A new momentum integral method for approximating bed shear stress

In nearshore environments, accurate estimation of bed stress is critical to estimate morphologic evolution, and benthic mass transfer fluxes. However, bed shear stress over mobile boundaries in wave environments is notoriously difficult to estimate due to the non-equilibrium boundary layer. Approximating the friction velocity with a traditional logarithmic velocity profile model is common, but an unsteady non-uniform flow field violates critical assumptions in equilibrium boundary layer theory. There have been several recent developments involving stress partitioning through an examination of the momentum transfer contributions that lead to improved estimates of the bed stress. For the case of single vertical profile observations, Mehdi et al. (2014) developed a full momentum integral-based method for steady-unidirectional flow that integrates the streamwise Navier-Stokes equation three times to an arbitrary position within the boundary layer. For the case of two-dimensional velocity observations, Rodriguez-Abudo and Foster (2014) were able to examine the momentum contributions from waves, turbulence and the bedform in a spatial and temporal averaging approach to the Navier-Stokes equations. In this effort, the above methods are combined to resolve the bed shear stress in both short and long wave dominated environments with a highly mobile bed. The confluence is an integral based approach for determining bed shear stress that makes no a-priori assumptions of boundary layer shape and uses just a single velocity profile time series for both the phase dependent case (under waves) and the unsteady case (under solitary waves). The developed method is applied to experimental observations obtained in a full scale laboratory investigation (Oregon State's Large Wave Flume) of the nearbed velocity field over a rippled sediment bed in oscillatory flow using both particle image velocimetry and a profiling acoustic Doppler velocimeter. This method is particularly relevant for small scale field observations and laboratory observations.