Revisiting the Dynamical Properties of Pedlosky's Two-Layer Model for Finite Amplitude Baroclinic Waves

TL;DR

This paper analyzes Pedlosky's two-layer model for finite amplitude baroclinic waves, revealing complex dynamical regimes, bifurcations, and chaos influenced by dissipation, using modern nonlinear techniques and computational methods.

Contribution

It revisits the classical model with modern tools, demonstrating integrability in the inviscid limit and detailed bifurcation analysis under dissipation effects.

Findings

Model is integrable in the inviscid limit.

Dissipation induces bifurcations leading to chaos.

Multiple attractors coexist depending on initial conditions.

Abstract

Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite perturbations - leveraging modern nonlinear techniques and computational resources. We show that the geophysical state of the baroclinic wave exhibits a rich diversity of dynamical regimes governed by the level of dissipation induced by Ekman boundary layers. In the inviscid limit, we demonstrate that the model is integrable. Upon increasing dissipation, the system undergoes a complex sequence of bifurcations. On one hand, deterministic chaos, identified by means of the Lyapunov exponents, provides a genuine mechanism for destabilization of the wave. On the other hand, in regimes where the wave equilibrates, dependence on the initial condition is crucial, eventually leading to the coexistence of multiple attractors. We study the governing equations of the model and their truncation to a finite-dimensional system of ordinary differential equations, together with the minimal low-order truncated system which is structurally equivalent to the Lorenz model. Its bifurcation diagram allows for elucidating the transition of the wave amplitude from stable equilibration to periodic oscillations - terminating in homoclinic orbits - and, ultimately, deterministic chaos through a period-doubling route. We finally comment on the robustness of these features for higher-dimensional models.