Modeling flow and sediment transport dynamics in the lowermost Mississippi River, Louisiana, USA, with an upstream alluvial‐bedrock transition and a downstream bedrock‐alluvial transition: Implications for land building using engineered diversions

Abstract

The lowermost Mississippi River, defined herein as the river segment downstream of the Old River Control Structure and hydrodynamically influenced by the Gulf of Mexico, extends for approximately 500 km. This segment includes a bedrock (or more precisely, mixed bedrock-alluvial) reach that is bounded by an upstream alluvial-bedrock transition and a downstream bedrock-alluvial transition. Here we present a one-dimensional mathematical formulation for the long-term evolution of lowland rivers that is able to reproduce the morphodynamics of both the alluvial-bedrock and the bedrock-alluvial transitions. Model results show that the magnitude of the alluvial equilibrium bed slope relative to the bedrock surface slope and the depth of bedrock surface relative to the water surface base level strongly influence the mobile bed equilibrium of low-sloping river channels. Using data from the lowermost Mississippi River, the model is zeroed and validated at field scale by comparing the numerical results with field measurements. The model is then applied to predict the influence on the stability of channel bed elevation in response to delta restoration projects. In particular, the response of the river bed to the implementation of two examples of land-building diversions to extract water and sediment from the main channel is studied. In this regard, our model results show that engineered land-building diversions along the lowermost Mississippi River are capable of producing equilibrated bed profiles with only modest shoaling or erosion, and therefore, such diversions are a sustainable strategy for mitigating land loss within the Mississippi River Delta.

Alluvial Morphodynamics of Bedrock Reaches Transporting Mixed‐Size Sand. Laboratory Experiments

“…The observed spatial changes in water depth partially confirm the numerical predictions of the Viparelli et al () formulation, i.e., at equilibrium in a low slope bedrock reach downstream of an alluvial‐bedrock transition, the flow is characterized by a reduction of the flow depth in the streamwise direction. The experimental results however showed that the problem is more complex than in the Viparelli et al () formulation due to the changes in bedform geometry and grain size distribution of the alluvial bed surface, which can occur even with very small changes in flow depth and velocity.…”

“…The results of Figures show that the response of the flow and of the bedload transport to the presence of an un‐erodible surface is more complex than that presented in Zhang et al () and Viparelli et al (). Notwithstanding the streamwise reduction of the flow resistances (Figures a, b, d, e, g, h, j, and k), downstream of the stable alluvial‐bedrock transitions, the bed material transport capacity tends to increase in the direction of the flow (Figure c, f, i, and l).…”

“…When ξ d is sufficiently small, the river reaches equilibrium conditions with exposed bedrock and steady but nonuniform flow (Viparelli et al, ) (Figure d). Here, we follow Viparelli et al (), and we introduce the minimum thickness of alluvial cover for complete alluviation of the channel bed, L ac . L ac represents the minimum thickness of the alluvial layer such that the presence of the bedrock surface with its irregularities (roughness) does not influence in‐channel sediment transport processes.…”

“…The bedrock slopes considered in this experimental study are comparable to the slopes of lowland sand bed rivers (10 ‐4 or less). For example, the bedrock slope in the mixed alluvial‐bedrock Mississippi River is 7x10 ‐6 in the New Orleans area and 1.2x10 ‐4 approximately 100 river kilometers upstream of the Gulf of Mexico (Viparelli et al, and references therein). These slopes are at least one order of magnitude milder than the slopes considered by Chatanantavet and Parker (), and equilibrium conditions on relatively mild bedrock slopes are not dependent on the initial alluvial cover of the model bedrock surface (Chatanantavet & Parker, ).…”

“…Very limited quantitative information is also available to account for the nonuniformity of the sediment size distribution in the presence of a bedrock surface (Hodge et al, 2011;Hodge et al, 2016). In the attempt to simplify the text, hereinafter "bedrock reach" is used to denote a mixed bedrock-alluvial reach as in Viparelli et al (2015). impact on the flow resistances.…”