From many to few: how modal analysis benefits active turbulence

Delighted to announce the publication of the first of our works from my time at Tufts University with Prof. Jeffrey Guasto in Physical Review Fluids! This work was driven by Olivia G. Martin, an exceptional undergraduate who joined our lab for their senior thesis. I’m particularly proud that this work has been highlighted as an Editors’ Suggestion, which was a very pleasant surprise!

In this paper, we took a tool typically reserved for convential turbulence systems – proper orthogonal decomposition (POD) – and applied it to the turbulent-like behaviour of dense suspensions of swimming bacteria. In such densities, these “active turbulence” suspensions form jets and vortices, and enhance the motility/transport of the individual cells. Aside from bulk statistical techniques, there has been limited experimental progress in understanding the underlying flow structures, and computational/numerical methods have been hamstrung by the sheer complexity and scale (and noise!) of the datasets required to capture the dynamics of such chaotic systems.

This is where POD comes into play – POD allows us to separate a flow field into fundamental components (“modes”), find a small collection of these modes that capture the majority of the energy of the system, then reconstruct a smoother, reduced-order flow field. In the bulk case, we find that as little as 3% of the original data is needed to reconstruct active turbulence whilst retaining the relevant spatio-temporal scales that define this system.

We then expanded this analysis to two specific case studies: what happens when active turbulence is subject to varying confinement, and when an external flow is applied. In these non-isotropic cases, POD accurately captured the transitions to chaotic flow, the boundary-driven flows, and the transport of coherent structures through the flow.

In summary, POD provides a highly-compact description of experimental data of active turbulence, and we anticpate that such low-dimensional representations will prove useful in future for helping faciliate data-driven models of active turbulence!

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