Effects of Porous Bed on Turbulent Stream Flow above Bed

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Abstract
An analysis of the effects of the passive plane porous bed of an open channel on the steady, uniform, fully developed, two‐dimensional turbulent shear flow is presented. The effect of the pervious boundary on the free flow is taken as a perturbation of an equivalent turbulent flow over an impervious bed of the same surface texture. The turbulence field is regarded as stationary and statistically homogeneous in planes parallel to the channel bottom. Expressions for the mean velocity, the Reynolds stress, and the induced stress distributions are derived and compared with available experimental data. The new concept of induced pressure is introduced, and its functional form is obtained. The presence of a porous bed will in general cause the friction factor to be directly proportional to the Reynolds number, which agrees with experimental findings. The validity of Phillips' formula for the computation of the induced stress is discussed and clarified. The presented analysis improves our understanding of the physics of the problem and offers new analytical results for further study.