Abstract
A conventional, small perturbation, stability analysis has been applied to a fully developed turbulent shear flow in a parallel duct with rough walls. This is an attempt to detect the inherent state of flow stability to quasi-regular disturbances emanating from the surface roughness elements. The surface roughness is represented by the usual roughness Reynolds number; it is fed into the analysis through an assumed mean velocity profile valid between the viscous sublayer and the inner (wall) region. An eddy viscosity model is used to secure the equation closure and the final equation for the perturbation amplitude has been solved numerically using the techniques developed for the Orr-Sommerfeld equation. Within the domain of realistic flow conditions, and for a range of surface roughness amplitudes, a local minimum of stability in terms of the longitudinal wave number has been found. However, it is not implied that it is a minimum minomorum, as only a limited range of surface roughnesses has been tried.
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