Randomness representation in turbulent flows with Kolmogorov complexity (In laminar-turbulent transition due to periodic injection in an inlet boundary layer in a circular pipe)

In the laminar-turbulent transition process of a mixing layer formed downstream of a two-dimensional nozzle exit, an analysis was performed based on various information measures. Shannon entropy, permutation entropy and Kullback-Leibler divergence were introduced, and former studies in which they were used in the turbulent analysis were then reviewed. In the present study, the probability distribution of time series of hot-wire output voltage data was obtained, then analyzed. The aim of the investigation was to clarify the effectiveness of the analysis for the transition and turbulent flow. In addition, equations which Shannon entropy must satisfy in the turbulent flow field were derived. The Shannon entropy of the fluctuating velocity changed monotonically in the downstream direction. Thus, it appears to measure the transition process in the mixing layer. The permutation entropy of the fluctuating velocity first increased, then decreased, then increased again, and decreased finally. It reflected the increase of the fluctuating velocity and change of fluctuation manner (from periodic to irregular fluctuation) during the transition process. The Kullback-Leibler divergence based on the probability density function of the fluctuating velocity increased first, then decreased downstream, and thus did not show a monotonic change during the transition process in the mixing layer.

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Various information and complexity measures for analyzing the laminar-turbulent transition process in mixing layer (Analysis of fluctuating vorticity and turbulent energy dissipation rate)

一宮¹,

中村²

2020

Transactions of the JSME (In Japanese)

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In this paper, the laminar-turbulent transition process of a mixing layer downstream of a two-dimensional nozzle exit was analyzed based on various information and complexity measures. Shannon entropy, permutation entropy, and approximated Kolmogorov complexity were also obtained. To obtain the Shannon entropy, the temporal probability distribution of the hotwire output voltage data was determined and analyzed. In addition to the fluctuating velocity, its time derivative and the square of this derivative were analyzed. The Shannon entropy of the time derivative and its square slightly decreased downstream, in accordance with the increase in the time scale of the turbulence. When the length of the extracted data was constant, the permutation entropy of the time derivative and its square increased around the peripheral region of the mixing layer, in accordance with the intermittent nature of the velocity signals. The region is at the 3-4 times farther from the jet centerline than the region where the fluctuating velocity becomes maximum. When the length of the extracted data was varied in accordance with the integral time scale of turbulence, the permutation entropy initially decreased in the potential core and subsequently increased after the disappearance of the potential core, as the transition progressed. The approximated Kolmogorov complexity of the time derivative and its square were smaller than that of the fluctuating velocity. Owing to the simplification of the data, they slowly increased after the disappearance of the potential core and then quickly decreased after the development of turbulence.

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Randomness representation in turbulent flows with Kolmogorov complexity (In laminar-turbulent transition due to periodic injection in an inlet boundary layer in a circular pipe)

Cited by 3 publications

References 21 publications

Complexity analysis of the environmental fluid flow time series

Complexity analysis of the environmental fluid flow time series

Analysis of laminar-turbulent transition process in mixing layer with various information measures

Various information and complexity measures for analyzing the laminar-turbulent transition process in mixing layer (Analysis of fluctuating vorticity and turbulent energy dissipation rate)

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