Deterministic chaos in a model of a simple delta network
Abstract
An important aspect of delta dynamics is how sediment flux is partitioned to different parts of the delta through time, affecting patterns of land-building/loss, and the formation of stratigraphy. Here, we present results from a model of a simple distributary network consisting of two orders of bifurcations: an upstream channel splits into two branches, each of which splits into two additional branches. The 1D bed elevation profiles of each branch are modeled through time, and a nodal condition accounting for a transverse bed slope just upstream of the bifurcation is used to partition the flow at bifurcations. The model generates surprisingly complex dynamics despite its simplicity. Constrained by the need to distribute sediment evenly between branches in the long-run, the system undergoes repeated full and partial avulsions. We find that the solution to the system is aperiodic, but bounded. We also observe a sensitive dependence on the initial conditions: simulations started with slightly different initial conditions diverge exponentially. These observations are the hallmark of chaos, summarized by Edward Lorenz as "where the present determines the future, but the approximate present does not approximately determine the future." In our model, chaos results from the two-way coupling between upstream and downstream bifurcations. We find that a single bifurcation may be periodic, but it is never chaotic. However, when coupled, avulsions in the upstream channel change the upstream boundary conditions for the downstream bifurcations, and conversely, avulsions in the downstream bifurcations affect the slope of their feeder channel, propagating upstream to the first bifurcation. We explore how the system generates stratigraphy, using the Shields stress at the time of deposition as a proxy. We compare the stratigraphy to the single bifurcation case, which is periodic rather than chaotic. We also examine stratigraphic completeness, and find that hiatuses in the upstream portion of the domain tend to be erosional, whereas hiatuses further downstream tend to represent pauses. Our work suggests that deltas have a limited window of predictability, and indicates that chaotic and cyclic avulsion sequences should be distinguishable in the stratigraphic record.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFMEP21B1843S
- Keywords:
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- 1825 Geomorphology: fluvial;
- HYDROLOGY;
- 1861 Sedimentation;
- HYDROLOGY;
- 3022 Marine sediments: processes and transport;
- MARINE GEOLOGY AND GEOPHYSICS;
- 4217 Coastal processes;
- OCEANOGRAPHY: GENERAL