Fernanda Hoefel¹ and Steve Elgar²

Onshore sediment transport and sandbar migration are important to the morphological evolution of beaches but are not well understood. Here, a model that accounts for fluid accelerations in waves predicts the onshore sandbar migration observed on an ocean beach. In both the observations and the model, the location of the maximum acceleration-induced transport moves shoreward with the sandbar, resulting in feedback between waves and morphology that drives the bar shoreward until conditions change. A model that combines the effects of transport by waves and mean currents simulated both onshore and offshore bar migration observed over a 45-day period.

¹ Massachusetts Institute of Technology/Woods Hole Oceanographic Institution (WHOI) Joint Program in Oceanography, WHOI, Mail Stop 09, Woods Hole, MA 02543, USA.
² WHOI, Mail Stop 11, Woods Hole, MA 02543, USA. E-mail: fhoefel{at}whoi.edu, elgar{at}whoi.edu

As waves enter shallow water, their shapes evolve from sinusoidal to peaky, with sharp wave crests separated by broad, flat wave troughs. It has been hypothesized that the larger onshore velocities under the peaked wave crests transport more sediment than the offshore velocities under the troughs (7, 8). However, models that account for the onshore-skewed velocities do not accurately predict onshore bar migration observed near the shoreline and in the surf zone (1, 2, 5, 6), although skewed velocities may be important outside the surf zone (9). As waves continue to shoal and break, they evolve from profiles with sharp peaks to asymmetrical, pitched-forward shapes with steep front faces. Water rapidly accelerates under the steep wave front, producing high onshore velocities, followed by smaller decelerations under the gently sloping rear of the wave (Fig. 1B) (10, 11). Large accelerations generate strong horizontal pressure gradients that act on the sediment (12-14). Although the precise mechanisms are not fully understood, it has been hypothesized that if accelerations increase the amount of sediment in motion (10, 12, 15, 16), there will be more shoreward than seaward transport under pitched-forward waves.

A surrogate for the effects of acceleration in pitched-forward waves is a dimensional form of acceleration skewness (12) (i.e., the difference in the magnitudes of accelerations under the front and rear wave faces), a_spike = a³/a², where a is the time series of acceleration and angle brackets denote averaging. Discrete-particle computer simulations of bedload transport driven by asymmetrical waves characteristic of surf zones indicate that sediment flux is proportional to a_spike once a threshold for sediment motion is exceeded (12). Unlike the monochromatic waves used in the numerical simulations, accelerations in random waves in a natural surf zone can be skewed either positively (onshore) or negatively (offshore). Thus, the expression for cross-shore (x) acceleration-driven bedload sediment transport Q_acc(x) suggested by the numerical simulations is extended to account for random waves by including a term that depends on the sign (i.e., the direction) of a_spike, yielding

(1)

where K_a is a constant, sgn[ ] is the sign of the argument, and a_crit is a threshold that must be exceeded for initiation of transport. By comparing model predictions with observations, the optimal values of K_a = 1.40 × 10⁴ m s and of a_crit = 0.20 m s² were determined. These parameter values are within a factor of 5 of those suggested by the highly idealized discrete-particle numerical simulations (12) (K_a = 0.26 × 10⁴ m s, a_crit = 1.00 m s²). Differences may be attributable to random waves, a distribution of sediment grain sizes and shapes, and breaking-induced turbulence in the ocean. If it is assumed that gradients in alongshore transport are negligible, mass conservation in the cross-shore direction yields

(2)

where dh/dt is the change in bed elevation h with time t and µ = 0.7 is a sediment packing factor. Extensions to Eq. 2 to account for alongshore changes are straightforward, but not necessary for the small alongshore gradients in transport inferred for the observations discussed here (2).

To test the hypothesis that the cross-shore distribution of near-bottom accelerations results in overall onshore sediment transport and sandbar migration when mean currents are weak, we compared morphological change predicted by the acceleration-based model (Eqs. 1 and 2) with observations made along a cross-shore transect extending about 400 m from the shoreline to 5 m water depth on the North Carolina coast (2, 17). The model was initialized (t = 0) with observed bathymetry and driven with accelerations observed with near-bottom-mounted current meters (Fig. 2). During a 5-day period with approximately 75-cm-high waves and cross-shore mean currents less than 30 cm s¹, the observed onshore sandbar migration of about 30 m was predicted accurately (Fig. 2). A widely used energetics sediment transport model (1, 2, 7, 8, 18) that accounts for transport both by velocity skewness (but not acceleration) and by mean currents predicted no change in the cross-shore depth profile and thus failed to predict the observed sandbar migration (2).

During the onshore sandbar migration event, acceleration skewness (a_spike) increased from small values offshore to a maximum near the bar crest and then decreased toward the shoreline (Fig. 3, A and C), producing cross-shore gradients in transport that are consistent with erosion offshore and accretion onshore of the bar crest (Fig. 3, B and C). The peak in acceleration skewness moved shoreward with the bar crest (Fig. 3), resulting in feedback between wave evolution and bathymetry that promoted continued onshore sediment transport and bar movement until conditions changed (Fig. 1B). Feedback also occurs between wave-breaking-induced offshore-directed mean currents (maximum just onshore of the bar crest) and morphology that results in offshore bar migration during storms (1, 2) (Fig. 1A).

Inclusion of the effects of skewed accelerations (Eq. 1) in the energetics-based sediment transport model (1, 2, 7, 8, 18) resulted in improved predictive skill, both when mean cross-shore currents were weak (Fig. 2) and during storms when mean currents were strong (Fig. 4). During a 45-day observational period, the bar crest migrated offshore about 130 m during storms and onshore about 40 m when waves and mean flows were small (Fig. 4B), resulting in a net offshore migration of 90 m. Although energetics models without acceleration-based transport predicted the offshore migration (1, 2), they had limited skill predicting the total change to the beach over 45 days because they failed to predict onshore migration between storms (2). The energetics model that was extended to include acceleration better predicted the change in the sea-floor both onshore and offshore of the bar crest (Fig. 4), and the overall evolution of the cross-shore depth profile (Fig. 5).

REFERENCES AND NOTES