Effect of an Adverse Pressure Gradient on the Local Similarity for a Turbulent Boundary Layer

Experiments have been performed to investigate the effect of an adverse pressure gradient to the scaling law of a turbulent boundary layer. An approximate equilibrium boundary layer was achieved using a power law distribution of a free stream velocity with an exponent of -0.188. The wall shear stress was measured with a direct measurement device equipped with a zero displacement floating element mechanism. The scaling law was examined by the use of the friction velocity and a local velocity scale estimated from the shear stress profile. The later scale is derived from the integration of the boundary layer equations in conjunction with the order analysis in the limit of that pressure gradient parameter tends to zero and can be expressed as a function of friction parameter, pressure gradient parameter and height from the wall. The mean velocity gradient normalized with distance from the wall and the friction velocity depends on the height, but with the local velocity scale has a constant value in the layer where the PDF profiles of streamwise and normal fluctuating velocities are similar. The inverse of the constant value that is Kármán constant is 0.45. The modified logarithmic velocity profile is proposed from the local velocity scale and Kármán constant of 0.45 and is well consistent with the present experimental data.