Podolsk, Moscow, Russian Federation
UDK 55 Геология. Геологические и геофизические науки
UDK 550.34 Сейсмология
UDK 550.383 Главное магнитное поле Земли
GRNTI 37.01 Общие вопросы геофизики
GRNTI 37.15 Геомагнетизм и высокие слои атмосферы
GRNTI 37.25 Океанология
GRNTI 37.31 Физика Земли
GRNTI 38.01 Общие вопросы геологии
GRNTI 36.00 ГЕОДЕЗИЯ. КАРТОГРАФИЯ
GRNTI 37.00 ГЕОФИЗИКА
GRNTI 38.00 ГЕОЛОГИЯ
GRNTI 39.00 ГЕОГРАФИЯ
GRNTI 52.00 ГОРНОЕ ДЕЛО
OKSO 05.00.00 Науки о Земле
BBK 26 Науки о Земле
TBK 63 Науки о Земле. Экология
BISAC SCI SCIENCE
The far fields of internal gravity waves from a radially symmetric initial perturbation of lines of equal density in a layer of a stratified medium of finite thickness, as well as the far fields of surface waves from an impulse source in a homogeneous liquid of finite depth, are studied. Integral representations of wave perturbations are obtained. Uniform and non-uniform asymptotic solutions are constructed that allow describing the amplitude-phase structure of the far fields of surface and internal waves. It is established that uniform asymptotics make it possible to effectively calculate long range wave fields both near and far from the wave front.
stratified medium, internal gravitational waves, far fields, surface waves, uniform asymptotics, wave front, Airy function.
1. Cherkesov L. V. Hydrodynamics of surface and internal waves. - Kyiv : Naukova Dumka, 1976. - P. 364. - (in Russian).
2. Abdilghanie A. M., Diamessis P. J. The internal gravity wave field emitted by a stably stratified turbulent wake // Journal of Fluid Mechanics. - 2013. - Vol. 720. - P. 104-139. - DOI:https://doi.org/10.1017/jfm.2012.640
3. Belyaev M. Y., Desinov L. V., Krikalev S. K., et al. Identification of a system of oceanic waves based on space imagery // Journal of Computer and Systems Sciences International. - 2009. - Vol. 48, no. 1. - P. 110-120. - DOI:https://doi.org/10.1134/s1064230709010109
4. Borovikov V. A. Uniform stationary phase method. - London : Institution of Electrical Engineers, 1994. - P. 233.
5. Broutman D., Brandt L., Rottman J. W., et al. A WKB derivation for internal waves generated by a horizontally moving body in a thermocline // Wave Motion. - 2021. - Vol. 105. - P. 102759. - DOI:https://doi.org/10.1016/j.wavemoti.2021.102759
6. Bulatov V. V., Vladimirov I. Y. Uniform Asymptotics of Internal Gravitational Wave Fields from an Initial Radially Symmetric Perturbation // Fluid Dynamics. - 2021a. - Vol. 56, no. 8. - P. 1112-1118. - DOI:https://doi.org/10.1134/s0015462821080103
7. Bulatov V. V., Vladimirov Y. V. Asymptotics of the Far Fields of Internal Gravity Waves Excited by a Source of Radial Symmetry // Fluid Dynamics. - 2021b. - Vol. 56, no. 5. - P. 672-677. - DOI:https://doi.org/10.1134/s0015462821050013
8. Bulatov V. V., Vladimirov Y. V., Vladimirov I. Y. Far fields of internal gravity waves from a source moving in the ocean with an arbitrary buoyancy frequency distribution // Russian Journal of Earth Sciences. - 2019. - Vol. 19, no. 5. - P. 1-9. - DOI:https://doi.org/10.2205/2019es000667
9. Bulatov V. V., Vladimirov Y. V., Vladimirov I. Y. Uniform and Nonuniform Asymptotics of Far Surface Fields from a Flashed Localized Source // Fluid Dynamics. - 2021a. - Vol. 56, no. 7. - P. 975-980. - DOI:https://doi.org/10.1134/s001546282107003x
10. Bulatov V. V., Vladimirov Y. V., Vladimirov I. Y., et al. Features of the Phase Structure of Internal Gravity Waves Generated by a Moving Source // Doklady Earth Sciences. - 2021b. - Vol. 501, no. 1. - P. 959-962. - DOI:https://doi.org/10.1134/s1028334x21090051
11. Bulatov V., Vladimirov Y. Generation of Internal Gravity Waves Far from Moving Non-Local Source // Symmetry. - 2020. - Vol. 12, no. 11. - P. 1899. - DOI:https://doi.org/10.3390/sym12111899
12. Bulatov V., Vladimirov Y. Far Fields of Internal Gravity Waves under Fast Density Variation in a Radial Symmetry Source // Izvestiya, Atmospheric and Oceanic Physics. - 2021c. - Vol. 57, no. 6. - P. 614-618. - DOI:https://doi.org/10.1134/s0001433821050029
13. Chai J., Wang Z., Yang Z., et al. Investigation of internal wave wakes generated by a submerged body in a stratified flow // Ocean Engineering. - 2022. - Vol. 266. - P. 112840. - DOI:https://doi.org/10.1016/j.oceaneng.2022.112840
14. Chen X.-B., Wu G. X. On singular and highly oscillatory properties of the Green function for ship motions // Journal of Fluid Mechanics. - 2001. - Vol. 445. - P. 77-91. - DOI:https://doi.org/10.1017/s0022112001005481
15. Dobrokhotov S. Y., Grushin V. V., Sergeev S. A., et al. Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections // Russian Journal of Mathematical Physics. - 2016. - Vol. 23, no. 4. - P. 455-474. - DOI:https://doi.org/10.1134/s1061920816040038
16. Fröman N., Fröman P. O. Physical Problems Solved by the Phase-Integral Method. - Cambridge: Cambridge University Press, 2002. - P. 214. - DOI:https://doi.org/10.1017/cbo9780511535086
17. Gnevyshev V., Badulin S. Wave patterns of gravity-capillary waves from moving localized sources // Fluids. - 2020. - Vol. 5, no. 4. - P. 219. - DOI:https://doi.org/10.3390/fluids5040219
18. Gushchin V. A., Matyushin P. V. Simulation and study of stratified flows around finite bodies // Computational Mathematics and Mathematical Physics. - 2016. - Vol. 56, no. 6. - P. 1034-1047. - DOI:https://doi.org/10.1134/s0965542516060142
19. Haney S., Young W. R. Radiation of internal waves from groups of surface gravity waves // Journal of Fluid Mechanics. - 2017. - Vol. 829. - P. 280-303. - DOI:https://doi.org/10.1017/jfm.2017.536
20. Kharif C., Pelinovsky E., Slunyaev A. Rogue Waves in the Ocean. - Springer Berlin Heidelberg, 2009. - P. 260. - DOI:https://doi.org/10.1007/978-3-540-88419-4
21. Khimchenko E. E., Frey D. I., Morozov E. G. Tidal internal waves in the Bransfield Strait, Antarctica // Russian Journal of Earth Sciences. - 2020. - Vol. 20, no. 2. - P. 1-6. - DOI:https://doi.org/10.2205/2020es000711
22. Kravtsov Y. A., Orlov Y. I. Caustics, Catastrophes and Wave Fields. - Springer Berlin Heidelberg, 1993. - P. 228. - DOI:https://doi.org/10.1007/978-3-642-59887-6
23. Lighthill M. J. Waves in fluids. - Cambridge University Press, 1978. - P. 524.
24. Matyushin P. V. Process of the Formation of Internal Waves Initiated by the Start of Motion of a Body in a Stratified Viscous Fluid // Fluid Dynamics. - 2019. - Vol. 54, no. 3. - P. 374-388. - DOI:https://doi.org/10.1134/s0015462819020095
25. Mei C. C., Stiassnie M., Yue D. K. Theory and applications of ocean surface waves. - London: World Scientific Publishing Co Pte Ltd, 2018. - P. 1240.
26. Miropol’sky Y. Z. Dynamics of Internal Gravity Waves in the Ocean / ed. by O. D. Shishkina. - Springer Netherlands, 2001. - P. 406. - DOI:https://doi.org/10.1007/978-94-017-1325-2.
27. Morozov E. G. Oceanic Internal Tides: Observations, Analysis and Modeling. - Springer International Publishing, 2018. - P. 317. - DOI:https://doi.org/10.1007/978-3-319-73159-9
28. Morozov E. G., Tarakanov R. Y., Frey D. I., et al. Bottom water flows in the tropical fractures of the Northern Mid-Atlantic Ridge // Journal of Oceanography. - 2018. - Vol. 74, no. 2. - P. 147-167. - DOI:https://doi.org/10.1007/s10872-017-0445-x
29. Özsoy E. Geophysical Fluid Dynamics II. - Springer International Publishing, 2021. - P. 323. - DOI:https://doi.org/10.1007/978-3-030-74934-7
30. Pedlosky J. Waves in the Ocean and Atmosphere. - Springer Berlin Heidelberg, 2003. - P. 260. - DOI:https://doi.org/10.1007/978-3-662-05131-3.
31. Sutherland B. R. Internal Gravity Waves. - Cambridge University Press, 2010. - P. 394. - DOI:https://doi.org/10.1017/cbo9780511780318.
32. Svirkunov P. N., Kalashnik M. V. Phase patterns of dispersive waves from moving localized sources // Physics-Uspekhi. - 2014. - Vol. 57, no. 1. - P. 80-91. - DOI:https://doi.org/10.3367/ufne.0184.201401d.0089.
33. The Ocean in Motion / ed. by M. G. Velarde, R. Y. Tarakanov, A. V. Marchenko. - Springer International Publishing, 2018. - P. 625. - DOI:https://doi.org/10.1007/978-3-319-71934-4.
34. Voelker G. S., Myers P. G., Walter M., et al. Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance // Dynamics of Atmospheres and Oceans. - 2019. - Vol. 86. - P. 116-133. - DOI:https://doi.org/10.1016/j.dynatmoce.2019.03.005.
35. Wang J., Wang S., Chen X., et al. Three-dimensional evolution of internal waves reflected from a submarine seamount // Physics of Fluids. - 2017. - Vol. 29, no. 10. - P. 106601. - DOI:https://doi.org/10.1063/1.4986167.
36. Watson G. N. A treatise on the theory of Bessel functions. - Cambridge University Press, 1995. - P. 804.
37. Wehausen J. V., Laitone E. V. Surface waves. Vol. 9. - Springer Verlag, 1960. - P. 446-778.
