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Internal Gravity Waves Generated by an Oscillating Disturbance Source in a Stratified Medium in the Presence of Two-Dimensional Shear Flows

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Abstract

The problem of generation of internal gravity waves by a local harmonic disturbance source in a stratified medium with two-dimensional linear shear flows is considered. Integral representations of the solutions are obtained under the assumption of constant buoyancy frequency in satisfying the Miles–Howard stability condition. The properties of the spectral problem are investigated for small wavenumbers. The results of numerical calculations of the dispersion curves and phase patterns of the excited wave fields are given for various linear distributions of shear flows. It is shown that taking the two-dimensional character of shear flows into account is the cause of appreciable asymmetry of both the dispersion curves and the isophase lines. Transformation of the phase patterns of the fields of internal gravity waves is studied numerically as a function of the generation parameters.

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REFERENCES

  1. Fabrikant, A.L. and Stepanyants, Yu.A., Propagation of Waves in Shear Flows, World Scientific Publ., 1998.

    Book  Google Scholar 

  2. Miropol’skii, Yu.Z. and Shishkina, O.V., Dynamics of Internal Gravity Waves in the Ocean. Boston: Kluwer Academic Publishers, 2001.

    Book  Google Scholar 

  3. Morozov, E.G., Oceanic Internal Tides. Observations, Analysis and Modeling, Berlin: Springer, 2018.

    Book  Google Scholar 

  4. Velarde, M.G., Tarakanov, R.Yu., and Marchenko, A.V. (Eds.), The Ocean in Motion, Springer Oceanography. Springer International Publishing AG, 2018.

  5. Vlasenko, V., Stashchuk, N., and Hutter, K., Baroclinic Tides, N.Y.: Cambridge University Press, 2005.

    Book  Google Scholar 

  6. Bulatov, V.V. and Vladimirov, Yu.V., Volny v stratifitsirovannykh sredakh (Waves in Stratified Media), Moscow: Nauka, 2015.

  7. Bulatov, V.V., Novye zadachi matematicheskogo modelirovaniya volnovoi dinamiki stratifitsirovannykh sred (New Problems of Mathematical Modeling of Wave Dynamics of Stratified Media), Moscow: OntoPrint, 2021.

  8. Young, W.R., Phines, P., and Garret, C.J.R., Shear flows dispersion, internal waves and horizontal mixing, J. Phys. Oceanography, 1982, vol. 12, no. 6, pp. 515–527.

    Article  ADS  Google Scholar 

  9. Bouruet-Aubertot, P.I. and Thorpe, S.A., Numerical experiments of internal gravity waves in accelerating shear flow, Dyn. Atm. Oceans, 1999, vol. 29, pp. 41–63.

    Article  ADS  Google Scholar 

  10. Meunier, P., Dizus, S., Redekopp, L., and Spedding, G., Internal waves generated by a stratified wake: experiment and theory, J. Fluid Mech., 2018, vol. 846, pp. 752–788.

    Article  ADS  Google Scholar 

  11. Fraternale, F., Domenicale, L., Staffilan, G., and Tordella, D., Internal waves in sheared flows: lower bound of the vorticity growth and propagation discontinuities in the parameter space, Phys. Rev., 2018, vol. 97, no. 6, p. 063102.

  12. Slepyshev, A.A. and Vorotnikov, D.I., Generation of vertical fine structure by internal waves in a shear flows, Open J. Fluid Mechanics, 2019, vol. 9, pp. 140–157.

    ADS  Google Scholar 

  13. Howland, C.J., Taylor, J.R., and Caulfield, C.P., Shear-induced breaking of internal gravity waves, J. Fluid Mechanics, 2021, vol. 921, p. A24.

    Article  ADS  MathSciNet  Google Scholar 

  14. Bulatov, V.V., Vladimirov, Yu.V., and Vladimirov, I.Yu., Internal gravity waves excited by an oscillating disturbance source in the ocean, Izv. Ross. Akad. Nauk, Fiz. Atm. Okeana, 2021, vol. 57, no. 3, pp. 362–373.

    Google Scholar 

  15. Bulatov, V.V., Vladimirov, Yu.V., and Vladimirov, I.Yu., Phase characteristics of the fields of internal gravity waves in the ocean with a flow velocity shear, Morsk. Gidrofiz. Zh., 2021, vol. 37, no. 4, pp. 473–489.

    Google Scholar 

  16. Bulatov, V.V. and Vladimirov, Yu.V., Dynamics of internal gravity waves in the ocean with shear flows, Russ. J. Earth Sciences, 2020, vol. 20, p. ES4004.

  17. Bulatov, V.V. and Vladimirov, Yu.V., Internal gravity waves in a stratified medium with model shear flow distributions, Fluid Dyn., 2020, vol. 55, no. 5, pp. 631–635. https://doi.org/10.1134/S0015462820050031

    Article  ADS  MathSciNet  Google Scholar 

  18. Morozov, E.G., Tarakanov, R.Yu., Frey, D.I., Demidova, T.A., and Makarenko, N.I., Bottom water flows in the tropical fractures of the Northern Mid-Atlantic Ridge, J. Oceanography, 2018, vol. 74, no. 2, pp. 147–167.

    Article  Google Scholar 

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

  20. Khimchenko, E. E., Frey, D.I., and Morozov, E.G., Tidal internal waves in the Bransfield Strait, Antarctica, Russ. J. Earth. Science, 2020, vol. 20, p. ES2006.

  21. Miles, J.W., On the stability of heterogeneous shear flow, J. Fluid Mech., 1961, vol. 10, no. 4, pp. 495–509.

    Article  ADS  MathSciNet  Google Scholar 

  22. Hirota, M. and Morrison, P.J., Stability boundaries and sufficient stability conditions for stably stratified, monotonic shear flows, Phys. Letters A, 2016, vol. 380, no. 21, pp. 1856–1860.

    Article  ADS  Google Scholar 

  23. Churilov, S., On the stability analysis of sharply stratified shear flows, Ocean Dynamics, 2018, vol. 68, pp. 867–884.

    Article  ADS  Google Scholar 

  24. Carpenter, J.R., Balmforth, N.J., and Lawrence, G.A., Identifying unstable modes in stratified shear layers, Phys. Fluids, 2010, vol. 22, p. 054104.

  25. Gavrileva, A.A., Gubarev, Yu.G., and Lebedev, M.P., The Miles theorem and the first boundary value problem for the Taylor–Goldstein equation, J. Appl. Industrial Math., 2019, vol. 13, no. 3, pp.460–471.

    Article  MathSciNet  Google Scholar 

  26. Nayfeh, A.H., Introduction to Perturbation Techniques, New York: Wiley, 1981.

    MATH  Google Scholar 

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Funding

The work is carried out in accordance with the themes of the State tasks nos. AAAA-A20-120011690131-7 (Bulatov) and FMWE-2021-0002 (Vladimirov) and with a partial financial support from the Russian Foundation for Basic Research (project no. 20-01-00111A).

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

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Translated by E.A. Pushkar

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Bulatov, V.V., Vladimirov, I.Y. Internal Gravity Waves Generated by an Oscillating Disturbance Source in a Stratified Medium in the Presence of Two-Dimensional Shear Flows. Fluid Dyn 57, 477–485 (2022). https://doi.org/10.1134/S0015462822040012

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  • DOI: https://doi.org/10.1134/S0015462822040012

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