Fluctuations, Response, and Resonances in a Simple Atmospheric Model

TL;DR

This paper investigates how a simple atmospheric model responds to different perturbations, revealing resonant behaviors and violations of classical statistical mechanics principles, with implications for understanding climate dynamics.

Contribution

It applies Ruelle response theory and Lyapunov analysis to identify resonant responses and their origins in a simplified atmospheric model, advancing climate dynamics understanding.

Findings

Resonant Rossby-like wave response to orographic forcing.

Violation of fluctuation-dissipation theorem in the model.

Resonance linked to unstable periodic orbits.

Abstract

We study the response of a simple quasi-geostrophic barotropic model of the atmosphere to various classes of perturbations affecting its forcing and its dissipation using the formalism of the Ruelle response theory. We investigate the geometry of such perturbations by constructing the covariant Lyapunov vectors of the unperturbed system and discover in one specific case - orographic forcing - a substantial projection of the forcing onto the stable directions of the flow. This results into a resonant response shaped as a Rossby-like wave that has no resemblance to the unforced variability in the same range of spatial and temporal scales. Such a climatic surprise corresponds to a violation of the fluctuation-dissipation theorem, in agreement with the basic tenets of nonequilibrium statistical mechanics. The resonance can be attributed to a specific group of rarely visited unstable periodic orbits of the unperturbed system. Our results reinforce the idea of using basic methods of nonequilibrium statistical mechanics and high-dimensional chaotic dynamical systems to approach the problem of understanding climate dynamics.