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Statistical model of laminar–turbulent transition onset caused by atmospheric particulates

Published online by Cambridge University Press:  18 March 2025

Pavel V. Chuvakhov Open the ORCID record for Pavel V. Chuvakhov [Opens in a new window]  and
Alexander V. Fedorov Open the ORCID record for Alexander V. Fedorov [Opens in a new window]
Pavel V. Chuvakhov*
Affiliation:
Central Aerohydrodynamic Institute named after Professor N.E. Zhukovsky, Zhukovsky, Russia Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia
Alexander V. Fedorov
Affiliation:
Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia
*
Corresponding author: Pavel V. Chuvakhov, [email protected]
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Abstract

Within the frameworks of the amplitude method and the linear stability theory, a statistical model of the initial stage of laminar–turbulent transition caused by atmospheric particulates (aerosols) penetrating into the boundary layer is developed. The model accounts for the process of boundary layer receptivity to particulates, asymptotic behaviour of unstable wave packets propagating downstream from particle–wall collisions and the amplitude criterion for the transition onset. The resulting analytical relationships can be used for quick predictions of the transition onset on bodies of relatively simple shape, where the undisturbed boundary layer is quasi-two-dimensional. The model allows us to explore the transition onset at realistic distributions of the particle concentration selected based on an analysis of known empirical data. As an example, a 14° half-angle sharp wedge flying in atmosphere at 20 km altitude and Mach number 4 is considered. It is shown that the transition onset corresponds to an N-factor of 15.3 for a flight under normal atmospheric conditions and 12.2 for a flight in a cloud after volcanic eruption. In accordance with physical restrictions, these values are below the upper limit $N\approx 16.8$ predicted for transition due to thermal fluctuations (perfectly ‘clean’ case). Nevertheless, they are significantly greater than $N=10$ which is commonly recommended for estimates of the transition onset in flight.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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