Unsteady stress partitioning and momentum transfer in the wave bottom boundary layer over movable rippled beds

Abstract

Observations of the nearbed velocity field over a rippled sediment bed under asymmetric wave forcing conditions were collected using a submersible particle image velocimetry (PIV) system. To examine the role of bed form-induced dynamics in the total momentum transfer, a double-averaging technique was implemented on the two-dimensional time-dependent velocity field by means of the full momentum equation. This approach allows for direct determination of the bed form-induced stresses, i.e., stresses that arise due to the presence of bed forms, which are zero in flat bed conditions. This analysis suggests that bed form-induced stresses are closely related to the presence of coherent motions and may be partitioned from the turbulent stresses. Inferences of stress provided by a bed load transport model suggest that total momentum transfer obtained from the double-averaging technique is capable of reproducing bed form mobilization. Comparisons between the total momentum transfer and stress estimates obtained from local velocity profiles show significant variability across the ripple and suggest that an array of sensors is necessary to reproduce bed form evolution. The imbalance of momentum obtained by resolving the different terms constituting the near-bed momentum balance (i.e., acceleration deficit, stress gradient, and bed form-induced skin friction) provides an estimate of the bed form-induced pressure that is consistent with flow separation. This analysis reveals three regions in the flow: the free-stream, where all terms are relatively balanced; the near-bed, where momentum imbalance is significant during flow weakening; and below ripple crests, where bed form-induced pressure is the leading order mechanism. Key Points: Double-averaging technique implemented on PIV observations of the WBBL Partitioning of stress due to wave-current, turbulence, viscosity, and bed forms Momentum balance in WBBL provides with estimates of bed form-induced pressure