On the distribution of the streamwise fluctuation velocity in wall bounded flows

Authors: Alfredsson, P.H., Örlü, R., Segalini, A. S.
Document Type: Conference
Pubstate: Accepted
Journal: Bulletin of the American Physical Society, 64rd Annual Meeting of the APS Division of Fluid Dynamics, November 20–22, 2011, Baltimore, Maryland
Volume: 56  
Year: 2011


The streamwise velocity fluctuations in wall-bounded flows has recently received renewed interest. Measurements and simulations at low Reynolds numbers ($Re$), as well as high $Re$ wind tunnel studies and data from the atmospheric boundary layer (ABL) are at hand but show sometime conflicting trends with $Re$. However, high $Re$ data often have some uncertainties associated with them, such as poor spatial resolution for laboratory data or other uncertainties associated with ABL experiments. Several models for the wall normal distribution of $u_{rms}$ have recently been proposed, based on various physical ideas together with empirical inputs. Here we propose a new model based on two observations: a) $u_{rms}$ normalized with the local velocity $U$ decreases linearly with respect to $U/U_\infty$ in the outer part of the flow, b) in the inner region $u_{rms}/U$ deviates from the linear trend at a specific value of $U/u_\tau(\approx 17)$, where $u_\tau$ is the friction velocity. Using this information it is possible to formulate a composite description of $u_{rms}$ in the wall normal direction for all Reynolds numbers. This shows two important results, namely the increase in $u_{rms}/u_\tau$ with $Re$ as well as a prediction of a second ``outer'' maximum when $Re$ is high enough, a debated feature that has been observed in ABL experiments as well as in some laboratory experiments at high $Re$. http://meetings.aps.org/link/BAPS.2011.DFD.R7.5