Fluid Dynamic Seminar
Abstract:
Unstable periodic orbits (UPOs) are the building blocks of chaotic attractors and possibly turbulent attractors too. The current state-of-the-art for finding UPOs in a turbulent flow – recurrent flow analysis – begins with a search for ‘near recurrences’ in a time series, measured as local minima in an $l_2$-norm between snapshots of the flow. The approach is crude and struggles to identify UPOs which are visited only fleetingly or which may be spatially localised. In this talk I will discuss two new approaches that appear to overcome these issues. The first is based on dynamic mode decomposition, which can be applied to short turbulent trajectories to identify the signature of nearby periodic orbits in phase space without needing to see a near recurrence, and also to build robust guesses for input to a Newton solver. The second approach utilises convolutional neural networks to find efficient low dimensional representations of a turbulent flow. These embeddings can be used to define new observables for recurrent flow analysis, allowing an order of magnitude more UPOs to be identified and converged in a long time series than with the standard approach.