The Role of 2D Circulation in Sand Bar Migration

Models of bar dynamics typically involve moments of the cross-shore flow, with offshore movement associated with the strong offshore directed undertow and onshore migration related to wave asymmetry and skewness [Gallagher, et al., 1998]. Based on these hypotheses, models and laboratory studies have used the alongshore-mean bar position and alongshore-uniform wave conditions (a 1DH approach) to study bar response to varying wave conditions. Commonly, cases of offshore migration were reproduced with reasonable accuracy, but predictions of onshore migration were less successful. However, examination of time-exposure images of waves show that during periods of offshore migration, bars tend to be alongshore uniform and move rapidly offshore, but during onshore migration, sand bars are rarely straight, instead becoming very sinuous, violating the 1DH approach. We hypothesize that under milder wave conditions, the 2DH circulation associated with this alongshore-variable morphology is, in fact, largely responsible for increased onshore net sand transport and the resulting onshore bar movement. We extend the work of Plant et al. [in review] that relates bar position, sinuosity, and wave forcing within a dynamical feedback model. The model consists of coupled differential equations that govern the rates of change of cross-shore position and horizontal sinuosity as a function of the current cross-shore position and sinuosity and a proxy for wave forcing. Using a short data set from Duck, NC, they solve for the unknown coupling coefficients by doing a least-squares fit. They find that the coefficients for the self-interaction terms have a negative sign, indicating the overall system is stable. The coefficients of the cross-interaction terms (the effect of sinuosity on rate of change of bar position and visa versa), however, are non-zero and have opposite signs indicating the systems are coupled and stability is not affected by these terms. We expand this study, relating bar position, sinuosity, and incident wave conditions, over a one-year period of time-exposure images of Palm Beach, Australia. The resulting analysis produces clear links between bar sinuosity and the rate of change of mean bar position, suggesting a 2DH approach should be used when modeling bar migration. Gallagher, E. L., et al. (1998), Observations of sand bar evolution on a natural beach, Journal of Geophysical Research, 103, 3203-3215. Plant, N. G., et al. (in review), A dynamical attractor governs beach response to storms, Journal of Geophysical Research.