Brad Murray¹, Rob Thieler², Andrew Ashton¹, and Emily Tang¹

¹Division of Earth and Ocean Science/Center for Nonlinear and Complex Systems

Duke University, Box 90320

Durham, NC, 27708

²U. S. Geological Survey, Coastal and Marine Geology Program

384 Woods Hole Road

Woods Hole, MA, 02543-1598

In nearly all analytical and numerical models of nearshore sediment transport and morphological development, sediment flux depends only on local flow conditions. However, in non-uniform flows, sediment transport may not be in equilibrium with local hydrodynamics. Such cases arise when, in a Lagrangian frame of reference, flow conditions change more rapidly than the time scale for adjustment of the suspended-sediment concentration profile. This time scale depends on the recent history of hydrodynamic conditions. For example, if sediment is suspended far from the bed by energetic turbulence, and a mean flow carries this profile rapidly into an area of considerably lower energy, the sediment flux could be considerably greater than that predicted by the local flow. We use two examples of nearshore and inner shelf flows to illustrate the importance of this effect.

On approximately planar beaches, rip channels develop after a period in which non-bathymetrically driven rip currents occur in apparently random locations. Observations and model results indicate that the excavation of these cross-shore oriented negative bed features results from suspended sediment fluxes that are not in equilibrium with local flow conditions. In a quasi-steady state, the cross-shore divergence of water flux in a rip current must be equaled by alongshore convergence. However, on a sloping beach, as the cross-shore flow moves into deeper water, the cross-shore divergence of the current velocity is decreased relative to the alongshore convergence of velocity. If sediment transport is treated as a function only of local conditions, the divergence of sediment flux depends on the divergence of the mean velocity. Such a treatment predicts either accumulation of sediment under a rip current, or gives an ambiguous prediction concerning erosion or deposition (depending on the particular sediment-transport equation used). Numerical-model results show that with an approximately realistic rip-current velocity field, using a common formulation for sediment transport under combined wave and mean current conditions, channels do not develop. Observations of plumes of sediment well outside the surf zone suggest that sediment suspended throughout the water column in the surf zone does not settle rapidly enough to remain in equilibrium with the decreasing current velocity and level of wave-generated turbulence as the flow moves offshore. Incorporating this lag effect into the numerical model does robustly produce rip channels on a planar beach.

This lag effect also plays a key role in a new hypothesis and preliminary model for the formation and development of "rippled scour depressions," which side-scan sonar observations are showing to be ubiquitous inner-shelf features. These accumulations of coarse material feature large wave-orbital ripples, with wavelengths on the order of a meter, and heights on the order of a decimeter. Diver observations indicate that turbulence from the interaction of wave-orbital motions with these large ripples suspends fine sediment approximately an order of magnitude farther from the bed than occurs over domains of fine material immediately adjacent to the coarse domains. As mean flows move across such features, the advected suspended-sediment concentrations will not adjust rapidly enough to stay in equilibrium with the local conditions; Over a concentration of coarse material, the suspended-sediment concentration does not saturate (reach capacity) immediately, resulting in the further removal of fines over extended areas in these domains, and the fines are spread over a large downstream area, rather than piling up at the border of the coarse feature. This interaction provides a feedback reinforcing concentrations of coarse material, and could lead to the development of the large-scale features observed.