Author(s): Sk Zeeshan Ali, Subhasish Dey
Linked Author(s): Sk Zeeshan Ali
Keywords: Fluvial hydraulics, hydrodynamics, turbulent flow, boundary layer, sediment transport
Abstract: A steady turbulent shear flow over a sinusoidal bed is investigated by applying the Reynolds averaged Navier-Stokes equations. The vertical acceleration induced by the sinusoidal bed yields a pressure profile having a departure from the linear hydrostatic pressure profile. Assuming a one-seventh power law of streamwise velocity, including the effects of curvilinear streamlines through Boussinesq approximation and using the Reynolds stress closure relation, the mathematical equations of the free surface profile and the Reynolds shear stress profile are obtained. The streamwise profiles of free surface and bed shear stress, and the vertical profiles of Reynolds shear stress at different streamwise locations are presented. In subcritical flow regime, the free surface profile is out of phase with the bed undulations; while the bed shear stress is nearly in phase with the bed. However, the free surface and the bed shear stress profiles in supercritical flow regime are contrary to those in subcritical flow regime. On the downstream portion of the crest of the sinusoidal bed, the Reynolds shear stress is characterized by a convex profile due to a decelerated flow; while on upstream of the crest of the bed, it is characterized by a concave profile due to an accelerated flow. However, over the crest and the trough of the bed, the Reynolds shear stress profiles are nearly linear, as observed in a zero-pressure gradient flow. The outcome of this study is used to analyze the sinusoidal erodible bed. The continuity equation of sediment motion is used to determine the phase lag distance between the locations of the maximum sediment flux and the maximum bed shear stress. The effects of the Froude number and the resistance parameter on the phase lag are investigated. The dependency of the Froude number on the phase lag is more noticeable than the resistance parameter
Year: 2017