Abstract
In this chapter, we discuss another aspect of the wave packet theory, wave packet progagation. Earlier chapters mainly focused on the structure and structural change of wave packets, without explicit discussions of the propagation property of wave packets, which is possible only when the structure independence theorem discussed in Chapter 2 holds. However, when the structure independence theorem is not valid, we have to take the propagation property of the wave packet into account, as discussed in Chapter 2. Moreover, the propagation property of wave packet is also of great importance. As shown in Chapter 2, the wave packet is always propagated along the group velocity, that is, the wave packet velocity. Many modern ideas on wave propagation were originated by Rayleigh, including the distinction between the phase velocity and the group velocity; this appears very early in Rayleigh’s work (1877). Since then, there have been numerous studies on wave packet propagation associated with the group velocity, including several monographs (Brillouin, 1946, 1953, 1960; Tolstoy, 1973). The study of wave packet propagation was started as soon as the concept of wave group or wave packet was introduced in wave mechanics (Brillouin, 1946).
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References
Bjerkness, J. (1969). Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev. 97, 162 – 172.
Brillouin, L. (1946). Wave Propagation in Periodic Structures. McGraw-Hill, London.
Brillouin, L. (1953). Wave Propagation in Periodic Structures, 2nd ed. Dover, New York.
Brillouin, L. (1960). Wave Propagation and Group Velocity. Academic Press, New York.
Charney, J.G. (1949). On a physical basis for numerical prediction of large-scale motions in the atmosphere. J. Meteorol. 6, 371 – 385.
Charney, J.G., and Drazin, P.G. (1961). Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res. 66, 38 – 109.
Dickinson, R.E. (1968). Planetary Rossby waves propagating vertically through weak westerly wind waveguides. J. Atmos. Sci. 25, 984 – 1002.
Dickinson, R.E. (1969). Vertical propagation of planetary Rossby waves through an atmosphere with Newtonian cooling. J. Geophys. Res. 74, 929 – 938.
Gambo, K., and Kudo, K. (1983). Three-dimensional teleconnections in the zonally asymmetric height field during the Northern Hemisphere winter. J. Meteorol. Soc. Japan 61, 36 – 50.
Grose, W.L., and Hoskins, B.J. (1979). On the influence of orography on large-scale atmospheric flow. J. Atmos. Sci. 36, 223 – 234.
Hayashi, Y. (1981). Vertical-zonal propagation of a stationary planetary wave packet. J. Atmos. Sci. 40, 1197 – 1205.
Held, I.M. (1983). Stationary and quasi-stationary eddies in the extratropic troposphere: Theory. In Large-Scale Dynamical Processes in the Atmosphere, B.J. Hoskins and R. Peace, Eds. Academic Press, New York.
Holton, J.R. (1972). Waves in the equatorial stratoposphere generated by tropospheric heat sources. J. Atmos. Sci. 29, 368 – 375.
Hoskins, B.J., and Karoly, D.J. (1981). The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci. 38, 1179 – 1196.
Huang, R., and Gambo, K. (1983). The response of an atmospheric multilevel model to forcing by topography and stationary heat sources in summer. J. Meteorol. Soc. Japan 61, 495 – 509.
Karoly, D.J. (1983). Rossby wave propagation in a barotropic atmosphere. Dyn. Atmos. Oceans, 7, 111 – 125.
Karoly, D.J., and Hoskins, B.J. (1982). Three-dimensional propagation of planetary wave. J. Meteorol. Soc. Japan 60, 109 – 123.
Longuet-Higgins, M.S. (1964a). Planetary waves on a rotating sphere I. Proc. Roy. Soc. London 279, 446 – 473.
Longuet-Higgins, M.S. (1964b). On group velocity and energy flux in planetary wave motions. Deep-Sea Res. 11, 35 – 42.
Longuet-Higgins, M.S. (1965). Planetary waves on a rotating sphere II. Proc. Roy. Soc. London 284, 40 – 68.
Longuet-Higgins, M.S. (1968). Double Kelvin waves with continuous depth profiles. J. Fluid Mech. 34, 49 – 80.
Lorenz, E.N. (1951). Seasonal and irregular variations of the Northern Hemisphere sea-level pressure profile. J. Meteorol. 8, 52 – 59.
Matsno, T. (1970). Vertical propagation of stationary planetary waves in the winter Northern Hemisphere. J. Atmos. Sci. 27, 871 – 883.
Newell, R.E., Kidson, J.W., Vincent, D.G., and Boer, B.I. (1972). The General Circulation of the Tropical Atmosphere and Interactions with Extratropical Latitudes, Vol. I. MIT Press, Cambridge, Mass.
Philander, S.G. (1990). El Nino, La Nina, and the Southern Oscillation. Academic Press, New York.
Phillips, N.A. (1973). Principles of large-scale numerical weather prediction. In Dynamical Meteorology, P. Morel, Ed. Reidel, Hingham, Mass., pp. 1 – 96.
Rayleigh, Lord (1877). Theory of Sound, Vol. I. Macmillan Company, London. Reprinted 1945, Dover, New York.
Rhines, P.B. (1969). Slow oscillation in an ocean of varying depth. Part I: Abrupt topography. J. Fluid Mech. 37, 161 – 189.
Rossby, C.G. (1945). On the propagation of frequencies and energy in certain types of oceanic and atmospheric waves. J. Meteorol. 2, 187 – 204.
Rossby, C.G. (1949). On the dispersion of planetary waves in a barotropic atmosphere. Tellus 1, 54 – 58.
Schopf, P.S., Anderson, D.L.T., and Smith, R. (1981). Beta-dispersion of low-frequency Rossby waves. Dyn. Atmos. Oceans 5, 187 – 214.
Skovgaard, O., Johsson, I.G., and Bertelson, J.A. (1975). Computation of wave heights due to refraction and friction. Proc. Am. Soc. Civ. Engr., J. Waterways, Harbors and Boastal Engin. Div. 101 (WWL), 15 – 32.
Skovgaard, O., Johsson, I.G., and Bertelson, J.A. (1976). Computation of wave heights due to refraction and friction (closure). Proc. Am. Soc. Civ. Eng., J. Waterways, Harbors and Coastal Engin. Div. 102 (WWL), 100 – 105.
Smith, R. (1971). The ray paths of topographic Rossby waves. Deep-Sea Res. 18, 477 – 483.
Tolstoy, I. (1973). Wave Propagation. McGraw-Hill, New York.
Trefethen, L.N. (1982). Group velocity in finite difference schemes. SIAM Rev. 23, 113 – 136.
Tung, K.K., and Lindzen, R.S. (1979a). A theory of stationary long waves. Part I: A simple theory of blocking. Mon. Wea. Rev. 107, 714 – 734.
Tung, K.K., and Lindzen, R.S. (1979b). A theory of stationary long waves. Part II: Resonant Rossby waves in the presence of realistic vertical shears. Mon. Wea. Rev. 107, 735 – 756.
Vichnevetsky, R. (1981). Energy, group velocity in semi-discretizations of hyperbolic equations. Math. Comp. Simulation 23, 333 – 343.
Vichnevetsky, R. (1984a). The energy flow equation. Math. Comp. Simulation 26, 93 – 101.
Vichnevetsky, R. (1984b). The mathematics of energy propagation in numerical approximations of hyperbolic equations. In Advances in Computer Methods for Partial Differential Equations V, R. Vichnevetsky and R.S. Stepleman, Eds. IMACS, New Brunswick, N.J., 133 – 166.
Vichnevetsky, R. (1987). Wave propagation and reflection in irregular grids for hyperbolic equations. Appl. Numer. Math. 3, 133-166; or In Numerical Fluid Dynamics, R. Vichnevetsky, Ed. North-Holland, Amsterdam.
Walker, G.T., and Bliss, E.W. (1932). World Weather V. Mem. Roy. Metero. Soc. 4, 53 – 84.
Wallace, J.M., and Gutzler, D.S. (1981). Teleconnections in the geopotential height field during the Northern Hemisphere winter. Mon. Wea. Rev. 109, 784 – 813.
Webster, P.J., and Holton, J.R. (1982). Cross equatorial response to middle-latitude forcing in a zonally varying basic state. J. Atmos. Sci. 39, 722 – 733.
Yang, H., and Yang, D. (1988). Jet stream and the stationary forcing Rossby wave packet in relation to the teleconnection in the atmosphere. Acta Meteor. Sinica 46, 403 – 411.
Yang, H., and Yang, D. (1990). Forced Rossby wave propagation and tele-connections in the atmosphere. Acta Meteor. Sinica 4, 18 – 26.
Yeh, T.C. (1949). On energy dispersion in the atmosphere. J. Meteorol. 6, 1 – 16.
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Yang, H. (1991). Wave Packets and Teleconnections. In: Wave Packets and Their Bifurcations in Geophysical Fluid Dynamics. Applied Mathematical Sciences, vol 85. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4381-4_8
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DOI: https://doi.org/10.1007/978-1-4757-4381-4_8
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