Interaction between high- and low-frequency waves

Abstract

We outline models for the interaction between high- and low-frequency waves that arise in plasma physics and atmosphere/ocean dynamics. The original ideas are embodied in the Zakharov equations, which describe the interaction between high-frequency (Langmuir) electrostatic waves and low-frequency (ion-acoustic) electron density perturbations. Analogous equations have been developed in atmospheric physics (describing the interaction between acoustic waves and internal gravity waves) and atmosphere/ocean dynamics in which the coupling between the higher-frequency inertial waves and lower-frequency planetary Rossby waves is analyzed. The last two cases are more complicated than the original Zakharov equations because of the dispersive and anisotropic nature of the natural modes of the system.