Bed shear stress in unsteady flow

Standard engineering methods of estimating bed shear stress using friction factors (i.e. τ = 1/2fρu ) can fail spectacularly in unsteady hydrodynamic conditions. This paper demonstrates this fact using direct measurements of bed shear stresses under irregular waves using a shear plate apparatus. The measurements are explained in terms of the influence of the horizontal pressure gradient and the shear stresses acting on the surface of the plate. The horizontal fluid velocity at the edge of the boundary layer and the water surface elevation and slope were also measured. The paper demonstrates that the water surface measurements can be used to obtain accurate estimates of the forces on the bed, by employing Fourier analysis techniques or an innovative convolution integral method. The experimental results indicate that an offshore bed shear stress may be recorded while the free stream velocity remains onshore at all times. This demonstrates the failure of the standard engineering friction factor method in this scenario, since negative friction factors would be required. Important questions are raised regarding the appropriate definition for the bed shear stress when the vertical gradient of the shear stress is large. It is shown that it is problematic to define a single value for a "bed" shear stress in the presence of a strong horizontal pressure gradient. It is also argued that the natural driver for any model used to predict bed shear stress is the pressure gradient (or its proxy the free stream acceleration), rather than the velocity. This allows for accurate calculation of both acceleration effects (more rapid acceleration leads to a thinner boundary layer and higher shear stress) and also the direct action of the horizontal pressure gradient