Direct estimates of friction factors for a mobile rippled bed

Abstract

New friction factor estimates are computed from the total momentum transfer applied to a rippled sediment bed. The total time‐dependent momentum flux is achieved by implementing the double‐averaged horizontal momentum equation on the nearbed flow field collected with PIV. Time‐independent friction factors are obtained by regressing the total momentum flux to the common quadratic stress law given by 12ρu∞|u∞|. The resulting friction factors compare favorably with available analysis techniques including energy dissipation, vertical turbulence intensity, and maximum shear stress, but can be 2‐6 times smaller than estimates determined with the model by Madsen (1994) and the formula of Swart (1974) using the ripple roughness.

Laboratory Observation of Turbulence and Wave Shear Stresses Under Large Scale Breaking Waves Over a Mild Slope

“…The large‐scale overturning jets of breaking waves provide comparable downward momentum for vortices to significantly alter . This is confirmed with the findings in Wilson et al () and Rodriguez‐Abudo and Foster (), in which the presence and ejection of vortices from wave breaking can significantly change the WSS. Moreover, Vander et al () measured the cross‐shore variation of WSS across a fixed bar.…”

“…Zou et al (, ) further developed a generalized solution of WSS distribution incorporating the effects of bottom slope and wave breaking, accounting for bottom dissipation with coupled wave and boundary layer flow. Moreover, several laboratory studies (De Serio & Mossa, ; Rodriguez‐Abudo & Foster, ; Ting & Nelson, ; Vander et al, ) and field studies (Elgar et al, ; Wilson et al, ; Zou et al, ) have confirmed that the magnitude of WSS is measurable. However, the measured magnitude and vertical distribution of WSS vary significantly in previous studies.…”

“…However, the measured magnitude and vertical distribution of WSS vary significantly in previous studies. Differing studies found that the time‐averaged magnitude of WSS is greater than that of TSS (De Serio & Mossa, ; Vander et al, ) or the same order as TSS (Rodriguez‐Abudo & Foster, ), while the instantaneous WSS is mostly less than TSS (Ting & Nelson, ). Furthermore, some WSS measurements in water columns are inconsistent with the theory of Zou et al ().…”

“…In order to estimate the contribution of each momentum transfer mechanism to the total stress in the water column, the vertical flux of horizontal momentum is commonly considered (Coleman et al, 2008;Rodriguez-Abudo & Foster, 2014, 2017van der Werf et al, 2017). For a two-dimensional oscillatory wave-current flow on the vertical x-z plane, the vertical distribution of the time-averaged total shear stress τ xz can be written in the form (Nielsen, 1992):…”

“…Equation (1) partitions the left-hand-side total shear stress into the right-hand-side viscous shear stress (the first term), the convective shear stress through momentum transfer induced by the mean flow of waves and currents (the second term), the (Reynolds) turbulent shear stress through turbulence momentum flux (the third term), and the wave shear stress through vertical momentum transfer arisen due to the presence of an uneven boundary and wave energy dissipation (the fourth term). In such turbulent flow, the viscous shear stress is several orders of magnitude lower than the total shear stress (Rodriguez-Abudo & Foster, 2014), so it may be negligible. Hence, the primary focus of the present study is on the last three terms of equation (1), especially on their relative role and variation under the near prototype, large-scale spilling, and plunging breakers over the impermeable 1/100 mild slope.…”