| Title:
|
On caustics associated with Rossby waves (English) |
| Author:
|
Gorman, Arthur D. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
5 |
| Year:
|
1996 |
| Pages:
|
321-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Rossby wave equations characterize a class of wave phenomena occurring in geophysical fluid dynamics. One technique useful in the analysis of these waves is the geometrical optics, or multi-dimensional WKB technique. Near caustics, e.g., in critical regions, 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 study Rossby waves near caustics. (English) |
| Keyword:
|
Rossby waves |
| Keyword:
|
caustics |
| Keyword:
|
turning points |
| Keyword:
|
Lagrange manifold |
| Keyword:
|
WKB |
| MSC:
|
34E20 |
| MSC:
|
35Q35 |
| MSC:
|
86A10 |
| idZBL:
|
Zbl 0870.34059 |
| idMR:
|
MR1404544 |
| DOI:
|
10.21136/AM.1996.134329 |
| . |
| Date available:
|
2009-09-22T17:51:59Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134329 |
| . |
| Reference:
|
[1] J. B. Keller: 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 |
| Reference:
|
[2] D. J. Karoly, B. J. Hoskins: Three dimensional propagation of planetary waves.J. Meteor. Soc. Japan. 60 (1982), 109–123. 10.2151/jmsj1965.60.1_109 |
| Reference:
|
[3] H. Yang: Wave Packets, Their Bifurcation in Geophysical Fluid Dynamics.Springer-Verlag, New York, 1991. MR 1077832 |
| Reference:
|
[4] C. Knessl, J. B. Keller: Rossby waves.Stud. Apl. Math. 94 (1995), 359–376. MR 1330881, 10.1002/sapm1995944359 |
| Reference:
|
[5] D. J. Karoly: Rossby wave propagation in a barotropic atmosphere.Dyn. Oceans and Atmos. 7 (1983), 111–125. |
| Reference:
|
[6] V. G. Gnevyshev, V. I. Shira: Monochromatic Rossby wave transformation in zonal critical layers.Izv. Atmos. Ocean Phys. 25 (1989), 628–635. MR 1083856 |
| Reference:
|
[7] H. Yang: Evolution of a Rossby wave packet in barotropic flows with asymmetric basic current, topography and $\delta $-effect.J. Atmos. Sci. 44 (1987), 2267–2276. 10.1175/1520-0469(1987)044<2267:EOARWP>2.0.CO;2 |
| Reference:
|
[8] V. I. Arnol’d: Characteristic class entering in quantification conditions.Funct. Anal. Appl. 1 (1967), 1–13. MR 0211415, 10.1007/BF01075861 |
| Reference:
|
[9] V. P. Maslov: Theorie des Perturbationes et Methodes Asymptotique.Dunod, Gauthier-Villars, Paris, 1972. |
| Reference:
|
[10] A. D. Gorman: Space-Time caustics.Int. J. Math. and Math. Sci. 9 (1986), 531–540. Zbl 0613.34046, MR 0859121, 10.1155/S0161171286000662 |
| Reference:
|
[11] A. D. Gorman: Vector fields near caustics.J. Math. Phys. 26 (1985), 1404–1407. Zbl 0568.58018, MR 0790091, 10.1063/1.526954 |
| Reference:
|
[12] K. C. Chen: Asymptotic theory of wave propagation in spatial and temporal dispersive inhomogeneous media.J. Math. Phys. 12 (1971), 743–753. MR 0287799, 10.1063/1.1665643 |
| . |
