A Non-Local Characterization of Coherent Regions in Turbulence: Disentangling Turbulence Eddies

The description of coherent motion in turbulent flows and the identification of eddies have been a topic of long standing debate. There exist numerous criteria based upon the velocity gradient, which can have their benefits, depending on the application, but suffer from a common shortcoming: they are all point-criteria, hence cannot account for the non-local structure of a coherent region, which we intuitively call an 'eddy'. We present a two-step method to overcome this. First, we introduce an instantaneous measure for spatial coherence, based upon a generalization of the two-point correlation: at each point in the velocity field, a correlation-vector is determined, by calculating a correlation-length along three orthogonal directions, using an invariant of the correlation-tensor. The iso-magnitude contours of this correlation-vector field represent a kernel of longer range coherent motions. Next, using Biot-Savart's law, the velocity field associated with isolated kernels can be reconstructed, which helps to isolate coherent motion in space, as well as scale. This procedure helps to visualize the dynamics of the eddies, possibly also giving a view into the ubiquitous eddy-breakup mechanism characteristic of the turbulence cascade, as summed up in Richardson's famous verse.