are studied, where the depths of the upper and lower layers of the fluid with
different densities are compared. The qualitative and quantitative coincidence with
the results of the real IIW observation experiment on the shelf of the Kamchatka
Peninsula is demonstrated. It is important that the analytical approach developed
here allows rapid assessment of the amplitude and structure of the IIW at any
arbitrary time with known hydrology and topography parameters of the surveyed
region. The possibility of detecting the features of an IIW at critical points by radar
images (recorded when sounding by the ship or shore radar) is demonstrated.
Acknowledgements This study was supported by the Russian Foundation for Basic Research
(projects 16-55-52022, 18-05-00292 and 17-05-41117 RGS). Numerical code development and
numerical modeling were supported by the Russian Science Foundation (grant 15-17-20009).
References
1. Battjes, J. A., Zitman, T. J., & Holtheijsen, L. H. (1987). A re-analysis of the spectra observed
in JONSWAP. Journal of Physical Oceanography, 17, 1288–1295.
2. Ermoshkin, A. V., Bakhanov, V. V., & Bogatov, N. A. (2015). Development of an empirical
model for Radar backscattering cross section of the ocean surface at grazing angles.
Sovremennye problemi distantsionnogo zondirovaniya Zemli iz kosmosa, 12(4), 51–59.
3. Gorshkov, K. A., & Ostrovsky, L. A. (1981). Interaction of solitons in nonintegrable systems.
Physica D: Nonlinear Phenomena, 3, 428–438.
4. Grimshaw, R., Pelinovsky, E., & Talipova, T. (2007). Modeling internal solitary waves in the
coastal ocean. Surveys In Geophysics, 28, 273–287.
5. Gorshkov, К. A., & Soustova, I. A. (2001). Interaction of solitons as compound structures in
the Gardner model. Radiophysics and Quantum Electronics, 44(5–6), 502–512.
6. Gorshkov, K. A., Ostrovsky, L. A., Soustova, I. A., & Irisov, V. G. (2004). Perturbation
theory for kinks and application for multisoliton interactions in hydrodynamics. Physical
Review E, 69, 1–10.
7. Gorshkov, K. A., Ostrovsky, I. A., & Soustova, I. A. (2011). Dynamics of strongly nonlinear
solitons in the two-layer fluid. Studies in Applied Mathematics, 126(1), 49–73.
8. Gorshkov, К. A., Ostrovsky, L. A., Soustova, I. A., & Shevz, L. M. (2011). The interaction of
intense internal waves within the framework of Choi-Camassa equation. Izvestiya RAN,
Atmosphere and Ocean Physics., 47(3), 339–347.
9. Gorshkov, K. A., Soustova, I. A., Ermoshkin, A. V., & Zaitseva, N. V. (2012). Evolution of
the composite soliton of the Gardner equation in media with variable parameter. Radiophysics
and Quantum Electronics, 55(5), 380–392.
10. Gorshkov, K. A., Soustova, I. A., & Ermoshkin, A. V. (2016). Field structure of a
quasisoliton approaching the critical point. Radiophysics Quantum Electronics, 58(10),
738–744.
11. Grimshaw, R., Pelinovsky, E., & Talipova, T. (1999). Solitary wave transformation in a
medium with sing-variable quadratic nonlinearity and cubic nonlinearity. Physica D:
Nonlinear Phenomena, 132, 40–62.
12. Gorshkov, K.A., Dolina, I. S., Soustova, I. A., & Troitskaya, Y. I. (2003). Transformation of
short waves in a nonuniform flow field on the ocean surface. The effect of wind growth rate
modulation. Radiophysics Quantum Electronics 46(7), 464–485.
13. Hughes, B. (1978). The effect of internal waves on surface wind waves. 2. Theoretical
analysis. Journal of Geophysical Research, 83(1), 455–465.
292
I. A. Soustova et al.
different densities are compared. The qualitative and quantitative coincidence with
the results of the real IIW observation experiment on the shelf of the Kamchatka
Peninsula is demonstrated. It is important that the analytical approach developed
here allows rapid assessment of the amplitude and structure of the IIW at any
arbitrary time with known hydrology and topography parameters of the surveyed
region. The possibility of detecting the features of an IIW at critical points by radar
images (recorded when sounding by the ship or shore radar) is demonstrated.
Acknowledgements This study was supported by the Russian Foundation for Basic Research
(projects 16-55-52022, 18-05-00292 and 17-05-41117 RGS). Numerical code development and
numerical modeling were supported by the Russian Science Foundation (grant 15-17-20009).
References
1. Battjes, J. A., Zitman, T. J., & Holtheijsen, L. H. (1987). A re-analysis of the spectra observed
in JONSWAP. Journal of Physical Oceanography, 17, 1288–1295.
2. Ermoshkin, A. V., Bakhanov, V. V., & Bogatov, N. A. (2015). Development of an empirical
model for Radar backscattering cross section of the ocean surface at grazing angles.
Sovremennye problemi distantsionnogo zondirovaniya Zemli iz kosmosa, 12(4), 51–59.
3. Gorshkov, K. A., & Ostrovsky, L. A. (1981). Interaction of solitons in nonintegrable systems.
Physica D: Nonlinear Phenomena, 3, 428–438.
4. Grimshaw, R., Pelinovsky, E., & Talipova, T. (2007). Modeling internal solitary waves in the
coastal ocean. Surveys In Geophysics, 28, 273–287.
5. Gorshkov, К. A., & Soustova, I. A. (2001). Interaction of solitons as compound structures in
the Gardner model. Radiophysics and Quantum Electronics, 44(5–6), 502–512.
6. Gorshkov, K. A., Ostrovsky, L. A., Soustova, I. A., & Irisov, V. G. (2004). Perturbation
theory for kinks and application for multisoliton interactions in hydrodynamics. Physical
Review E, 69, 1–10.
7. Gorshkov, K. A., Ostrovsky, I. A., & Soustova, I. A. (2011). Dynamics of strongly nonlinear
solitons in the two-layer fluid. Studies in Applied Mathematics, 126(1), 49–73.
8. Gorshkov, К. A., Ostrovsky, L. A., Soustova, I. A., & Shevz, L. M. (2011). The interaction of
intense internal waves within the framework of Choi-Camassa equation. Izvestiya RAN,
Atmosphere and Ocean Physics., 47(3), 339–347.
9. Gorshkov, K. A., Soustova, I. A., Ermoshkin, A. V., & Zaitseva, N. V. (2012). Evolution of
the composite soliton of the Gardner equation in media with variable parameter. Radiophysics
and Quantum Electronics, 55(5), 380–392.
10. Gorshkov, K. A., Soustova, I. A., & Ermoshkin, A. V. (2016). Field structure of a
quasisoliton approaching the critical point. Radiophysics Quantum Electronics, 58(10),
738–744.
11. Grimshaw, R., Pelinovsky, E., & Talipova, T. (1999). Solitary wave transformation in a
medium with sing-variable quadratic nonlinearity and cubic nonlinearity. Physica D:
Nonlinear Phenomena, 132, 40–62.
12. Gorshkov, K.A., Dolina, I. S., Soustova, I. A., & Troitskaya, Y. I. (2003). Transformation of
short waves in a nonuniform flow field on the ocean surface. The effect of wind growth rate
modulation. Radiophysics Quantum Electronics 46(7), 464–485.
13. Hughes, B. (1978). The effect of internal waves on surface wind waves. 2. Theoretical
analysis. Journal of Geophysical Research, 83(1), 455–465.
292
I. A. Soustova et al.