The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number

Smooth flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century. However, there is a relative dearth of measurements at Reynolds numbers typical of full-scale marine and aerospace transportation systems (Re-theta = U-e theta/nu > 10(5), where U-e = free-stream speed, theta = TBL momentum thickness and nu = kinematic viscosity). This paper presents new experimental results for the TBL that forms on a smooth flat plate at nominal Re-theta values of 0.5 x 10(5), 1.0 x 10(5) and 1.5 x 10(5). Nominal boundary layer thicknesses (delta) were 80-90 mm, and Karman numbers (delta(+)) were 17 000, 32 000 and 47 000, respectively. The experiments were conducted in the William B. Morgan Large Cavitation Channel on a polished (k(+) < 0.2) flat-plate test model 12.9m long and 3.05 m wide at water flow speeds up to 20 ms(-1). Direct measurements of static pressure and mean wall shear stress were obtained with pressure taps and floating-plate skin friction force balances. The TBL developed a mild favourable pressure gradient that led to a streamwise flow speed increase of similar to 2.5% over the 11 m long test surface, and was consistent with test section sidewall and model surface boundarylayer growth. At each Re-theta, mean streamwise velocity profile pairs, separated by 24 cm, were measured more than 10 m from the model's leading edge using conventional laser Doppler velocimetry. Between these profile pairs, a unique near-wall implementation of particle tracking velocimetry was used to measure the near-wall velocity profile. The composite profile measurements span the wall-normal coordinate range from y(+) < 1 to y > 2 delta. To within experimental uncertainty, the measured mean velocity profiles can be fit using traditional zero-pressure-gradient (ZPG) TBL asymptotics with some modifications for the mild favourable pressure gradient. The fitted profile pairs satisfy the von-Karman momentum integral equation to within 1%. However, the profiles reported here show distinct differences from equivalent ZPG profiles. The near-wall indicator function has more prominent extrema, the log-law constants differ slightly, and the profiles' wake component is less pronounced.