Multiscale Sample Entropy of 2D Decaying Turbulence

Kolmogorov-Sinai entropy has been used to quantify degrees of complexity of spatiotemporally chaotic systems. However, it is not always convenient to implement in real experiments. Recently a Multiscale Sample Entropy (MSE) measure has been proposed, which allows easier analyses of time series. In this study, we have generated decaying turbulence in a two-dimensional soap film and have measured velocity fluctuations as functions of time and downstream distance using a laser Doppler velocimeter. We performed MSE analysis and found there is a time scale $\tau _0 $ at which the MSE is maximized. The value of $\tau _0 $, which correlates well with the large-eddy turn-over time, gets larger as turbulence decays. Other aspects of 2D turbulence are also analyzed using the velocity time series.