Finite-Dimensional Turbulence of Planetary Waves

TL;DR

This paper investigates finite-dimensional wave turbulence in planetary (Rossby) waves, classifying energy flux scenarios, analyzing chaotic dynamics, and highlighting differences from infinite-system wave turbulence, with broad applicability across various physical systems.

Contribution

It provides a classification of energy cascade termination scenarios and analyzes chaotic dynamics in finite wave clusters, emphasizing differences from kinetic wave turbulence in infinite systems.

Findings

Classified all energy cascade termination cases.

Analyzed free and forced chaotic dynamics in wave clusters.

Confirmed fundamental differences from infinite wave turbulence.

Abstract

Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finite-dimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wave kinetic equations that account for interactions with overlapping quasi-resonances of finite amplitude waves. The present results are directly applicable to finite-dimensional wave turbulence in any wave system in finite domains with 3-mode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.