Unraveling Turbulent Pipe Flow Dynamics: Data-Driven Models at Re = 2500

Fluid flows can be computationally demanding due to the need for a large number of degrees of freedom (a high state-space dimension) for accurate simulation. However, despite this requirement, certain flows exhibit a phenomenon where their long-term behaviour can be effectively represented using a much smaller number of dimensions. This behaviour is due to the rapid dissipation of small-scale features through viscous diffusion, leading to the emergence of a finite-dimensional invariant manifold on which the long-time dynamics lie. In this work, we explore the minimal flow unit turbulent pipe flow at Re = 2500, where a fully resolved solutions requires O(10⁵) degrees of freedom. Using only data from this simulation we build models with fewer than 30 degrees of freedom that quantitatively capture key characteristics of the flow. Advanced autoencoders are used for dimension reduction and we apply both a function space approach (Koopman) and state space approach (neural ODE) to build these data-driven models. Our results demonstrate that both frameworks can be used to generate data-driven dynamic models of spatiotemporally chaotic solutions to PDEs in manifold coordinates.