Trojan Skeletons in the Climate System: Effective Hamiltonian Structures in Dissipative Ocean-Atmosphere Dynamics

Abstract

This paper introduces the Trojan Skeleton framework, which provides a mathematical explanation for how coherent structures persist in the dissipative, forced climate system. Despite being driven by irreversible processes like turbulent mixing and radiative transfer, climate subsystems such as Arctic sea ice, the Atlantic Meridional Overturning Circulation, and El Niño-Southern Oscillation exhibit remarkably organized behavior over long timescales. The core insight is that these systems possess an effective Hamiltonian skeleton that emerges through center manifold reduction and averaging. This skeleton consists of two dominant oscillatory modes, a finite spectral gap between their frequencies, and a near-integrable architecture that suppresses chaotic transport. For this skeleton to persist, dissipation and external forcing must remain small relative to the spectral gap. The paper introduces two key diagnostic ratios: the Dissipation-Gap Ratio and the Forcing-Gap Ratio. When both remain below unity, the system is in the Trojan regime and maintains coherent behavior. When either ratio exceeds unity, the skeleton breaks and the system becomes transport-dominated, potentially leading to regime shifts. The framework connects naturally to existing quasipotential theory for AMOC tipping, where the barrier height is inversely related to the resonance gap. For ENSO, the recharge oscillator model emerges as the prototypical Trojan Skeleton. The paper provides a practical procedure for computing these diagnostics from model output and offers a falsifiable prediction: climate subsystems with small dissipation and forcing ratios should exhibit Trojan stability, while those with large ratios are vulnerable to collapse.