Nascent fractal scaling during flat plate boundary layer transition to turbulence
As a boundary layer developing on a smooth surface transitions from a laminar to a turbulent state, spatially localized patches (spots) of turbulence often appear. These grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. Here, we pose this question for geometric scaling properties of the interface separating the turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension near D = 7/3, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuation’s spatial increments. The data used in this study to examine geometric scaling properties are from a direct numerical simulation (DNS). Based on these data, we show that the spot boundaries (interfaces) can be determined by using an unsupervised machine-learning method that identifies such interfaces without the need to choose arbitrary thresholds. Scaling properties of the interface are studied and links to fractal properties of turbulent non-turbulent interfaces in high Reynolds number flows are established. This work has been performed with Drs. Zhao Wu and Tamer Zaki, while the database (supported by the NSF) has resulted from a long-term collaboration with the JHTDB team.
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