Forecasting Fluid Flows Using the Geometry of Turbulence

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.

References in corpus (1)

• Relative periodic orbits in transitional pipe flow

Cited by in corpus (30)

• Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
• Optimal Control of Active Nematics
• Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits
• Data-driven discovery of partial differential equation models with latent variables
• Symmetry-reduced Dynamic Mode Decomposition of Near-wall Turbulence
• Closed-loop adaptive control of extreme events in a turbulent flow
• Exact coherent structures and shadowing in turbulent Taylor-Couette flow
• Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states
• Heteroclinic path to spatially localized chaos in pipe flow
• Complexity of the laminar-turbulent boundary in pipe flow
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
• Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states
• Linear feedback control of invariant solutions in channel flow
• A novel subcritical transition to turbulence in Taylor-Couette flow with counter-rotating cylinders
• Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow
• Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers
• Observing a Dynamical Skeleton of Turbulence in Taylor-Couette Flow Experiments
• Mechanism for Sequestering Magnetic Energy at Large Scales in Shear-Flow Turbulence
• Analysis and modeling of localized invariant solutions in pipe flow
• Stably stratified exact coherent structures in shear flow: the effect of Prandtl number
• Jacobian-Free Variational Method for Constructing Connecting Orbits in Nonlinear Dynamical Systems
• Data-driven guessing and gluing of unstable periodic orbits
• Adjoint-based variational method for constructing periodic orbits of high-dimensional chaotic systems
• Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
• A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows
• Dynamics-based machine learning of transitions in Couette flow
• Exploring the role of diffusive coupling in spatiotemporal chaos
• Data-driven detection of drifting system parameters