ANALYTICAL PROPERTIES OF THE DISPERSION RELATIONS OF THE INTERNAL GRAVITY WAVES EQUATION WITH MODEL AND ARBITRARY BUOYANCY FREQUENCY DISTRIBUTIONS
https://doi.org/10.26583/vestnik.2023.212
Abstract
In this paper we investigated the analytical properties of the dispersion relations of the equation of internal gravity waves with model and arbitrary distributions of the buoyancy frequency. For the analytical solution of the problem we used the model distribution of the buoyancy frequency, which is used in applied oceanological calculations in the presence of a seasonal thermocline. We have obtained implicit forms of dispersion dependences, which are expressed in terms of the Bessel function of the real index. For wave numbers other than zero, we proposed an asymptotic method for studying the dispersion relation, based on the construction of Bessel functions uniform asymptotics for large values of the real index and argument, which are expressed in terms of the Airy functions. For an arbitrary distribution of the buoyancy frequency, using the perturbation method and the WKBJ method, we obtained asymptotic representations of the dispersion relations for small wave numbers. The solutions constructed in this work make it possible to further calculate the amplitude-phase characteristics of the fields of internal gravity waves with model and arbitrary buoyancy frequency distributions
About the Authors
V. V. Bulatov
Ishlinsky Institute for Problems in Mechanics RAS
Russian Federation
Russian Federation
I. Yu. Vladimirov
Shirshov Institute of Oceanology RAS
Russian Federation
Russian Federation
References
1. Miropol'skii Yu.Z., Shishkina O.V. Dynamics of internal gravity waves in the ocean. Boston: Kluwer Academic Publishers, 2001. 406 p.
2. Pedlosky J. Waves in the ocean and atmosphere: introduction to wave dynamics. Berlin-Heildelberg: Springer, 2010. 260 p.
3. Sutherland B.R. Internal gravity waves. Cambridge: Cambridge University Press, 2010. 394 p.
4. Ozsoy E. Geophysical fluid dynamics II. Stratified rotating fluid dynamics of the atmosphere-ocean. Springer Textbook in Earth Sciences. Geography and Environment. Switzerland AG Cham, Springer Nature, 2021. 323 p.
5. Bulatov V.V., Vladimirov Yu.V. Volni v stratifistirovannikh sredakh [Waves in stratified medium]. M.: Nauka Publ., 2015. 735 p. (in Russian).
6. Abdilghanie A.M., Diamessis P.J. The internal gravity wave field emitted by a stably stratified turbulent wake. J. Fluid Mech. 2013. Vol. 720. P. 104–139.
7. Voelker G.S., Myers P. G., Walter M., Sutherland B. R. Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance. Dynamics Atm. Oceans. 2019. Vol. 86. P. 116–133.
8. Chai J., Wang Z., Yang Z., Wang Z. Investigation of internal wave wakes generated by a submerged body in a stratified flow. Ocean Engineering. 2022. Vol. 266. P. 112840.
9. Wang J., Wang, S., Chen X., Wang W., Xu Y. Three-dimensional evolution of internal waves rejected from a submarine seamount. Physics Fluids. 2017. Vol. 29. P. 106601.
10. Borovikov V.A., Bulatov V.V., Vladimirov Yu.V. Internal gravity waves excited by a body moving in a stratified fluid. Fluid Dyn. Res. 1995. Vol. 5. Р. 325–336.
11. Svirkunov P.N., Kalashnik M.V. Phase patterns of dispersive waves from moving localized sources. Phys.-Usp. 2014. Vol. 57 (1). P. 80–91.
12. Gnevyshev V., Badulin S. Wave patterns of gravity–capillary waves from moving localized sources. Fluids. 2020. Vol. 5. P. 219.
13. Bulatov V., Vladimirov Yu. Generation of internal gravity waves far from moving non-local source. Symmetry. 2020. Vol. 12(11). P. 1899.
14. Morozov E.G. Oceanic internal tides. Observations, analysis and modeling. Berlin: Springer. 2018. 317 p.
15. Velarde M.G., Tarakanov R.Yu., Marchenko A.V. (Eds.). The ocean in motion. Springer Oceanography. Switzerland AG Cham, Springer Nature, 2018. 625 p.
16. Garrett C., Munk W. Space-time scales of internal waves. Geophys. Fluid Dyn. 1972. Vol. 3. P. 225–264.
17. Watson G.N. A treatise on the theory of Bessel functions (2nd Edition). Cambridge: Cambridge University Press, 1995. 814 p.
18. Dobrokhotov S.Yu., Minenkov D.S., Nazaikinskii V.E. Representation of Bessel function by the Maslov canonical operator. Theor. Math. Physics. 2021. Vol. 208(2). P. 1018–1037
Review
For citations:
Bulatov V.V., Vladimirov I.Yu. ANALYTICAL PROPERTIES OF THE DISPERSION RELATIONS OF THE INTERNAL GRAVITY WAVES EQUATION WITH MODEL AND ARBITRARY BUOYANCY FREQUENCY DISTRIBUTIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(1):3-8. (In Russ.) https://doi.org/10.26583/vestnik.2023.212
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