GALCIT Colloquium

The answer is yes. Turbulent flows in the presence of bounding surfaces, as those occurring in oceanic and atmospheric currents, around vehicles, or inside pipes, may be apprehended as a collection of whirls or eddies. These eddies follow a regeneration cycle, i.e, existing eddies are seeds for the origin of new ones and so forth.  Understanding this process is critical for the modeling and control of geophysical and industrial flows where a non-negligible fraction of the energy is dissipated by turbulence in the immediate vicinity of walls. In the present work, we examine the causal interactions among energy-containing eddies in wall-bounded turbulence by measuring how the knowledge of past states of the eddies reduces the uncertainty of future states. Our approach unveils, in a simple manner, that causality of energy-eddies at a given scale is essentially universal and independent of the eddy-size.  This observation is accompanied by striking implications for control and modeling of turbulent flows. We show, using neural networks as an example, that novel eddy prediction techniques can be devised for the computationally more affordable smaller eddies, while still being a faithful approach applicable to larger eddies which are intractable even with the current state-of-the-art supercomputers.