Summary
A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ω is equal to\(\sqrt {(\gamma - 1)/(4\gamma )}\), all horizontal waves are periodic. Here, γ is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.
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Venkatachalappa, M., Rudraiah, N. & Sachdev, P.L. Propagation of quasi-simple waves in a compressible rotating atmosphere. Acta Mechanica 88, 153–166 (1991). https://doi.org/10.1007/BF01177093
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DOI: https://doi.org/10.1007/BF01177093