Georgia Institute of Technology College of Sciences

Several recent papers presented exact time-periodic solutions in shear flow simulations at moderate Reynolds numbers. Although some of these studies demonstrated similarities between turbulence and the unstable periodic orbits, whether one can utilize these orbits for turbulence modeling remained unclear. We argue that this can be achieved by measuring the frequency of turbulence's visits to the periodic orbits. To this end, we adapt methods from computational topology and develop a metric that quantifies shape similarity between the projections of turbulent trajectories and periodic orbits. We demonstrate our method by applying it in a numerical study of the three-dimensional Navier--Stokes equations under sinusoidal forcing. Streamed online: https://gatech.bluejeans.com/7678987299