Vertical and horizontal structure in cross-shore flows: An example of undertow and wave set-up on a barred beach

Eulerian measurements of the horizontal, cross-shore velocity field in the lowermost meter of the water column, in association with measurements of waves and the mean elevation of the water surface, across a nontidal, low relief, barred surf-zone reveal: (a) spatially coherent patterns of the time-averaged first, second and third moments of the velocity field, which vary temporally in direct response to the incident waves; (b) large asymmetries in the flow field, with offshore-directed mean flows upto 0.20 m s−1 and onshore-directed velocity skewness (the third moment normalized by the standard deviation) upto +0.60; (c) mean flows decrease and oscillatory flows (measured by the standard deviation of the velocity field) increase towards the water surface; (d) a fourth-order polynomial provides the best fit to the cross-shore set-up, reflecting the influence of variable energy dissipation due to topographic controls on wave breaking; (e) significant linear correlations exist between the cross-shore mean velocities and the maximum set-up of the still-water surface near to the shoreline (upto 82% of the observed variability in the former can be accounted for by linear regressions); (f) set-up is highly correlated with the incident wave height (86% of the observed variability in the former can be accounted for by a linear regression); (g) gradients in the mean water surface are significantly less than those predicted by a linear function of beach slope as originally proposed by Bowen et al.1 even using an appropriate breaking criterion (0.4–0.6) for the spilling breakers recorded. Cross-shore circulation over the low relief, barred nearshore slope is predominantly two-dimensional over the outer bar in this case study. The near-bed mean flow is an undertow responding to the balance between the wave-generated, depth-dependent momentum flux directed onshore, the stress induced by the onshore mass transport under waves and wind, and the hydraulic pressure gradient induced by set-up of the mean water-level