Prediction of closed diffusion barriers in axisymmetric Taylor-Couette flow

Reliable identification of Lagrangian coherent structures (LCS) plays a key role in understanding and predicting how the transport of mass and momentum organises itself in turbulent fluid flows. A newly developed method (Haller et al. PNAS, subm.) enables us to detect elliptic LCS as vortex-type barriers to diffusive transport. These diffusion barriers (DB) are constructed mathematically as closed material surfaces that block the diffusion of passive scalars more than any other neighbouring surface.

Here, we apply this method for the first time to axisymmetric Taylor-Couette flow. By means of direct numerical simulations we generated dense time series of the full velocity field for a substantial range of Re ≤ 20000 using our pseudo-spectral Navier-Stokes solver nsCouette (Shi et al. Comp. Fluids 106, 2015). Here Re = ^du/_ν is the Reynolds number based on the gap width d, viscosity ν and rotation speed u of the inner cylinder, whereas the outer cylinder is kept stationary. Thus, we were able to identify closed diffusion barriers and track their individual evolution in time for different realisations of the instantaneous flow field. Furthermore, we track how DB change and disappear as Re increases.