average method
on three terms (Fig. 9.3). This reduces the noise contribution in dispersion calculation. Prior spectral analysis indicated that there are no significant energies at very
high frequencies (~4 cph, corresponding to periods of less than 15 min).
9 Inertial Currents in Western Continental Black Sea Shelf
145