Identifying causal significance in three-dimensional isotropic turbulence

Abstract

Flow patterns of causal significance to three-dimensional isotropic turbulence are identified through the recently introduced algorithm of Jim\'enez (2018). Localised perturbations are introduced at arbitrary regions of a triple-periodic decaying flow at ${Re}_\lambda \approx 190$, and their evolution is used as a marker of the significance of said regions to the flow. Their dimensions are found to be an important parameter, with sizes of the order of the integral scale being controlled by the kinetic energy content, and sizes within the dissipative range, by the enstrophy and dissipation. The three quantities are found to be important at intermediate (inertial) scales. Prominent differences emerge between regions of high and low significance. The former typically contain strong gradients and/or kinetic energy and the latter are weak. An analysis of the structure of significant and insignificant flow patterns reveals that strain is more efficient than vorticity at propagating the contents of the perturbation to other regions of the flow. Moreover, the flow patterns of significant regions are found to be more complex, typically containing vortex clusters, while simpler vortex sheets are found in insignificant regions. The present results suggest that strategies aiming to manipulate the flow should focus on strain-dominated vortex clusters, avoiding enstrophy-dominated vortex sheets. This is confirmed through an assimilation experiment, in which greater synchronisation between two simulations is achieved when simulations share significant regions rather than insignificant ones. These conclusions have implications for both the control of turbulent flows and the making of predictions based on limited or noisy measurements.