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ID 57484
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Obuse, Kiori 1Graduate School of Environmental and Life Science, Okayama University Kaken ID researchmap
Yamada, Michio Research Institute for Mathematical Sciences, Kyoto University
Abstract
This paper addresses three-wave resonant interactions of Rossby-Haurwitz waves in two-dimensional turbulence on a rotating sphere. Zonal modes are often omitted from the "resonant wave set" even when they satisfy the conditions for three-wave resonant interactions, as they do not transfer any energy to other modes in a resonant manner. However, the presence of zonal flows induces phase shifts in other modes, and it is not at all clear that their influence is negligible. Since it is expected that three-wave resonant interactions govern the entire dynamics of turbulence if the rotation rate of the sphere is sufficiently high, by analogy with the theorem regarding three-wave resonant interactions of Rossby waves on a beta plane with sufficiently large beta previously proven by Yamada and Yoneda [Physica D 245, 1 (2013)], an appropriate definition of the resonant wave set was determined by comparing the time evolution of several wave sets on a rapidly rotating sphere. It was found that zonal waves of the form Y-l(m=0) exp(i omega t) with odd l, where Y(l)(m )are the spherical harmonics, should be considered for inclusion in the resonant wave set to ensure that the dynamics of the resonant wave set determine the overall dynamics of the turbulence on a rapidly rotating sphere. Consequently, it is suggested that the minimal resonant wave set that must be considered in the discussion of the three-wave interaction of Rossby-Haurwitz waves is the set consisting of nonzonal resonant waves and zonal waves of the form Y-l(0) exp(icot) with odd l.
Published Date
2019-02-01
Publication Title
Physical Review Fluids
Volume
volume4
Issue
issue2
Publisher
American Physical Society
Start Page
024601
ISSN
2469990X
Content Type
Journal Article
language
英語
OAI-PMH Set
岡山大学
Copyright Holders
©2019 American Physical Society
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publisher
DOI
Web of Science KeyUT
Related Url
isVersionOf https://doi.org/10.1103/PhysRevFluids.4.024601
Funder Name
Japan Society for the Promotion of Science
助成番号
17H02860
15K13458
24340016