Multiscale Sample Entropy of Two-Dimensional Decaying Turbulence

Figures

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  Figure 1. Experimental setup. Using a comb, we created a turbulent flow on a flowing soap film channel. The velocity field was measured at several locations downstream of the comb using laser Doppler velocimetry.

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  Figure 2. Example of raw (circles) and interpolated time series (thick lines). Laser Doppler velocimetry measured the flow velocity at random times. Therefore, we re-sampled the data using Equation (1) at 10,000 Hz .

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  Figure 3. A flowchart to calculate the sample entropy.

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  Figure 4. Sample entropy calculated for turbulent flow in Soap Film 1. At shorter time scales, the transverse component is more unpredictable. However, at a longer time scale, the opposite is true. We note that the sample entropy naturally decreases with τ because the coarse-grained time series are not normalized. The time series is normalized only once for α=1.

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  Figure 5. Sample entropy calculated for turbulent flow in Soap Film 2.

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  Figure 6. Multiscale sample entropy of the longitudinal velocities of Soap Film 1.

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  Figure 7. Multiscale sample entropy of the transversal velocities of Soap Film 1.

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  Figure 8. Coarse-graining time maximizing the sample entropy analysis, τmax, is plotted with respect to the downstream distance X.