ON THE FEATURES OF THE PULSRODON DYNAMICS

  • V. V. Galushko Geophysical Survey of the Russian Academy of Sciences
DOI: 10.29006/1564-2291.JOR-2022.50(3).1
Keywords: pulson, rodon, pulsrodon, shallow water equations, reduced gravity, elliptical vortex, deep water lens, first integrals, parametric space

Abstract

Equations are considered that describe the dynamics of pulsrodon in a moving coordinate system associated with the center of mass and the principal axes of an elliptical vortex. A simple and clear general solution of the system of equations in quadratures is found. A complete study of solutions depending on the parameters of the problem has been carried out. New particular solutions are obtained, which are of interest to researchers.

References


  1. Ball, F. K., 1963: Some general theorems concerning the finite motion of a shallow rotating liquid lying on a paraboloid. J. Fluid Mech., 17 (2), 240–256.

  2. Coushman-Rozin, B., W. H. Heil, and D. Nof, 1985: Oscillations and rotations of elliptical warm-core rings. J. Geophys. Res., 90 (11), 756–764.

  3. Coushman-Rozin, B., 1986: Linear stability of large, elliptical warm–core rings. J. Phys. Oceanography, 16, 1158–1164.

  4. Coushman-Rozin, B., 1987: Exact analytical solutions for elliptical warm–core rings. Tellus, 39A, 235–244.

  5. Monin, A. S. and G. M. Zhikharev, 1990: Ocean eddies. Physics Uspekhi, 33 (5), 313–339.

  6. Ripa, P., 1987: On the stability of elliptical vortex solutions of the shallow–water equations. J. Fluid Mech., 183, 343–363.

  7. Rogers, C., 1989: Elliptic warm–core theory: the pulsrodon. Physics Letters, 138 (6) 267–273.

  8. Rogers, C. and W. K. Schief, 2011: The pulsrodon in 2+1 – dimensional magneto-gasdynamics: Hamiltonian structure and integrability. J. Math. Phys., 52.

  9. Rogers, C. and W. K. Schief, 2011: On the integrability of a Hamiltonian reduction of a 2+1 –dimensional non-isothermal rotating gas cloud system. Nonlinearity, 24 (11).

  10. Rubino, A. and S. Dotsenko, 2006: The stratified pulson. J. Phys. Oceanography, 36, 711–719.

  11. Young, W. R., 1986: Elliptical vortices in shallow water. J. Fluid Mech., 171, 101–119.

  12. Zatsepa, S. N. and V. V. Galushko, 2009: O dinamike zhidkoj linzy v dvuxslojno-stratificiro­vannoj srede (On the dynamics of a liquid lens in a two–layer stratified medium). Proceedings of the State Oceanographic Institute, Moscow, 212, 226–238.

  13. Zharniczkij, E. V., 1990: Analiticheskaya model dinamiki arkticheskoj vixrevoj linzy (Analytical model of the dynamics of the Arctic vortex lens). Oceanology, 30 (5), 736–742.

  14. Zharniczkij, E. V., 1992: K dinamike e`llipticheskogo vihrya so svobodnoj poverhnost`yu (On the dynamics of an elliptical vortex with a free surface). Oceanology, 32 (3), 436–445.
Published
2022-11-28
Issue
Vol 50 No 3 (2022): Journal of Oceanological Research
Section
Ocean physics and climate

Transfer of copyrights occurs on the basis of a license agreement between the Author and Shirshov Institute of Oceanology, RAS