On the structure of oscillatory boundary layers

An empirical analysis is performed on the most detailed, recent measurements of turbulent oscillatory boundary layer flow. The measurements show that throughout elevations where the flow can be considered horizontally uniform, one deficit model is sufficient for describing the fundamental mode. Some general properties of the non dimensional velocity deficit D₁(z) appear with striking consistency. First of all the identity $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦ ≡}\text{Arg}\text{D}{}_{\mathrm{<mtext>1</mtext>}}$, which is a theoretical result for smooth laminar flow, seems to hold with great accuracy for a large range of turbulent flow conditions as well. This is of principal theoretical interest because all previous analytical eddy viscosity models as well as numerical mixing length models predict a consistent and fairly large difference between Arg D₁ and $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$. If the identity between $\text{ln}\text{¦D}{}_{\mathrm{<mtext>1</mtext>}}\text{¦}$ and Arg D₁ extends all the way to the bed, it means that the bed shear stress leads the free stream velocity by 45 degrees. It is also found that the structure of smooth turbulent oscillatory flows as measured by Kalkanis (1964) corresponds to a sharp maximum in the normalized energy dissipation rate.