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On caustics associated with the linearized vorticity equation

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Abstract

The linearized vorticity equation serves to model a number of wave phenomena in geophysical fluid dynamics. One technique that has been applied to this equation is the geometrical optics, or multi-dimensional WKB technique. Near caustics, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to determine an asymptotic solution of the linearized vorticity equation and to study associated wave phenomena on the caustic curve.

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References

  1. Haltiner G. J., Williams R. T.: Numerical Prediction and Dynamic Meteorology. 2nd Edition, John Wiley & Sons, New York, 1980.

    Google Scholar 

  2. Yang H.: Evolution of a Rossby wave packet in barotropic flows with asymmetric basic current, topography and δ-effect. J. Atmos. Sci. 44 (1987), 2267–2276.

    Google Scholar 

  3. Keller J. B.: A Geometrical Theory of Diffraction in Calculus of Variations and its Applications. Vol. VIII, Proc. Symp. Appl. Math., ed. L.M. Graves, McGraw-Hill, New York, 1958.

    Google Scholar 

  4. Karoly D. J., Hoskins B. J.: Three dimensional propagation of planetary waves. J. Meteor. Soc. Japan. 60 (1982), 109–123.

    Google Scholar 

  5. Yang H.: Wave Packets and their Bifurcation in Geophysical Fluid Dynamics. Springer-Verlag, New York, 1991.

    Google Scholar 

  6. Knessl C., Keller J. B.: Rossby waves. Stud. Apl. Math. 94 (1995), 359–376.

    Google Scholar 

  7. Karoly D. J.: Rossby wave propagation in a barotropic atmosphere. Dyn. Oceans and Atmos. 7 (1983), 111–125.

    Google Scholar 

  8. Gnevyshev V. G., Shira V. I.: Monochromatic Rossby wave transformation in zonal critical layers. Izv. Atmos. Ocean Phys. 25 (1989), 628–635.

    Google Scholar 

  9. Arnol'd V. I.: Characteristic class entering in quantification conditions. Funct. Anal. Appl. 1 (1967), 1–13.

    Google Scholar 

  10. Maslov V. P.: Theorie des Perturbationes et Methodes Asymptotique. Dunod, Gauthier-Villars, Paris, 1972.

    Google Scholar 

  11. Gorman A. D.: On caustics associated with Rossby waves. Appl. Math. 4 (1996), 321–328.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Lafayette College, Easton, Pennsylvania, (18042), USA

    Petya N. Ivanova & Arthur D. Gorman

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  1. Petya N. Ivanova
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  2. Arthur D. Gorman
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Ivanova, P.N., Gorman, A.D. On caustics associated with the linearized vorticity equation. Applications of Mathematics 43, 255–262 (1998). https://doi.org/10.1023/A:1023265821269

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  • DOI: https://doi.org/10.1023/A:1023265821269

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