LDA measurements of the mean velocity 0 in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U~ from the value of ~O/~y at the wall. The trend of the Reynolds number dependence of O + = O/U~ is similar to the direct numerical simulations of Spalart (1988).
I IntroductionA source of difficulty in low R o turbulent boundary layers is the accurate determination of the friction velocity U~. At such Reynolds numbers there is no rigorous basis for the log law, viz.
+ = x -i In y+ +C(1) (where x and C are constants; standard notation is used) and therefore no reason why low R o effects cannot penetrate well into the buffer layer. Consequently, the use of the Clauser chart technique [which is based on (1)] and of the Preston tube method may not be accurate. Under these conditions, a more direct and reliable estimate of U~ (=--w'rl/2, Tw is the kinematic wall shear stress) from the slope of the mean velocity profile at the wall using the relation rw = v .(2) y=0The use of (2) is prohibitive when a hot wire is used because of the wall conduction problem. Near-wall LDA measurements do not suffer from the same difficulty as hot wire measurements (e.g. Mazumder et al., 1981) and should in principle allow a reasonably accurate estimate of U~ from (2) [e.g. Reischman and Tiederman, 1975;Neiderschulte et al., 1990]. The purpose of this note is to show that U~ can be determined with sufficient accuracy from (2) to allow the effect of R o on 0 + to be assessed.
Experimental conditions and procedure
Experimental conditionsThe measurements were made in a closed circuit vertical water tunnel which consists of a constant head recirculating two-tank system (a brief description of the tunnel is given in Zhou and Antonia, 1992). The working section has a vertical square cross-section (0.26 m • 0.26 m) with a height of 2 m. All walls of the cross section are transparent (20 mm thick perspex). One of the walls, which is removable, was used as the smooth wall for the present boundary layer study. The maximum value of U1, the free stream velocity, is about 42 cm/s. At this speed, the boundary layers on the working section wall are laminar. Tripping was therefore required to achieve a turbulent regime. Three-dimensional roughness elements (pebbles of about 4.5 mm in height) were glued onto a 30 mm large perspex strip. This strip was recessed into a groove, located approx. 10 cm downstream of the contraction exit, so that the side of the strip onto which the pebbles were glued was flush with the working section wall. The measurement station was located 1,100 mm downstream of the trip. The boundary layer thickness 6 is about 35 mm at this station. Three values of R o (560, 1,033, 1,320) were used. Spalart (1988) reported direct numerical simulation (DNS) results for R o = 300, 670 and 1,410. In the present investigation, it was not possible to achieve Ro values less than about 500. Visualisations of dye injected at the wall and in the flow revealed that the boundary layer was laminar for R o < 500. ...