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Free tides in two-dimensional uniform-depth basins

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Abstract

The problem of free tidal wave propagation in two-dimensional uniform-depth basins is considered. To solve the problem, a numerical algorithm, a version of the Babenko method, is developed. The algorithm makes it possible to solve the problem in a singly-connected domain admitting conformal mapping onto a circle. A solution can be obtained for both nonrotating and rotating basins. The first natural frequencies are determined for elliptic basins with different eccentricities and angular velocities and certain characteristic natural shapes demonstrating the distinctive features of tidal flows in elliptic basins are constructed. The time evolution of modes in a rotating elliptic basin is studied.

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REFERENCES

  1. L. N. Sretenskii (1987) Dynamic Theory of Tides Nauka Moscow

    Google Scholar 

  2. H. Lamb (1932) Hydrodynamics Cambridge Univ. Press Cambridge

    Google Scholar 

  3. J. Proudman (1928) ArticleTitleOn the tides in a flat semi-circular sea of uniform depth Mon. Not. Roy. Astr. Soc. Geophys. Suppl. 2 32

    Google Scholar 

  4. J. Proudman (1913) ArticleTitleOn some cases of tidal motion of rotating sheets of water Proc. London Math. Soc. (2) 12 453

    Google Scholar 

  5. H. Jeffreys (1924) ArticleTitleOn certain approximate solutions of linear differential equations of the second order Proc. London Math. Soc. (2) 23 428

    Google Scholar 

  6. H. Jeffreys (1924) ArticleTitleOn certain solutions of Mathieu’s equation Proc. London Math. Soc. (2) 23 437

    Google Scholar 

  7. H. Jeffreys (1924) ArticleTitleThe free oscillations of water in an elliptical lake Proc. London Math. Soc. (2) 23 455

    Google Scholar 

  8. S. Goldstein (1928) ArticleTitleA note on certain approximate solutions of linear differential equations of second order with an application to the Mathieu equation Proc. London Math. Soc. (2) 28 91

    Google Scholar 

  9. S. Goldstein (1928) ArticleTitleThe free oscillations of water in a canal of elliptic plan Proc. London Math. Soc. (2) 28 91

    Google Scholar 

  10. S. Goldstein (1928) ArticleTitleA special case of tidal motion in elliptic basins Mon. Not. Roy. Astr. Soc. Geophys. Suppl. 2 44

    Google Scholar 

  11. S. Goldstein (1929) ArticleTitleTidal motion in a rotating elliptic basin of constant depth Mon. Not. Roy. Astr. Soc. Geophys. Suppl. 2 213

    Google Scholar 

  12. S. D. Akulenko, S. A. Kumakshev and S. V. Nesterov “Natural oscillations of a heavy fluid in an elliptic vessel”Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4, 129 (2001)

  13. K. I. Babenko (1986) Foundations of Numerical Analysis Nauka Moscow

    Google Scholar 

  14. S. D. Algazin (2002) Numerical Saturationless Algorithms in Classical Problems of Mathematical Physics Nauchnyi Mir Moscow

    Google Scholar 

  15. K. I. Babenko and S. D. Algazin, “A numerical algorithm for solving the eigenvalue problem for linear differential operators,” USSR Academy of Sciences, Keldysh Institute of Applied Mathematics, Preprint No. 46 (1978).

  16. S. D. Algazin, “Numerical algorithms of classical mathematical physics. I. Spectral problems for the Laplace equation,” Russian Academy of Sciences, Keldysh Institute of Applied Mathematics, Preprint No. 671 (2000).

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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 119–130. Original Russian Text Copyright © 2004 by Ivanov.

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Ivanov, M.I. Free tides in two-dimensional uniform-depth basins. Fluid Dyn 39, 779–789 (2004). https://doi.org/10.1007/s10697-005-0012-9

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  • DOI: https://doi.org/10.1007/s10697-005-0012-9

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