Turbulence profiles from a smooth flat-plate turbulent boundary layer at high Reynolds number

Abstract

Much is known about smooth-flat-plate turbulent boundary layers (TBLs) at laboratory-scale Reynolds numbers because of a wealth of experimental data. However, smooth-flat-plate TBL data are much less common at the high Reynolds numbers typical of aerodynamic and hydrodynamic applications (Rex∼108–1010), and at the even higher Reynolds numbers of many geophysical flows. This paper presents new LDV-measured profiles of the stream-wise velocity variance, the wall-normal velocity variance, and the Reynolds shear stress from the TBL that formed on a smooth flat plate at Karman numbers from 15,000 to 60,000 (Rex from 75 million to 220 million). 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 3.05m wide at water flow speeds up to 20ms−1. The TBL on the model developed in a mild favorable pressure gradient having an acceleration parameter K∼10−10. When plotted with the usual inner and outer scalings, the stream-wise velocity variance profiles display a Reynolds number dependence that is consistent with prior lower Reynolds-number zero-pressure-gradient TBL measurements. However, using the same normalizations, the profiles of wall-normal velocity variance and Reynolds shear stress are found to be Reynolds number independent, or nearly so, when experimental uncertainties are considered.