Forecasting Fluid Flows Using the Geometry of Turbulence

TL;DR

This paper uncovers how unstable solutions of the Navier-Stokes equations, called exact coherent structures, influence turbulence dynamics in fluid flows, with implications for improved flow prediction.

Contribution

It combines experimental and numerical methods to identify and demonstrate the significance of unstable equilibrium solutions in turbulent flow evolution.

Findings

Turbulent flows frequently visit neighborhoods of unstable equilibrium solutions.

Unstable manifolds can predict flow evolution over significant time periods.

Experimental and simulation data show consistent signatures of these solutions.

Abstract

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully-resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.