Stabilising a travelling wave from 2D turbulence —Dan Lucas (Keele University)

This movie shows the direct numerical simulation of a two-dimensional body-forced incompressible Navier-Stokes flow with periodic boundary conditions. At early times the movie shows typical 2D turbulence at Re=200. We then apply a time-delayed feedback term in the equations (Pyragas Phys. Letters A 1992). This term allows us to stabilise the T1 travelling wave reported in Chandler & Kerswell (J. Fluid Mech. 2013). This is made possible by making use of the underlying symmetry of the target solution to avoid the well-known "odd-number" limitation, and we dynamically adapt the translation (in the streamwise direction) of the feedback term to match the phase speed of the solution. We find several solutions can be stabilised in this way.