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Fractal dimension of transitional boundary layer spot interfaces detected by a self- organizing map

Event Type: 
Date and Time: 
Thursday, August 22, 2019 - 10:00
Location: 
CTR Conference Room 103
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Speaker(s): 
Dr. Zhao Wu

An unsupervised machine-learning algorithm, the self-organizing map (SOM), is used to identify the turbulent boundary layer (TBL) and non-TBL regions in bypass transition. The data employed for the analysis are from an archived direct simulation publicly available in the Johns Hopkins Turbulence Databases (JHTDB, http://turbulence.pha.jhu.edu). The data points in the entire flow domain are automatically classified into TBL and non-TBL regions by the SOM, based on their standardized velocity, velocity fluctuations, velocity gradients and their spatial locations. Thus the SOM identifies the turbulent-boundary-layer interface (TBLI) without the usual need for choosing thresholds on e.g. vorticity or velocity fluctuations. The TBLI is found to be a hyperplane in the input space. The SOM distinguishes the streaks in the laminar region and the weak free-stream turbulence from TBL region. Results from our approach are shown to be consistent with threshold-based methods in the special cases when those are applicable.

This approach is then used to study the turbulent spots. The nature of turbulent spots in transitional boundary layers, and whether their internal structure shares characteristics of equilibrium turbulence, remain open questions of considerable interest. Here we study scaling properties of the interface separating the spots from the outside flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling with a fractal dimension near D=2+1/3, where the 1/3 can be related to the Kolmogorov scaling of velocity fluctuations (e.g. de Silva et al. PRL 2013). We measure the volume-area fractal scaling of the naturally triggered turbulent spots. Results from the volume-area fractal dimension confirm D=7/3, i.e. trends consistent with fully developed turbulence. Applying an alternative area-perimeter analysis on planar cuts at various heights shows D decreasing then increasing. It is argued that these trends could be associated to changes in the thickness of the interface at different heights from the wall.

Bio: 
Dr. Zhao Wu received his doctoral degree in Mechanical Engineering from The University of Manchester, UK in 2017. During his PhD, his research was focused on direct numerical simulations of fluid flow and conjugate heat transfer. He then joined Johns Hopkins University as a postdoctoral researcher working on the Johns Hopkins Turbulence Databases (JHTDB). His research interests include machine learning, data compression, high-performance computing and computational fluid dynamics.