Multidimensional simple waves in gas dynamics

G. M. Webb, R. Ratkiewicz, M. Brio, G. P. Zank

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A formalism for multidimensional simple waves in gas dynamics using ideas developed by Boillat is investigated. For simple-wave solutions, the physical variables depend on a single function φ(r, t). The wave phase φ(r, t) is implicitly determined by an equation of the form(φ) = r·n(φ)-λ(φ)t, where n(φ) denotes the normal to the wave front, λ is the characteristic speed of the wave mode of interest, r is the position vector, t is the time, and the function f(φ) determines whether the wave is a centred (f(φ) = 0) or a non-centred (f(φ) ≠ 0) wave. Examples are given of time-dependent vortex waves, shear waves and sound waves in one or two space dimensions. The streamlines for the wave reduce to two coupled ordinary differential equations in which the wave phase φ plays the role of a parameter along the streamlines. The streamline equations are expressed in Hamiltonian form. The roles of Clebsch variables, Lagrangian variables, Hamiltonian formulations and characteristic surfaces are briefly discussed.

Original languageEnglish (US)
Pages (from-to)417-460
Number of pages44
JournalJournal of Plasma Physics
Issue number3
StatePublished - Apr 1988


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  • Ion-molecule reactions

ASJC Scopus subject areas

  • Condensed Matter Physics


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