What Controls the Transition from Confined to Unconfined Flow? Analysis of Hydraulics in a Coastal River Delta

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Abstract
Recent field work at the Wax Lake Delta (WLD) in coastal Louisiana indicates lateral outflow from channels to islands upstream of the receiving basin; in this region of the delta the flow transitions from confined to unconfined (i.e., from a uniform discharge profile to a nonuniform discharge profile). The hydraulics of this transition zone and the controls exerted by vegetation, topography, and river discharge fluctuations are analyzed in this work. The shallow water equations are numerically solved in two model domains: an idealized channel-island complex and the full domain of the WLD. In both domains, a significant fraction of the river discharge flows laterally from the channels to deltaic islands before reaching the receiving basin. Vegetation roughness within the delta islands significantly impacts the fraction and rate of lateral outflow from the channel, while river discharge fluctuations have a limited effect, due to the backwater control on the subcritical flow. The presence of vegetation in the islands tends to increase velocities within the channel, except in the region upstream of significant lateral outflow, where the velocity increases with decreasing vegetation roughness due to the lowered water level that reduces the flow cross-section. The topography establishes a lateral water surface gradient between the channel and the islands even with low vegetation roughness, which drives lateral flow. A velocity spreading angle is used to mark the transition from confined to unconfined flow; the angle generally increases up to the onset of unconfined flow and then decreases as the flow approaches the receiving basin and the flow in the island tends to align with that of the channel. The lateral outflow from the primary channels influences the hydraulics of the flow throughout the backwater length. The transition between confined and unconfined flow in coastal river deltas has a significant impact on the flow hydraulics and the resulting transport dynamics of solids and solutes.

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