Session: 06-16-01 Wave Mechanics, Modeling and Wave Effects

Submission Number: 157186

Revisiting the Logarithmic Law of Turbulent Boundary Layer in Oscillatory Flows 

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 (BL) in zero-pressure-gradient flows and fully developed pipe/channel flows, where the shear stress distribution is approximate to a constant value. LL is widely adopted in engineering analyses/designs related to boundary layer flows, such as scour assessments and velocity predictions.
LL has also been demonstrated to be appliable to the BLs in oscillatory flows with kinds of equivalent‘constant-shear-stress’(CSS) restrictions. Jensen et al. (1989) noted that when the phase angle ranges from 70° to 110°, the velocity distribution closely resembles that of the steady flow, where the fluid pressure gradient is approximate to zero, approximately satisfying the CSS restriction. Sumer et al. (1987) stated that the logarithmic layer can appear at any phase as long as the thickness of the oscillatory boundary layer δ exceeds a certain critical value, but the resultant friction velocity based on LL fitting should no longer be the wall shear velocity. Despite this, CSS restriction seem to be disregarded in some more recent research and engineering applications. This work revisits the LL of turbulent BLs in oscillatory flows to examine what the LL fitting represents without CSS restriction.
To address this issue, numerical simulations of oscillatory turbulent BLs are conducted with kinds of turbulence closure models, such as k-ε, k-ω, Reynolds stress model (RSM) and Large eddy simulation model (LES), using commercial software STAR CCM+. The shear stress distribution is determined based on the velocity distribution via the momentum-integral method and then compared with the LL fitting results.
Some initial simulation results show that in most phases, particularly in accelerating phases, CSS restriction fails and LL fitting results are not relevant to the bed shear stress. Differences yielded by various turbulence closure models are to be discussed later on. 
Keywords: Logarithmic Law; Boundary Layers; Oscillatory flows; numerical simulations

Presenting Author: Bairen Chen South China University of Technology

Presenting Author Biography: Graduate students of the School of Marine Science and Engineering, South China University of Technology.