Javier Jiménez: Fake Turbulence

Abstract

Turbulence is a high-dimensional dynamical system with known equations of motion. It can be numerically integrated, but the simulation results are also high-dimensional and hard to interpret. Lower-dimensional models are not dynamical systems, because some dynamics is discarded in the projection, and a stochastic Perron-Frobenius operator substitutes the equations of motion. Using as example turbulent flows at moderate but non-trivial Reynolds number, we show that particularly deterministic projections can be identified by either Monte-Carlo or exhaustive testing, and can be interpreted as coherent structures. We also show that they can be used to construct data-driven ‘fake’ models that retain many of the statistical characteristics of the real flow.