Journal of Fluid Mechanics

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Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer

J. SHENGa1 p1, E. MALKIELa1 and J. KATZa1 p1 c1

a1 Department of Mechanical Engineering, The Johns Hopkins University, Baltimore MD 21218, USA

Abstract

Three-dimensional velocity distributions and corresponding wall stresses are measured concurrently in the inner part of a turbulent boundary layer over a smooth wall using digital holographic microscopy. The measurements are performed in a square duct channel flow at Reδ = 50000 and Reτ = 1470. A spatial resolution of 3–8 wall units (δυ = μm) in streamwise and spanwise directions and 1 wall unit in the wall-normal direction are sufficient for resolving buffer layer structures and for measuring the instantaneous wall shear stresses from velocity gradients in the viscous sublayer. Mean velocity and Reynolds stress profiles agree well with previous publications. Rudimentary observations classify the buffer layer three-dimensional flow into (i) a pair of counter-rotating inclined vortices, (ii) multiple streamwise vortices, some of them powerful, and (iii) no apparent buffer layer structures. Each appears in about one third of the realizations. Conditional sampling based on local wall shear stress maxima and minima reveals two types of three-dimensional buffer layer structures that generate extreme stress events. The first structure develops as spanwise vorticity lifts from the wall abruptly and within a short distance of about 10 wall units, creating initially a vertical arch. Its only precursors are a slight velocity deficit that does not involve an inflection point and low levels of vertical vorticity. This arch is subsequently stretched vertically and in the streamwise direction, culminating in formation of a pair of inclined, counter-rotating vortices with similar strength and inclination angle exceeding 45°. A wall stress minimum exists under the point of initial lifting. A pair of stress maxima develops 35δυ downstream, on the outer (downflow) sides of the vortex pair and is displaced laterally by 35–40δυ from the minimum. This flow structure exists not only in the conditionally averaged field but in the instantaneous measurement as well and appears in 16.4% of the realizations. Most of the streamwise velocity deficit generated by this phenomenon develops during this initial lifting, but it persists between the pair of vortices. Distribution of velocity fluctuations shows that spanwise transport of streamwise momentum plays a dominant role and that vertical transport is small under the vortices. In other regions, e.g. during initial lifting, and between the vortices, vertical transport dominates. The characteristics of this structure are compared to early experimental findings, highlighting similarities and differences. Abundance of pairs of streamwise vortices with similar strength is inconsistent with conclusions of several studies based on analysis of direct numerical simulation (DNS) data. The second buffer layer structure generating high wall stresses is a single, predominantly streamwise vortex, with characteristic diameter of 20–40δυ and inclination angle of 12°. It generates an elongated, strong stress maximum on one side and a weak minimum on the other and has been observed in 20.4% of the realizations. Except for a limited region of sweep above the high-stress region, this low-lying vortex mostly induces spanwise momentum transport. This structure appears to be similar to those observed in several numerical studies.

(Received October 20 2008)

(Revised February 28 2009)

Correspondence:

c1 Email address for correspondence: katz@jhu.edu

p1 Present address: Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis MN 55455, USA.

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