Morphodynamic equilibrium of tidal channels
ABSTRACT: We explore the problem of morphodynamic equilibrium of tidal channels, bounded seaward by a tidal sea and shoaling landward as observed in coastal lagoons and estuaries. These channels are typically landward converging, meandering and bounded by tidal flats periodically flooded by the tidal wave. We then attempt to provide an answer to the following questions. How is equilibrium defined for tidal channels? Do tidal channels have an equilibrium length with a predictable bed profile? Why are channels typically converging? What fundamental differences exist between lagoon channels and estuaries? We identify three distinct cases. The first (coastal) case concerns the ’short’ tidal channels observed in coastal wetlands and lagoons: their distinct feature is the absence of a fluvial supply of fresh water and sediments. This case has been fully explored. In particular, Seminara et al. (2010) showed that rigorous conditions of static equilibrium exist and require that the sediment flux must vanish at each instant throughout the tidal cycle. The equilibrium length is proportional to the inlet depth and decreases as convergence, roughness or tidal amplitude increase. These channels satisfy the so called O’Brien law. Results have been substantiated by detailed laboratory measurements of Tambroni et al. (2005a). The second (fluvial) case concerns the transition of a river into a tidal channel characterized by fairly ‘small’ tidal oscillations. We derive a perturbation solution for flow and bed topography showing that equilibrium arises from a balance between the aggrading effect of channel divergence and the opposite effect of the residual sediment flux driven by tide propagation. The third (estuarine) case concerns the transition of a river into a tidal channel characterized by fairly ‘large’ tidal oscillations. We derive a numerical solution for flow and bed topography able to describe conditions intermediate between the two limit cases discussed previously. Results show that the model is able to describe a wide class of settings: ranging from fluvial dominated estuaries to tidally dominated estuaries, where the equilibrium profile tends to the ‘coastal’ profile, with some correction needed in order for the hydrodynamics to accommodate the fluvial transport.