velocities (about 5–10% of all waves) varies in space in the amplitude range 0.5–1.5
m/s, and the frequency of occurrence of flow velocities of different signs is
approximately the same at every spatial point.
Summary
The problem of generation of small-scale intense internal waves in the Arctic
regions north of the so-called critical latitude is discussed. It is well known, that
baroclinic waves at such latitudes cannot propagate as free waves. However, due to
the nonlinear generation of higher harmonics, which can propagate, highly nonlinear small-scale internal waves are excited. This process has been studied in the
regions of the Franz-Victoria Trough in the Barents Sea and in the Arctic Ocean,
where such waves, generated by the interaction of the barotropic tidal flow with
uneven bottom, were observed several times (with the participation of Professor
Eugene Morozov). The adapted numerical model of K. G. Lamb, solving the
two-dimensional Euler equations on the rotating Earth, is used for calculations.
Modeling results confirmed that, similarly to the in situ records, 40 m-amplitude
waves are generated in this region and their wavelengths (6–12 km) also agree with
the observations. These waves conserved significant amplitudes of isopycnal displacements at a distance of about 20 km from the zone of generation. They appear
twice per the semidiurnal tide period and conserve their state for about 6.2 h, slowly
propagating out of the peak of the underwater hill. More intense waves were
generated in the ebb phase and when the ebb velocity vanished. The largest
observed height between the crest and trough (about 80 m) appeared at the end of
the ebb phase each 12.4 h period. The time evolution of the horizontal velocity field
is also modeled, and significant values of flow velocities are obtained, the maximal
value is 1.5 times greater than the amplitude of the barotropic tidal flow at the time
moments of the maximal tide. A spectrum of isopycnal displacement corresponding
to undisturbed density at 70 m depth reveals significant values to the fifth harmonic.
The amplitudes of spectral peaks of the second and third harmonics are half of the
order of the first harmonic amplitude. The zones of internal wave generation over
the flanks of the hills are found using two methods, and both give similar results.
The frequency of the appearance of large peak values in the velocity field is also
calculated. In particular, the fraction of large velocities in the range 0.5–1.5 m/s
(approximately 5–10% of all waves) varies in space significantly growing in the
supercritical regions. The frequency of the occurrence of the flow velocities of
different signs is approximately the same at each spatial point.
Acknowledgements This study was initiated in the framework of the state task programme in the
sphere of scientific activity of the Ministry of Education and Science of the Russian Federation
(projects No. 5.4568.2017/6.7 and No. 5.1246.2017/4.6) and financially supported by this programme, grant of the President of the Russian Federation (NSh-2685.2018.5) and Russian
Foundation for Basic Research (grant No. 16-05-00049).
Numerical Modeling of Internal Wave Generation at High Latitudes
579
m/s, and the frequency of occurrence of flow velocities of different signs is
approximately the same at every spatial point.
Summary
The problem of generation of small-scale intense internal waves in the Arctic
regions north of the so-called critical latitude is discussed. It is well known, that
baroclinic waves at such latitudes cannot propagate as free waves. However, due to
the nonlinear generation of higher harmonics, which can propagate, highly nonlinear small-scale internal waves are excited. This process has been studied in the
regions of the Franz-Victoria Trough in the Barents Sea and in the Arctic Ocean,
where such waves, generated by the interaction of the barotropic tidal flow with
uneven bottom, were observed several times (with the participation of Professor
Eugene Morozov). The adapted numerical model of K. G. Lamb, solving the
two-dimensional Euler equations on the rotating Earth, is used for calculations.
Modeling results confirmed that, similarly to the in situ records, 40 m-amplitude
waves are generated in this region and their wavelengths (6–12 km) also agree with
the observations. These waves conserved significant amplitudes of isopycnal displacements at a distance of about 20 km from the zone of generation. They appear
twice per the semidiurnal tide period and conserve their state for about 6.2 h, slowly
propagating out of the peak of the underwater hill. More intense waves were
generated in the ebb phase and when the ebb velocity vanished. The largest
observed height between the crest and trough (about 80 m) appeared at the end of
the ebb phase each 12.4 h period. The time evolution of the horizontal velocity field
is also modeled, and significant values of flow velocities are obtained, the maximal
value is 1.5 times greater than the amplitude of the barotropic tidal flow at the time
moments of the maximal tide. A spectrum of isopycnal displacement corresponding
to undisturbed density at 70 m depth reveals significant values to the fifth harmonic.
The amplitudes of spectral peaks of the second and third harmonics are half of the
order of the first harmonic amplitude. The zones of internal wave generation over
the flanks of the hills are found using two methods, and both give similar results.
The frequency of the appearance of large peak values in the velocity field is also
calculated. In particular, the fraction of large velocities in the range 0.5–1.5 m/s
(approximately 5–10% of all waves) varies in space significantly growing in the
supercritical regions. The frequency of the occurrence of the flow velocities of
different signs is approximately the same at each spatial point.
Acknowledgements This study was initiated in the framework of the state task programme in the
sphere of scientific activity of the Ministry of Education and Science of the Russian Federation
(projects No. 5.4568.2017/6.7 and No. 5.1246.2017/4.6) and financially supported by this programme, grant of the President of the Russian Federation (NSh-2685.2018.5) and Russian
Foundation for Basic Research (grant No. 16-05-00049).
Numerical Modeling of Internal Wave Generation at High Latitudes
579