Discrete resonant Rossby/drift wave triads: an explicit parameterisation and a fast direct numerical search algorithm
arXiv:1804.03092 · doi:10.1016/j.cnsns.2019.104896
Abstract
We report results on the explicit parameterisation of discrete Rossby-wave resonant triads of the Charney-Hasegawa-Mima equation in the small-scale limit (i.e. large Rossby deformation radius), following up from our previous solution in terms of elliptic curves (Bustamante and Hayat, 2013). We find an explicit parameterisation of the discrete resonant wavevectors in terms of two rational variables. We show that these new variables are restricted to a bounded region and find this region explicitly. We argue that this can be used to reduce the complexity of a direct numerical search for discrete triad resonances. Also, we introduce a new direct numerical method to search for discrete resonances. This numerical method has complexity , where is the largest wavenumber in the search. We apply this new method to find all discrete irreducible resonant triads in the wavevector box of size , in a calculation that took about days on a -core machine. Finally, based on our method of mapping to elliptic curves, we discuss some dynamical implications regarding the spread of quadratic invariants across scales via resonant triad interactions, in the form of sharp bounds on the size of the interacting wavevectors.
References in corpus (18)
- A weak turbulence theory for incompressible MHD
- Symmetry and resonance in periodic FPU chains
- Mesoscopic wave turbulence
- Discreteness and its effect on the water-wave turbulence
- Discrete and mesoscopic regimes of finite-size wave turbulence
- A Model of Intra-seasonal Oscillations in the Earth atmosphere
- Discrete Wave Turbulence
- Statistical State Dynamics: a new perspective on turbulence in shear flow
- Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system
- Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems
- Laminated Wave Turbulence: Generic Algorithms III
- Complete classification of discrete resonant Rossby/drift wave triads on periodic domains
- Externally forced triads of resonantly interacting waves: boundedness and integrability properties
- Laminated Wave Turbulence: Generic Algorithms II
- Laminated Wave Turbulence: Generic Algorithms I
- Quadratic invariants for discrete clusters of weakly interacting waves
- On the convergence of the normal form transformation in discrete Rossby and drift wave turbulence
- Direct Statistical Simulation of a Jet