An Analytical Model to Predict the Response of Mounds Placed in the Offshore rrs. &my. Cqq%5 :& BnglnsPra

PURPOSE: An analytical model to predict the response of mounds placed in the offshore is presented, with the overall aim of providing a technique for the preliminary design of mounds subjected mainly to cross-shore sediment-transport processes induced by non-breaking waves. For example, offshore mounds created from dredged material can be used to protect sandy beaches by dissipating wave energy during severe storms or used as a source of beach nourishment. The model discussed here employs a diffusion equation to describe the mound response with respect to an equilibrium beach profile, where the diffusion coefficient is related to the local wave conditions at the mound. Analytical solutions to the diffision equation are readily available provided the initial and boundary conditions are sufficiently simplified. Solutions yield characteristic quantities that are useful in preliminary design of offshore mounds when a number of project alternatives are considered and evaluated. The model provides quantitative information on how quickly a mound disperses under the influence of non-breaking waves at a particular site. With this information, one can estimate how quickly a beach may be nourished with material from the mound or how long the mound may protect the beach from severe storms (via attenuation of incident wave energy). BACKGROUND: Recognizing the positive effects of bars for promoting beach growth and protecting beaches, a number of mounds have been constructed from dredged material (e.g., Zwamborn et al. 1970; McLellan 1990; Otay 1995; Foster et al. 1996). If a nearshore mound is intended to be stationary, it is referred to as a “stable” mound; whereas, if the mound is expected to move, it is called an “active” mound. Here, a mound is regarded as stable if the cross-shore sediment transport is small enough to only induce negligible changes in the mound shape (perhaps slight diffusion of the mound) according to some predefined criterion. Movement of an active mound might involve translation of its center-of-mass and/or significant dispersion. In the present note it is assumed that the mound is constructed from beachquality sand, whether it is a stable or an active mound. In general, mounds need not be composed of such material, but the methods developed here are for sand mounds. Also, only mounds subjected to transport by nonbreaking waves are discussed, and are alternatively referred to as offshore mounds. Lastly, the methods presented in this note are most applicable to mounds that are constructed as long, linear, shore-parallel bars where changes primarily take place in the cross-shore direction. A brief summary of the sediment-transport model employed to describe the transport rate under non-breaking waves, taking into account wave asymmetry and gravity, is provided first. After certain assumptions are made, the sediment-transport equation is combined with the sand volume conservation equation to yield a diffusion equation for which many analytical solutions are available. Based on the analytical solutions, characteristic quantities are derived that summarize the main features of how mounds respond to the local wave conditions. Two applications (Silver Strand, California, and Cocoa Beach, Florida) are then shown, where the diffusion model was employed to describe temporal mound response using the diffusion coefftcient as a fitting