On the Coriolis Effect for Internal Ocean Waves
Rossen Ivanov
download PDFAbstract. A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth’s rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.
Keywords
Internal Waves, Hamiltonian, KdV Equation, Boussinesq Equation, Ostrovsky Equation, Tidal Motion
Published online , 6 pages
Copyright © 2022 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Rossen Ivanov, On the Coriolis Effect for Internal Ocean Waves, Materials Research Proceedings, Vol. 20, pp 20-25, 2022
DOI: https://doi.org/10.21741/9781644901731-3
The article was published as article 3 of the book Floating Offshore Energy Devices
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] V.V. Bulatov, Y.V. Vladimirov, Fundamental problems of internal gravity waves dynamics in ocean, Journal of Basic & Applied Sciences 9 (2013) 69-81. https://doi.org/10.6000/1927-5129.2013.09.12
[2] R. Choudhury, R.I. Ivanov and Y. Liu, Hamiltonian formulation, nonintegrability and local bifurcations for the Ostrovsky equation, Chaos, Solitons and Fractals 34 (2007) 544-550. https://doi.org/10.1016/j.chaos.2006.03.057
[3] A. Compelli, Hamiltonian approach to the modelling of internal geophysical waves with vorticity, Monatsh. Math. 179(4) (2016), 509-521. https://doi.org/10.1007/s00605-014-0724-1
[4] A. Compelli, R.I. Ivanov, The dynamics of at surface internal geophysical waves with currents, Journal of Mathematical Fluid Mechanics, 19, (2017) 329-344. https://doi.org/10.1007/s00021-016-0283-4
[5] E. Coyle, B. Basu, J. Blackledge and W. Grimson, Harnessing Nature: Wind, Hydro, Wave, Tidal, and Geothermal Energy, in: Understanding the Global Energy Crisis by E. Coyle and R. Simmons (Eds.), Purdue University Press. (2014), URL: https://www.jstor.org/stable/j.ctt6wq56p.9
[6] A. Constantin, R.I. Ivanov, E.M. Prodanov, Nearly-Hamiltonian structure for water waves with constant vorticity, J. Math. Fluid Mech. 9 (2007), 1-14; arXiv:math-ph/0610014
[7] W. Craig, P. Guyenne, H. Kalisch, Hamiltonian long wave expansions for free surfaces and interfaces, Comm. Pure Appl. Math. 24 (2005), 1587-1641. https://doi.org/10.1002/cpa.20098
[8] G. Grahovski, R. Ivanov, Generalised Fourier transform and perturbations to soliton equations. Discrete Contin. Dyn. Syst. Ser. B 12 (2009), 579-595. https://doi.org/10.3934/dcdsb.2009.12.579
[9] R. Grimshaw, L. Ostrovsky, V. Shrira, Y. Stepanyants, Long nonlinear surface and internal waves in a rotating ocean, Surveys Geophys. 19 (1998) 289-338. https://doi.org/10.1023/A:1006587919935
[10] R.S. Johnson, Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid. Mech. 457 (2002), 63-82. https://doi.org/10.1017/S0022112001007224
[11] A.I. Leonov, The effect of the Earth’s rotation on the propagation of weak non-linear surface and internal long oceanic waves, Ann. NY Acad. Sci. 373 (1981) 150-159. https://doi.org/10.1111/j.1749-6632.1981.tb51140.x
[12] L.A. Ostrovsky, Nonlinear internal waves in a rotating ocean. Okeanologia 18 (1978) 181-191.
[13] V. Varlamov, Y. Liu, Cauchy problem for the Ostrovsky equation. Discrete and Contin. Dyn. Systems 10 (2004) 731-751. https://doi.org/10.3934/dcds.2004.10.731
[14] V.E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Zh. Prikl. Mekh. Tekh. Fiz. 9 (1968), 86-94 (in Russian); J. Appl. Mech. Tech. Phys. 9 (1968), 190-194 (English translation).
““