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Complete classification of discrete resonant Rossby/drift wave triads on periodic domains

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We consider the set of Diophantine equations that arise in the context of the partial differential equation called “barotropic vorticity equation” on periodic domains, when nonlinear wave interactions are studied to leading order in the amplitudes. The solutions to this set of Diophantine equations are of interest in atmosphere (Rossby waves) and Tokamak plasmas (drift waves), because they provide the values of the spectral wavevectors that interact resonantly via three-wave interactions. These wavenumbers come in “triads”. We provide the full solution to the Diophantine equations in the physically sensible limit when the Rossby deformation radius is infinite.

Author(s):

Miguel Bustamante    
University College Dublin
Ireland

Umar Hayat    
University College Dublin
Ireland