Time-delay embedding of Lagrangian turbulence to identify precursors of extreme events

Lagrangian evolution of turbulence dissipation rate and its extreme occurrences may depend on the temporal history of evolution of dissipation rate itself and other flow quantities. This dependence is not well understood and difficult to isolate. In this work, we investigate the latent dynamics of turbulence intermittency present in the time-delay embedding of Lagrangian evolution of energy dissipation rate obtained from direct numerical simulations (DNS) of forced isotropic turbulence. The three-dimensional attractor constructed from its leading eigen-time-delay coordinates, representing the most dominant self-similar features of energy dissipation rate, shows a unique structure in isotropic turbulent flows. To predict the occurrence of extreme events in dissipation rate, we further investigate the time-delay embedding of other turbulence quantities including pressure which is experimentally easily measurable. Delay-embedded chaotic time series is decomposed into linear dynamics and nonlinear (intermittent) forcing using a Hankel alternative view of Koopman (HAVOK) model. Trained on part of a Lagrangian trajectory, the model closely reconstructs the test portion of the trajectory, especially for less intermittent time series. Finally, we demonstrate the use of this intermittent forcing of eigen-time-delay coordinates of pressure and its Hessian as potential precursors for predicting the occurrence of extreme dissipation rate in a turbulent flow.