Streamwise inclination angle of wall-attached eddies in turbulent channel flows

Author:

Cheng ChengORCID,Shyy Wei,Fu LinORCID

Abstract

We develop a new methodology to assess the streamwise inclination angles (SIAs) of the wall-attached eddies populating the logarithmic region with a given wall-normal height. To remove the influences originating from other scales on the SIA estimated via two-point correlation, the footprints of the targeted eddies in the vicinity of the wall and the corresponding streamwise velocity fluctuations carried by them are isolated simultaneously, by coupling the spectral stochastic estimation with the attached-eddy hypothesis. Datasets produced with direct numerical simulations spanning $Re_{\tau } \sim O(10^2)\unicode{x2013}O(10^3)$ are dissected to study the Reynolds number effect. The present results show, for the first time, that the SIAs of attached eddies are Reynolds-number-dependent in low and medium Reynolds numbers, and tend to saturate at $45^{\circ }$ as the Reynolds number increases. The mean SIA reported by vast previous experimental studies are demonstrated to be the outcomes of the additive effect contributed by multi-scale attached eddies. These findings clarify the long-term debate and perfect the picture of the attached-eddy model.

Funder

Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone

Guangdong Basic and Applied Basic Research Foundation

Center for Ocean Research in Hong Kong and Macau

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics

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