Distributary Channel Networks as Moving Boundaries: Causes and Morphodynamic Effects

Abstract

We propose an exploratory model to describe the morphodynamics of distributary channel network growth on river deltas. The interface between deep channels and the shallow, unchannelized delta front deposits is modeled as a moving boundary. Steady flow over the unchannelized delta front is friction dominated and modeled by Laplace's equation. Shear stress along the network boundary produces nonlinear erosion rates at the interface, causing the boundary to move and network elements (channels and branches) to form. The model was run for boundary conditions resembling the Wax Lake Delta in coastal Louisiana, 20 parameterizations of sediment transport, and 3 parameterizations of discharge. In each case, the model produced a complex channel network with channel number, width, bifurcation angle, and channel shape depending on the sediment transport formula. For reasonable sediment transport parameters and gradually increasing water discharge, the model produced network characteristics and progradation rates similar to the Wax Lake Delta. This suggests that the model contains the processes responsible for network growth, despite its abstract formulation. Key Points:• Prograding distributary channel networks of varying morphology can be modeled as a simple moving boundary • Nonlinearities in the sediment transport formula dictate channel width, number of branches, bifurcation angle, and channel shape • Evolution is dictated by network morphology, sediment transport, and water discharge Supporting Information:• Supporting Information S1

Application of the Schwarz-Christoffel map to the Laplacian growth of needles and fingers

“…Such needle models have been proposed as representative of growing "arms" in the star shaped clusters typically formed in diffusion-limited aggregation, e.g., [12][13][14]. Similar radial needlelike structures were reported in the recent numerical solution of a Laplacian growth model for evolving river deltas [4]. Theoretical results for these models are usually confined to two arms or symmetric arrangements of multiple arms.…”

“…Even in two dimensions, Laplacian growth leads to complicated, often beautiful, patterns. Examples include Saffman-Taylor fingering [1], diffusion-limited aggregation [2], the formation of ramified river valley networks by groundwater flow [3], erosion of sediment to form narrow channels in river deltas [4], combustion fronts [5], magnetic flux dendrite formation in superconductors [6], and growth of bacterial colonies [7]. In these examples instability at the interface leads to long narrow protrusions-fingers-of one phase penetrating the other.…”

Validation of Streaklines as Recorders of Synoptic Flow Direction in a Deltaic Setting

“…It is valuable that the streaklines have an increased accuracy close to the channel network. The morphology of the channel network boundary exerts an important control on the delta evolution [9,12]. The results of this study show that streaklines are a legitimate means of validating flow patterns in this location, where streaklines have been previously used [21,22].…”

“…The results of this study show that streaklines are a legitimate means of validating flow patterns in this location, where streaklines have been previously used [21,22]. This is likely due to the importance of the subaqueous channel network boundary in setting the delta front flow patterns [12]. Spatial trends in accuracy can also be attributed to the scale of the travel time for a parcel of water through the system, relative to the temporal scale of the tidal influence.…”

“…Sediment transport divergence and bed change can be examined through use of hydraulic models, which vary in complexity and application [8][9][10][11][12][13][14][15][16]. However, such models require information about boundary conditions (e.g., bathymetry, grain sizes, and hydraulic conditions) in order to investigate specific river deltas.…”