When and where do free bars in estuaries and tidal channels form?

The incipient formation of free bars in weakly converging tidal channels and estuaries is mathematically framed within a unified two-dimensional shallow water and sediment mass balance model. The analysis is driven by the recognition that none of the theoretical models introduced so far account for the spatially varying character of the planform morphology, which characterizes estuaries and creeks forming networks in coastal wetlands and in the tide-dominated reaches of deltas. The problem is tackled by means of a linear stability analysis, by observing that width variations act on a spatial scale that is typically much longer than bars wavelength, allowing for an analytical treatment of the governing system of equations. We focus on two limit cases: first, the river transition into a micro-tidal sea (estuarine case); second, a tidal channel in the absence of a fluvial supply of freshwater and sediment (coastal case). In the estuarine case, bars arise as a result of an intrinsic instability of the equilibrium state. Width increases toward the mouth leading to channel shallowing, which in turn promotes the development of multiple bars. This effect is partially counteracted by the channel deepening produced by the tidal action, which tends to reduce bar growth and migration rate. In the coastal case, tidal bars form far from the equilibrium state of the system, adapting instantaneously to the evolving bed profile, which in turn affects channel flow conditions. Noteworthy, the model suggests that the spatial-temporal distribution of bars observed in nature reflects the evolutionary history of the system