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Number theoretical views on resonant Rossby wave triads: graphs with vertices on quartics. (English) Zbl 1440.76013

Summary: The paper provides new insights and new results for resonance triads of Rossby waves which are described as solutions of a Diophantine equation: we have derived a new description using undirected graphs and we have proven their most essential properties as well as a suitably complementary description by fourth degree curves – bicircular quartics.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
11Z05 Miscellaneous applications of number theory
11D25 Cubic and quartic Diophantine equations
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