Extracting Coherent Structures from Turbulence

We consider the problem of extracting dynamically-important exact solutions of the Navier-Stokes equations directly from turbulent flows. By monitoring near-recurrences of the flow in direct numerical simulations of 2D body-forced turbulence, we uncover an array of equilibrium points, travelling waves and periodic orbits over a range of Reynolds numbers, which underpin the complicated dynamics seen. Progress will be discussed in determining whether these solutions can then be used to predict the mean statistics of the turbulence (in the spirit of Kawahara \& Kida 2001).