Topological modes of variability of the wind-driven ocean circulation

Area of Science:

• Complex Systems Dynamics
• Topology in Physics
• Oceanography

Background:

• Templexes are topological objects representing flow organization in phase space.
• Understanding variability in complex systems often requires methods beyond linear dynamics.

Purpose of the Study:

• Introduce topological modes of variability (TMVs) as dynamical manifestations of topological cycles (generatexes).
• Link abstract topological invariants to time-dependent behavior in models and observations.
• Provide a new framework for analyzing variability in complex systems.

Main Methods:

• Building upon the concept of templexes.
• Defining topological modes of variability (TMVs) from generatexes.
• Applying the approach to a low-order wind-driven ocean circulation model.

Main Results:

• Demonstrated the emergence and vanishing of TMVs in response to periodic and aperiodic forcing.
• Showcased TMVs as dynamical manifestations of algebraic cycles within templexes.
• Illustrated a concrete link between topological invariants and time-dependent behavior.

Conclusions:

• TMVs offer a qualitatively new understanding of variability in complex systems.
• This approach is particularly valuable where linear modes are insufficient for nonlinear dynamics.
• TMVs provide a powerful tool for analyzing complex system behavior in nonautonomous settings.