Abstract
Suppose the medium is not homogeneous. For example, gravity waves impinging on a beach see of varying depth as the waves run up the beach, acoustic waves see fluid of varying pressure and temperature as they propagate vertically, etc. Then a pure plane wave in which all attributes of the wave are constant in space (and time) will not be a proper description of the wave field. Nevertheless, if the changes in the background occur on scales that are long and slow compared to the wavelength and period of the wave, a plane wave representation may be locally appropriate (Fig. 2.1). Even in a ho¬mogeneous medium, the wave might change its length if the wave is a superposition of plane waves (as we shall see later).
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References
Bretherton FP (1971) The general linearized theory of wave propagation. In: Reid WH (ed) Mathematical problems in the geophysical sciences, vol 1. American Mathematical Society, pp 61–102
Pedlosky J (1987) Geophysical fluid dynamics. Springer-Verlag, New York, pp 710
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Pedlosky, J. (2003). Kinematic Generalization. In: Waves in the Ocean and Atmosphere. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05131-3_2
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DOI: https://doi.org/10.1007/978-3-662-05131-3_2
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