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

Abstract

Greenwood, B. and Osborne, P.D., 1990. Vertical and horizontal structure in cross-shore flows: An example of undertow and wave set-up on a barred beach. Coastal Eng., 14: 543-580. 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 timeaveraged 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-a 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. ~ 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.~Bowen et al. (1968).0378-3839/90/$03.50

Momentum Balance Across a Barrier Reef

“…It is associated with bottom return flow in the offshore part of the surf zone. This observation should be related to the undertow current widely documented on sandy beach systems (Faria et al, 2000;Feddersen & Guza, 2003;Greenwood & Osborne, 1990;Petitjean et al, 2016;Putrevu & Svendsen, 1993;Reniers et al, 2004). The main difference is that here only a portion of the onshore volume flux is returned in the undertow because of the onshore transport over the reef.…”

Vertical structure of the undertow outside the surf zone

“…Detailed laboratory measurements of the undertow include those of Stive and Wind [1982], Nadaoka and Kondoh [1982] (hereinafter referred to as N & K), $vendsen [1984, 1986], Okayasu et al [1986,1988] and F. Ting and J. Kirby (Observation of undertow and turbulence in a laboratory surf zone, submitted to Coastal Engineering, 1993, hereinafter referred to as T & K). Field measurements include those of Wright et al [1982], Guza and Thornton [1985] and Greenwood and Osborne [1990]. However, the models for the calculation of undertow have so far only been applied to calculate the undertow inside the surf zone.…”

Wave-Dominated Coasts

“…Generally, the faster offshore speeds are found in the bottom half of the water column, close to the bed ( Figure 14). In reality, undertow is more complex on account of oblique wave approach and varying breaker positions (Haines and Sallenger, 1994); however, now there are many field mea surements of undertow on both barred Davidson-Arnott and McDonald, 1989;Greenwood and Osborne, 1990;Masselink, 2004;Goodfellow and Stephenson, 2005;Houser et al, 2006) and nonbarred coasts (Miles and Russell, 2004;Reniers et al, 2004;Aagaard and Vinther, 2008).…”