Yamada, Michio; Yoneda, Tsuyoshi A note on resonant interaction of Rossby waves in two-dimensional flow on a \(\beta\) plane. (English) Zbl 1298.35159 Chen, Hua (ed.) et al., Emerging topics on differential equations and their applications. Proceedings on Sino-Japan conference of young mathematicians (SJCYM), Nankai University, Tianjin, People’s Republic of China, December 5–9, 2011. Hackensack, NJ: World Scientific (ISBN 978-981-4449-74-8/hbk; 978-981-4449-76-2/ebook). Nankai Series in Pure, Applied Mathematics and Theoretical Physics 10, 239-246 (2013). Summary: An incompressible two-dimensional flow on a \(\beta\) plane is considered. Rossby waves are generally expected to dominate the \(\beta\) plane dynamics, and here in this paper we introduce a mathematical theorem that at a high \(\beta\), the flow dynamics are governed exclusively by the resonant interactions of Rossby waves.For the entire collection see [Zbl 1279.35001]. MSC: 35Q35 PDEs in connection with fluid mechanics 76B65 Rossby waves (MSC2010) 76W05 Magnetohydrodynamics and electrohydrodynamics Keywords:Navier-Stokes equations; \(\beta\) plane; Rossby waves; three-wave resonance PDFBibTeX XMLCite \textit{M. Yamada} and \textit{T. Yoneda}, Nankai Ser. Pure Appl. Math. Theor. Phys. 10, 239--246 (2013; Zbl 1298.35159) Full Text: DOI