Friction coefficient for oscillatory flow: The rough-smooth turbulent transition

Observations of turbulent, oscillatory boundary-layer flows show that the behavior of the friction coefficient in the transition from hydraulically rough to smooth regimes is not well captured by existing semi-empirical expressions obtained for unidirectional flows. A revised formulation for the friction coefficient for oscillatory flows is presented. Dimensional analysis and similarity methods are used to assess the dimensionless parameters governing the relation between the outer flow and the bottom shear stress. Further progress is made using analogies between oscillatory and unidirectional boundary layer flows, from which analytical expressions are calibrated. An expression for the phase lead between the maximum bed shear stress and the maximum free-stream velocity is obtained. An example describing the computational procedure needed to estimate the friction coefficient and phase lead using the new expressions is presented to show their practical application to both laboratory and field conditions.