Abstract
Multiscale sample entropy analysis has been developed to quantify the complexity and the predictability of a time series, originally developed for physiological time series. In this study, the analysis was applied to the turbulence data. We measured time series data for the velocity fluctuation, in either the longitudinal or transverse direction, of turbulent soap film flows at various locations. The research was to assess the feasibility of using the entropy analysis to qualitatively characterize turbulence, without using any conventional energetic analysis of turbulence. The study showed that the application of the entropy analysis to the turbulence data is promising. From the analysis, we successfully captured two important features of the turbulent soap films. It is indicated that the turbulence is anisotropic from the directional disparity. In addition, we observed that the most unpredictable time scale increases with the downstream distance, which is an indication of the decaying turbulence.
Highlights
The traditional discipline of turbulence research focuses on the flow of energy in phase space
The tradition continued as Kraichnan found the discrepancy between two-dimensional (2D) and three-dimensional (3D) turbulence in 1963, characterized by the inverse energy cascade and the forward enstrophy cascade [2]. These results are the milestones of turbulence research and the archetypes showing the importance of the flow of energy in this curriculum
We present a typical raw time series directly measured from LDV in Figure 2 with closed circles
Summary
The traditional discipline of turbulence research focuses on the flow of energy in phase space. This tradition began when Kolmogorov first derived the famous four-fifth law in 1941, as a direct inference of the Navier–Stokes equation, to illustrate that the second moment of velocity is always transferred from the large scale to the small scale [1]. The tradition continued as Kraichnan found the discrepancy between two-dimensional (2D) and three-dimensional (3D) turbulence in 1963, characterized by the inverse energy cascade and the forward enstrophy cascade [2]. These results are the milestones of turbulence research and the archetypes showing the importance of the flow of energy in this curriculum. “data science” is considered as an independent discipline, and there is an increasing number of studies that treat fluid motion as data flow [9,10]
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