Quantification of the complexity and unpredictability of a turbulent cylinder wake using excess entropy

The complexity of a turbulent wake flow is studied using the excess entropy method. Turbulent complexity originates from the deterministic but unpredictable nature of the governing equation, and the excess entropy method is useful in providing a systematic way to quantify the random and coherent patterns in a flow field using information-per-letter and degree-of-complexity, respectively. In this study, the excess entropy calculated using the transverse velocity component decreases considerably along the stream-wise direction, which is consistent with the fact that large-scale structures dissociate and disappear in the far wake. The flow gradually becomes more random and unpredictable. On the other hand, the excess entropy obtained from the streamwise velocity sequence reveals that the pattern of small-scale structures remains largely unchanged during the flow evolution, even though their intensity becomes weaker. Quantifying the coherence and randomness of turbulence provides a more complete description of a complex flow field. The parameter selection in the complexity evaluation is also discussed in the paper.