Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow

• URL: http://arxiv.org/abs/2301.04638v1
• Date: Wed, 11 Jan 2023 18:50:08 GMT
• Title: Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow
• Authors: Alec J. Linot and Michael D. Graham
• Abstract summary: We show that a description of turbulent Couette flow is possible using a data-driven manifold dynamics modeling method. We build models with fewer than $20$ degrees of freedom that quantitatively capture key characteristics of the flow. For comparison, we show that the models outperform POD-Galerkin models with $sim$2000 degrees of freedom.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this manifold, the state of the system can be exactly described in a coordinate system parameterizing the manifold. Describing the system in this low-dimensional coordinate system allows for much faster simulations and analysis. We show, for turbulent Couette flow, that this description of the dynamics is possible using a data-driven manifold dynamics modeling method. This approach consists of an autoencoder to find a low-dimensional manifold coordinate system and a set of ordinary differential equations defined by a neural network. Specifically, we apply this method to minimal flow unit turbulent plane Couette flow at $\textit{Re}=400$, where a fully resolved solutions requires $\mathcal{O}(10^5)$ degrees of freedom. Using only data from this simulation we build models with fewer than $20$ degrees of freedom that quantitatively capture key characteristics of the flow, including the streak breakdown and regeneration cycle. At short-times, the models track the true trajectory for multiple Lyapunov times, and, at long-times, the models capture the Reynolds stress and the energy balance. For comparison, we show that the models outperform POD-Galerkin models with $\sim$2000 degrees of freedom. Finally, we compute unstable periodic orbits from the models. Many of these closely resemble previously computed orbits for the full system; additionally, we find nine orbits that correspond to previously unknown solutions in the full system.

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