Abstract. The spatial distribution of the mean cross-shore flow (undertow) over a barred beach is examined with field data obtained on three energetic wave days during the Duck94 experiment. The vertical structure of the undertow is modeled using a turbulent eddy viscosity closure and includes the important effects of wave breaking (described using the roller concept) and convective acceleration of the current. Other than a more realistic description of observed turbulence variations, a depth-dependent eddy viscosity (compared with a constant) does not improve the agreement between predicted and observed undertow profiles. The effect of using different boundary conditions is investigated by extending the formulations of Stive and Wind [1986] and Svendsen et al. [1987] to include random waves by ensemble averaging over the wave height distribution. The contribution of breaking wave rollers to the surface mass flux can be of the same order or greater than the contribution associated with the organized wave motion. The largest discrepancies between model predictions and observations occur over the sandbar, where the mass transport of the breaking waves appears to be underestimated. IntroductionThe local vertical imbalance between the wave setup pressure gradient, which is uniform with depth, and the depthvarying wave radiation stress is conceptually responsible for driving the undertow There is a general consensus throughout the literature of using local conservation of mass over the vertical as one boundary condition. Commonly, the second boundary condition is either the stress at the trough level [Stive and Wind, 1986] or the no-slip condition at the bottom combined with the steady streaming generated by the bottom boundary layer (BBL) [Svendsen, 1984]. Despite significant physical differences both approaches reduce to the same form between the trough level and the top of the bottom boundary layer within the surf zone as contributions from steady streaming and bed shear stress are outweighed by mean water slope and wave forcing gradients.The wave-induced onshore mass flux in the region between the wave crest and trough is critical to predicting the magnitude of the undertow, which is predicted heuristically by adding the contribution from breaking wave rollers to the mass transport given by an irrotational wave theory [Svendsen, 1984].•Now at Marinha-Directoria de Hidrografiea e Navegacao, Rio de Janeiro, Brazil.

Abstract. The vertical structure of the mean wave-driven longshore current over a barred beach is examined on three strong current days during the DUCK94 experiment, and it is found that the bottom boundary layer is well described by a logarithmic profile (mean correlation coefficient for all 22 profiles, 0.98). The logarithmic profile fits better in the trough, where turbulent bottom boundary layer processes predominate, than over the bar, where breaking-wave-induced turbulence generated at the surface modifies the profile. The surface layer in the presence of waves is well described by adjusting the logarithmic profile for the intermittent presence of water and adding the alongshore component of the mass transport velocity (slope of the least squares linear regression between model predictions and observations, 1.005 and root-mean-square (rms) error of 7%). Bed shear stresses calculated from logarithmic velocity profiles are equated to a quadratic bottom shear stress formulation. The associated bed shear stress coefficients vary by more than an order of magnitude across the surf zone (0.0006-0.012). Bottom roughness was measured throughout the nearshore using a sonic altimeter mounted on a moving platform. The bed shear stress coefficients are positively correlated with bottom roughness (linear correlation coefficient, 0.6). A higher linear correlation coefficient (0.8) is obtained by subtracting skin friction from the total bed shear stress.

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