High-Reynolds-number fractal signature of nascent turbulence during transition

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that 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. In this study, the question is posed for geometric scaling properties of the interface separating 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$D≈7/3$, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of$D=2.36±0.03$over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining more »

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Award ID(s):
Publication Date:
NSF-PAR ID:
10133533
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
117
Issue:
7
Page Range or eLocation-ID:
p. 3461-3468
ISSN:
0027-8424
Publisher:
Proceedings of the National Academy of Sciences
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