Relaxation effects observed for turbulent flow over a wavy surface

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Abstract
Measurements are presented for different flow rates of the time-averaged wall shear stress and of the root-mean-square value of the turbulent fluctuations along a small-amplitude sinusoidally shaped solid surface. The stresses are found to have a variation along the wave surface which is also sinusoidal. The influence of flow rate and of wavelength on the amplitude and phase angle can be correlated by using a wave-number α+ made dimensionless with wall parameters.It is found that for α+ > 10−2 a frozen-turbulence assumption can be made whereby the influence of the wave-induced variation of the mixing length can be ignored. For α+ < 10−4 the flow can be described by assuming the Reynolds stresses are given by an equilibrium assumption. The relaxation from this equilibrium condition is characterized by a sharp change in the phase angle for 6 × 10−4 < α+ < 10−3.This relaxation is associated with physical processes in the viscous wall region which are not yet understood. It is argued that these are principally related to the wave-induced variation of the pressure gradient.The wave-induced variation of the turbulent fluctuations in the wall shear stress also indicate a relaxation in that the maximum turbulence intensity is located in a region of favourable pressure gradient.