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# l1-based sparsification of energy interactions in unsteady lid-driven cavity flow

Rubini, Riccardo, Lasagna, Davide and Da Ronch, Andrea (2020) l1-based sparsification of energy interactions in unsteady lid-driven cavity flow. Journal of Fluid Mechanics, 905, [A15].

Record type: Article

## Abstract

In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach produces interpretable, sparsely-connected models that reproduce the original dynamical behaviour at a much lower computational cost, as fewer triadic interactions need to be evaluated. The key feature of the approach is that dominant interactions are selected systematically from the solution of a convex optimisation problem, with a unique solution, and no a priori assumptions on the structure of scale interactions are required. We demonstrate this approach on models of two-dimensional lid-driven cavity flow at Reynolds number $Re = 2 \times 10^4$, where fluid motion is chaotic. To understand the role of the subspace utilised for the Galerkin projection on sparsity characteristics, we consider two families of models obtained from two different modal decomposition techniques. The first uses energy-optimal Proper Orthogonal Decomposition modes, while the second uses modes oscillating at a single frequency obtained from Discrete Fourier Transform of the flow snapshots. We show that, in both cases, and despite no a priori physical knowledge is incorporated into the approach, relevant interactions across the hierarchy of modes are identified in agreement with the expected picture of scale interactions in two-dimensional turbulence. Yet, substantial structural changes in the interaction pattern and a quantitatively different sparsity are observed. Finally, although not directly enforced in the procedure, the sparsified models have excellent long-term stability properties and correctly reproduce the spatio-temporal evolution of dominant flow structures in the cavity.

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l_1-based sparsification of energy interactions in unsteady lid-driven cavity flow - Accepted Manuscript

Accepted/In Press date: 15 August 2020
e-pub ahead of print date: 26 October 2020
Published date: 1 December 2020
Keywords: l1 regularization, Triadic Interactions, Reduced order model

## Identifiers

Local EPrints ID: 443537
URI: http://eprints.soton.ac.uk/id/eprint/443537
ISSN: 0022-1120
PURE UUID: 88b48bc7-ab21-44d9-8b7c-5534ba0c8f07
ORCID for Davide Lasagna: orcid.org/0000-0002-6501-6041
ORCID for Andrea Da Ronch: orcid.org/0000-0001-7428-6935

## Catalogue record

Date deposited: 28 Aug 2020 16:31

## Contributors

Author: Riccardo Rubini
Author: Davide Lasagna
Author: Andrea Da Ronch