Distinguishing coherence and randomness in turbulence using excess entropy

Turbulent flow involves both coherent motion and random fluctuation, and emphasizing only one of these two aspects is inadequate to understand the flow’s behavior. In this research, we utilize excess entropy to study the relationship between coherence and probability in a turbulent wake flow downstream of a cylinder, where the Re number is 8100. The unpredictability is quantified by entropy-per-signal and the coherence is characterized using excess entropy. In the stream-wise direction, the entropy-per-signal of the vertical velocity component keeps increasing, and at the same time, the excess entropy of that velocity component, Ev, decreases. This observation is consistent with the fact that the large-scale organized structures dissociate and the flow becomes more random. On the other hand, the wake flow is highly anisotropic. The excess entropy of the horizontal velocity fluctuation, Eu, has no significant variation in the stream-wise direction because this velocity component is largely controlled by small-scale structures, which do not undergo a significant change. Quantification of the coherence and randomness in a flow provides a new perspective to study turbulence.