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Amplitude-phase Structure of Internal Gravity Waves Fields in Ocean with Shear Flows

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Abstract

The problem of the harmonic internal gravity waves generation in the ocean with real and model hydrological characteristics is solved. For real and model distributions of the buoyancy frequency and background shear flows the results of numerical calculations of the wave fields amplitude-phase characteristics are presented. The transformation of the internal gravity waves fields amplitude-phase patterns is studied numerically. Numerically it is shown that relatively short-wave packets can concentrate at depths where there are extrema of a function that depends on the components of the wave vector and the vector of shear currents. It is also shown that the spatial variability of the wave packets propagation direction can lead to a rather noticeable vertical amplitude rearrangement of the eigenfunctions. It is shown that the use of model representations for the main hydrological characteristics (buoyancy frequency and background shear currents) makes it possible to simplify the main spectral problem. It is shown that model representations of hydrological characteristics make it possible to qualitatively correctly describe the main features of dispersion surfaces and wave fields phase structures. To describe the wave fields amplitude dependences it is necessary to use the results of a main spectral problem numerical solutions.

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REFERENCES

  1. J. Lighthill, Waves in Fluids (Cambridge Univ. Press, Cambridge, 1978).

    Google Scholar 

  2. Y. Z. Miropolsky, Dynamics of Internal Gravity Waves in the Ocean (Springer, Berlin, 2001).

    Book  Google Scholar 

  3. J. Pedlosky, Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics (Springer, Berlin, 2010).

    Google Scholar 

  4. A. L. Fabrikant and Yu. A. Stepanyants, Propagation of Waves in Shear Flows (World Scientific Publishing, Singapore, 1998).

    Book  Google Scholar 

  5. E. G. Morozov, Oceanic Internal Tides. Observations, Analysis and Modeling (Springer, Berlin, 2018).

    Book  Google Scholar 

  6. M. G. Velarde, R. Yu. Tarakanov, and A. V. Marchenko, The Ocean in Motion (Springer, Berlin, 2018).

    Book  Google Scholar 

  7. V. V. Bulatov and Yu. V. Vladimirov, A General Approach to Ocean Wave Dynamics Research: Modelling, Asymptotics, Measurements (OntoPrint, Moscow, 2019).

    Google Scholar 

  8. A. A. Gavrileva, Yu. G. Gubarev, and M. P. Lebedev, “The Miles theorem and the first boundary value problem for the Taylor–Goldstein equation,” J. Appl. Ind. Math. 13 (3), 460–471 (2019).

    Article  Google Scholar 

  9. K. R. Khusnutdinova and X. Zhang, “Long ring waves in a stratified fluid over a shear flow,” J. Fluid Mech. 794, 17–44 (2016).

    Article  Google Scholar 

  10. F. Fraternale, L. Domenicale, G. Staffilan, and D. Tordella, “Internal waves in sheared flows: Lower bound of the vorticity growth and propagation discontinuities in the parameter space,” Phys. Rev. 97, 063102 (2018).

    Google Scholar 

  11. V. V. Bulatov and Yu. V. Vladimirov, “Dynamics of internal gravity waves in the ocean with shear flows,” Russ. J. Earth Sci. 20, ES4004 (2020).

    Article  Google Scholar 

  12. V. Bulatov and Yu. Vladimirov, “Analytical approximations of dispersion relations for internal gravity waves equation with shear flows,” Symmetry 12 (11), 1865 (2020).

    Article  Google Scholar 

  13. V. V. Bulatov, Yu. V. Vladimirov, and I. Yu. Vladimirov, “Internal gravity waves from an oscillating source in the ocean,” Izv., Atmos. Ocean. Phys. 57 (3), 321–328 (2021).

    Article  Google Scholar 

  14. J. W. Miles, “On the stability of heterogeneous shear flow,” J. Fluid Mech. 10, 495–509 (1961).

    Article  Google Scholar 

  15. M. Hirota and P. J. Morrison, “Stability boundaries and sufficient stability conditions for stably stratified, monotonic shear flows,” Phys. Lett. A 380 (21), 1856–1860 (2016).

    Article  Google Scholar 

  16. S. Churilov, “On the stability analysis of sharply stratified shear flows,” Ocean Dyn. 68, 867–884 (2018).

    Article  Google Scholar 

  17. E. E. Khimchenko, D. I. Frey, and E. G. Morozov, “Tidal internal waves in the Bransfield Strait, Antarctica,” Russ. J. Earth. Sci. 20, ES2006 (2020).

    Article  Google Scholar 

  18. E. G. Morozov, R. Yu. Tarakanov, D. I. Frey, T. A. Demidova, and N. I. Makarenko, “Bottom water flows in the tropical fractures of the Northern Mid-Atlantic Ridge,” J. Oceanogr. 74 (2), 147–167 (2018).

    Article  Google Scholar 

  19. D. I. Frey, A. N. Novigatsky, M. D. Kravchishina, and E. G. Morozov, “Water structure and currents in the Bear Island Trough in July–August 2017,” Russ. J. Earth Sci. 17, ES3003 (2017).

    Article  Google Scholar 

  20. N. Froman and P. Froman, Physical Problems Solved by the Phase-Integral Method (Cambridge Univ. Press, Cambridge, 2002).

    Book  Google Scholar 

  21. Yu. Kravtsov and Yu. Orlov, Caustics, Catastrophes and Wave Fields (Springer, Berlin, 1999).

    Book  Google Scholar 

Download references

Funding

This work was funded by Russian Foundation for Basic Research (RFBR), project no. 20-01-00111A.

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Correspondence to V. V. Bulatov or I. Yu. Vladimirov.

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Bulatov, V.V., Vladimirov, I.Y. Amplitude-phase Structure of Internal Gravity Waves Fields in Ocean with Shear Flows. Izv. Atmos. Ocean. Phys. 57, 680–685 (2021). https://doi.org/10.1134/S0001433821200020

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  • DOI: https://doi.org/10.1134/S0001433821200020

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