Route to chaos and resonant triads interaction in a truncated rotating nonlinear shallow–water model
Francesco Carbone, Denys Dutykh, Qiang Li, Qiang Li, Qiang Li
TL;DR
This paper studies how a rotating shallow-water model transitions to chaos through two distinct routes as energy increases.
Contribution
A novel phase-amplitude reformulation reveals piece-wise phase locking and stochastic phase shifts in chaotic dynamics.
Findings
Two distinct transitions to chaos occur as energy increases, following Feigenbaum bifurcations and quasi-periodic to chaotic shifts.
Phase components exhibit prolonged locking followed by abrupt ±π shifts, while amplitudes remain chaotic.
Stochastic phase interactions arise from triad combinations and nonlinear terms, even at low energy levels.
Abstract
The route to chaos and the phase dynamics of the large scales in a rotating shallow-water model have been rigorously examined through the construction of an autonomous five-mode Galerkin truncated system employing complex variables, useful in investigating how large/meso-scales are destabilized and how their dynamics evolves and transits to chaos. This investigation revealed two distinct transitions into chaotic behaviour as the level of energy introduced into the system was incrementally increased. The initial transition manifests through a succession of bifurcations that adhere to the established Feigenbaum sequence. Conversely, the subsequent transition, which emerges at elevated levels of injected energy, is marked by a pronounced shift from quasi-periodic states to chaotic regimes. The genesis of the first chaotic state is predominantly attributed to the preeminence of inertial…
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Taxonomy
TopicsOceanographic and Atmospheric Processes · Tropical and Extratropical Cyclones Research · Ocean Waves and Remote Sensing