A detailed study of the Charney–Hasegawa–Mima model and its extensions is presented.
These simple nonlinear partial differential equations suggested for both Rossby waves in …

Nonlinear resonance analysis is a unique mathematical tool that can be used to study
resonances in relation to, but independently of, any single area of application. This is the first …

We study the modulational instability of geophysical Rossby and plasma drift waves within
the Charney–Hasegawa–Mima (CHM) model both theoretically, using truncated (four-mode …

Two fundamental facts of the modern wave turbulence theory are 1) existence of power
energy spectra in k-space, and 2) existence of “gaps” in this spectra corresponding to the …

In this letter we propose discrete wave turbulence (DWT) as a counterpart of classical
statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the …

We present a theoretical and numerical study of Fourier-space triad phase dynamics in the
one-dimensional stochastically forced Burgers equation at Reynolds number. We …

Motivated by the question of whether and how wave–wave interactions should be
implemented into atmospheric gravity‐wave parametrizations, the modulation of triadic …

A robust energy transfer mechanism is found in nonlinear wave systems, which favors
transfers toward modes interacting via triads with nonzero frequency mismatch, applicable in …

In a linearly stratified fluid, two sets of resonant triads with one member in common, hence
coupled, can arise for a wide range of wave numbers where all five waves travel in the same …

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave
equation. A cluster consists of N modes forming a total of M connected triads. We investigate …