Research Talk: Energy Cascades, Coherent Structures, and the Arrow of Time in Turbulence

Doug Kelley

The colorful swirls in this image represent measurements of how energy flows in turbulent fluids.

Turbulent fluids are ubiquitous — from the blood in your heart, to the air flow around a baseball, to the currents in the ocean and weather. These fluid flows play crucial roles in the transport of energy and other substances through the world. Despite its importance and ubiquity, understanding turbulence is among the most challenging problems in science and engineering. 

If you would like to learn more about turbulence, please come hear Doug Kelley, from the University of Rochester, speak on his lab's fundamental research on turbulence at 4 p.m. Friday, Nov. 22, in Physics Building 133. This talk is sponsored by the Department of Physics.

Turbulent and chaotic fluid flows are classic examples of nonlinear physics. Their hallmarks include interactions among length scales that lead to energy transfer, and rapid scalar mixing, often characterized using Lagrangian Coherent Structures (LCS).

LCS come in two types, which mark regions of strongest nonlinearity in forward- and backward-time flow, respectively. But prior observations have shown a time asymmetry: in two-dimensional (2D) flow, backward-time LCS move around more than forward-time LCS. What sets the arrow of time in turbulence?

Kelley's research links the time asymmetry to energy cascades. They show that a prescribed toy-model flow with the same asymmetry transfers energy to larger length scales, as in real 2D flow, but a prescribed flow with the opposite asymmetry transfers energy to smaller scales, which is non-physical. They also show that in three-dimensional (3D) simulations and in a 3D prescribed flow, the asymmetry of LCS motion is reversed along with the cascade direction, such that forward-time LCS move around more if and only if energy cascades to smaller length scales, as in real 3D flow.

Kelley's results suggest a deep connection between the irreversibility of LCS motion and the energy cascade direction, and could contribute to forecasting LCS dynamics.