Turbulent flow over small amplitude solid waves

Measurements were made of the variation of wall shear stress and of the root mean square level of the fluctuating shear stress along a solid wavy surface with an amplitude of 0.014 in. and a wavelength of 2 in. The phase angle associated with the spatial variation of the wave-induced shear stress passes through a well defined maximum when measured as a function of the dimensionless wave number, alpha = 2 pi nu/lambda u star. Measurements of the wall shear stress and in particular the location of this maximum provide an extremely sensitive test of turbulence models which pay particular attention to the viscous wall region. The use of a quasi-laminar assumption, whereby the wave induced changes of the Reynolds stresses are ignored, gives good agreement with the measurements of the variation of the wall shear stress for large values of alpha. An equilibrium turbulence assumption in which the wave induced Reynolds stresses are assumed to adjust instantaneously to changes in flow conditions along the wave surface is valid for only small values of alpha. In the range of 0.0005 < alpha < 0.2 it is necessary to use a model for wave induced Reynolds stresses which takes account of the fact that the turbulence does not respond immediately to changes in the flow conditions. The mixing length model of Loyd et al. provides the best fit of the data. A modification of this model which takes into account the effect of streamline curvature on the mixing length provides an improved fit of the available pressure measurements over over a wavy surface.