Forecasting the evolution of three-dimensional turbulent recirculating flows from sparse sensor data
Author(s)
Lu, Shengqi
Papadakis, George
Type
Journal Article
Abstract
A data-driven algorithm is proposed that employs sparse data from velocity and/or scalar sensors to forecast the future evolution of three-dimensional turbulent flows. The algorithm combines time-delayed embedding together with Koopman theory and linear optimal estimation theory. It consists of three steps: dimensionality reduction, currently with proper orthogonal decomposition (POD); construction of a linear dynamical system for current and future POD coefficients; and system closure using sparse sensor measurements. In essence, the algorithm establishes a mapping from current sparse data to the future state of the dominant structures of the flow over a specified time window. The method is scalable (i.e. applicable to very large systems), physically interpretable and provides sequential forecasting on a sliding time window of prespecified length. It is applied to the turbulent recirculating flow over a surface-mounted cube (with more than 10⁸ degrees of freedom) and is able to forecast accurately the future evolution of the most dominant structures over a time window at least two orders of magnitude larger that the (estimated) Lyapunov time scale of the flow. Most importantly, increasing the size of the forecasting window only slightly reduces the accuracy of the estimated future states.
Date Issued
2026-03-10
Date Acceptance
2026-01-26
Citation
Journal of Fluid Mechanics, 2026, 1030
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Journal of Fluid Mechanics
Volume
1030
Copyright Statement
© The Author(s), 2026. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Publication Status
Published
Article Number
A21
Date Publish Online
2026-03-02