Finite-Time Analysis of Crises in a Chaotically Forced Ocean Model

TL;DR

This paper analyzes how chaotic attractors in a coupled ocean model undergo crises as forcing increases, revealing new types of boundary crises and the loss of hyperbolicity, with implications for understanding climate system stability.

Contribution

It introduces a detailed finite-time analysis of crises in a coupled ocean model, including a novel vanishing basin crisis and the generality of these phenomena across different strange attractors.

Findings

Identification of a new vanishing basin crisis subtype.

Visualization of chaotic saddle collisions during boundary crises.

Demonstration of the robustness of crisis phenomena across models.

Abstract

We consider a coupling of the Stommel box model and the Lorenz model, with the goal of investigating the so-called "crises" that are known to occur given sufficient forcing. In this context, a crisis is characterized as the destruction of a chaotic attractor under a critical forcing strength. We document the variety of chaotic attractors and crises possible in our model, focusing on the parameter region where the Lorenz model is always chaotic and where bistability exists in the Stommel box model. The chaotic saddle collisions that occur in a boundary crisis are visualized, with the chaotic saddle computed using the Saddle-Straddle Algorithm. We identify a novel sub-type of boundary crisis, namely a vanishing basin crisis. For forcing strength beyond the crisis, we demonstrate the possibility of a merging between the persisting chaotic attractor and either a chaotic transient or a ghost attractor depending on the type of boundary crisis. An investigation of the finite-time Lyapunov exponents around crisis levels of forcing reveals a convergence between two near-neutral exponents, particularly at points of a trajectory most sensitive to divergence. This points to loss of hyperbolicity associated with crisis occurrence. Finally, we generalize our findings by coupling the Stommel box model to other strange attractors and thereby show that the behaviours are quite generic and robust.