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Resonant interaction of Rossby waves in two-dimensional flow on a \(\beta\) plane. (English) Zbl 1264.35180

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 prove a mathematically rigorous theorem: that at a high \(\beta \), the flow dynamics is governed exclusively by the resonant interactions of Rossby waves.

MSC:

35Q35 PDEs in connection with fluid mechanics
76B65 Rossby waves (MSC2010)
35D30 Weak solutions to PDEs
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