Laboratory study of bed shear stress in gradually varied flow over a sudden change in bed roughness

Abstract The evolution of bed shear stress in open-channel flow due to a sudden change in bed roughness was investigated experimentally for rough-to-smooth (RTS) and smooth-to-rough (STR) transitions. The velocity field was measured in the longitudinal-vertical plane from upstream to downstream using a Particle Image Velocimetry system. The bed shear stress was determined from the measured velocity profile and water depth using various methods. It was found that the variation of bed shear stress in gradually varied flow through a roughness transition was influenced by both flow depth and bottom roughness. In both RTS and STR transitions, the bed shear stress adjusted to the new bed condition almost immediately even though the velocity profile away from the bed was still evolving, but unlike external and close-conduit flows the bed shear stress in open-channel flows continued to evolve until the flow depth was uniform. It is shown that the evolution of bed shear stress in a STR transition is dependent on the choice of the displacement height on the rough bed, which affects the mixing length used to derive the logarithmic velocity profile and equivalent roughness. Bed shear stress variation consistent with published data was obtained when the $${k}_{s}/{d}_{90}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>90</mml:mn> </mml:msub> </mml:mrow> </mml:math> ratio was determined as a function of the $$h/{d}_{90}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>90</mml:mn> </mml:msub> </mml:mrow> </mml:math> ratio, where $${k}_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> is the equivalent roughness height, $$h$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>h</mml:mi> </mml:math> is the flow depth, and $${d}_{90}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mn>90</mml:mn> </mml:msub> </mml:math> is the grain diameter with 90% of finer particles.