Boundary Shear Stress

As a fluid flows across its bed, a stress that opposes the motion of the fluid exists at the bed surface. ^[1] This stress - the boundary shear stress - is distinct from fluid shear stress within the body of the flow. It is defined as force per unit area parallel to the bed, that is, the tangential force per unit area of surface, which is equal to the mean shear stress acting over the wetted perimeter. ^[1] Understanding boundary shear stress is fundamental to predicting sediment erosion and transport, because it is the stress that the flow actually exerts on the grains sitting on the bed - the direct mechanical agent of entrainment.

Formula and Controlling Variables

Boundary shear stress τ₀ is expressed as: ^[1]

τ₀ = ρghs

where ρ is fluid density, g is gravitational acceleration, h is flow depth, and s is the slope of the parallel bed and water surface (gradient). ^[1] The bed shear stress increases linearly with depth and slope. ^[1]

Boundary shear stress is also a function of velocity of flow, although the mathematical relationship is complex. ^[1] It tends to increase as velocity increases, though not in a direct way. ^[1]

Significance for Sediment Transport

Because boundary shear stress is determined by the force that a flow is able to exert on the sediment bed and is related to flow velocity, it is an important variable in determining the erosion and transport of sediment on the bed below a flow. ^[1] The formula shows that boundary shear stress increases directly with increasing density of the moving fluid, increasing diameter and depth of the stream channel, and increasing slope of the streambed. ^[1]

Other factors being equal, greater boundary shear stress - and therefore greater ability to erode and transport sediment - is expected in water flows than in air flows, in larger stream channels than in smaller channels, and in high-gradient streams than in low-gradient streams. ^[1] These predictions match field observation well. Mountain rivers cut through bedrock precisely because their steep gradients generate very high boundary shear stresses - stresses large enough to move boulders that a lowland river at the same depth would never touch.

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