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Modeling the Equilibrium of a Carbonate Tidal Channel. Preliminary Results

Abstract

The definition of the equilibrium profile of a tidal channel bounded seaward by the ocean and without a landward supply of water and sediment is a problem that has a long been the focus of study for clastic systems. The equilibrium of a clastic tidal channel is related to a constant relative base level and relatively coarse bed material, i.e. sand, defined as a condition in which the tidal channel does not experience net aggradation or degradation over a tidal cycle. In this study we compare the equilibrium of clastic and carbonate tidal channels with fine sand sediment size as bed materials, i.e. we neglect particles in the silt/mud range and the role of tidal flats. In the case of a carbonate system the problem is more complex than in the case of a clastic system since in situ “production of carbonate sediments” occurs in conjunction with geochemical processes that modify the carbonate particles and their properties. Our model for the long-term evolution of a carbonate tidal channel is based on assumptions and simplifications which involve modeling carbonate accumulation in terms of a specified depth-dependent carbonate “production rates” based on modern rates of carbonate accumulation. We further assume that 1) there is no input of clastic sediments to the system, 2) cementation processes are slow when compared to carbonate accumulation, 3) there is an absence of particles in the silt/mud range, and 4) we treat the carbonate sediments as non-cohesive particles. The one-dimensional de Saint Venant equations and the equation of conservation of bed material are solved numerically using an explicit finite difference scheme to study the case of a channel with constant width, and a finite volume scheme to account for more complex channel geometries. We present 1) a comparison of equilibrium profiles of clastic and carbonate tidal channels under constant base level conditions for different channel shapes, and 2) numerical results on how the equilibrium of a carbonate system changes under conditions of rising relative base level. Our preliminary results show that the in situ accumulation of carbonate sediments is responsible for the different equilibrium profiles of clastic and carbonate tidal channels. Further, due to the in situ accumulation of carbonate sediments the idea of morphodynamic equilibrium can be extended to the case of rising relative base level in a carbonate system.