A comparison of different analytical techniques for identifying structures in turbulence

Vortical structures play an important role in the kinematics and dynamics of turbulence, but in order to understand this role we require techniques to identify and classify them. Proper Orthogonal Decomposition (POD), conditional sampling with ensemble statistics, and conditional sampling with conditional statistics are applied to a simple test function and the results are compared to determine the strengths and weaknesses of each approach. The second method gives the closest approximation to the test signal and is the easiest to use, although it is sensitive to the choice of conditions. None of these techniques can give much insight into the dynamics of turbulence, or into the organisation of eddies with complex, fine-scale structure.New methods for investigating complex (self-similar) structures based on fractal and wavelet analyses are presented. Methods of distinguishing between locally (accumulating) and globally (fractal) self-similar structures are suggested.