Revisiting the Logarithmic Law of Turbulent Boundary Layer in Oscillatory Flows

Abstract The logarithmic law (LL) originally describes the streamwise velocity as the function of the wall-normal distance in the overlap region of turbulent boundary layers in zero-pressure-gradient flows and fully developed pipe/channel flows, where the shear stress distribution is approximate to a constant value. In oscillatory flows, LL has also been demonstrated to be appliable with kinds of equivalent ‘constant-shear-stress’ (CSS) restrictions. However, this CSS restriction seems to be disregarded in some more recent researches and engineering applications related to oscillatory/wave boundary layers (OBL). This work revisits the LL in turbulent OBLs to examine what the LL fitting represents for without CSS restriction. Numerical simulations are conducted with the Reynolds stress model (RSM), using the commercial software STAR CCM+. The shear stress distribution is determined based on the momentum-integral method (MIM) and then compared with the LL fittings. Results show that in most phases when CSS restriction fails, LL fitting results are not relevant to the bed shear stress.