Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Linearized vorticity equation; caustics; turning points; WKB
Linearized vorticity equation; caustics; turning points; WKB
Summary:
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.
References:
[1] Haltiner G. J., Williams R. T.: Numerical Prediction and Dynamic Meteorology. 2nd Edition, John Wiley & Sons, New York, 1980.
[2] Yang H.: Evolution of a Rossby wave packet in barotropic flows with asymmetric basic current, topography and $\delta $-effect. J. Atmos. Sci. 44 (1987), 2267–2276. DOI 10.1175/1520-0469(1987)044<2267:EOARWP>2.0.CO;2
[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. MR 0094120
[4] Karoly D. J., Hoskins B. J.: Three dimensional propagation of planetary waves. J. Meteor. Soc. Japan. 60 (1982), 109–123. DOI 10.2151/jmsj1965.60.1_109
[5] Yang H.: Wave Packets and their Bifurcation in Geophysical Fluid Dynamics. Springer-Verlag, New York, 1991. MR 1077832
[6] Knessl C., Keller J. B.: Rossby waves. Stud. Apl. Math. 94 (1995), 359–376. DOI 10.1002/sapm1995944359 | MR 1330881
[7] Karoly D. J.: Rossby wave propagation in a barotropic atmosphere. Dyn. Oceans and Atmos. 7 (1983), 111–125.
[8] Gnevyshev V. G., Shira V. I.: Monochromatic Rossby wave transformation in zonal critical layers. Izv. Atmos. Ocean Phys. 25 (1989), 628–635. MR 1083856
[9] Arnol’d V. I.: Characteristic class entering in quantification conditions. Funct. Anal. Appl. 1 (1967), 1–13. DOI 10.1007/BF01075861 | MR 0211415
[10] Maslov V. P.: Theorie des Perturbationes et Methodes Asymptotique. Dunod, Gauthier-Villars, Paris, 1972.
[11] Gorman A. D.: On caustics associated with Rossby waves. Appl. Math. 4 (1996), 321–328. MR 1404544 | Zbl 0870.34059
Search
Partner of
