A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves

Kinsler, Paul (2018) A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves. Journal of Physics Communications, 2. ISSN 2399-6528

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Abstract

The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with remarkable efficiency; but propagating in time is more physical and gives correctly behaved reflections and scattering without effort. Which should be chosen in a given situation, and what compromises might have to be made? Here the natural behaviors of each choice of propagation are compared and contrasted for an ordinary second order wave equation, the time-dependent diffusion wave equation, an elastic rod wave equation, and the Stokes'/ van Wijngaarden's equations, each case illuminating a characteristic feature of the technique. Either choice of propagation axis enables a partitioning the wave equation that gives rise to a directional factorization based on a natural "reference" dispersion relation. The resulting exact coupled bidirectional equations then reduce to a single unidirectional first-order wave equation using a simple "slow evolution" assumption that minimizes effect of subsequent approximations, while allowing a direct term-to-term comparison between exact and approximate theories.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Physics Communications
ID Code:
89800
Deposited By:
Deposited On:
22 Jan 2018 16:54
Refereed?:
Yes
Published?:
Published
Last Modified:
28 Nov 2020 05:11