The mean-field model for alluvial river channel geometry: it's not wrong, even if it's boring
Abstract
Early mechanistic models for alluvial rivers describe their averaged behavior using time and space averaged hydraulic and sedimentary variables, with a landmark example being the threshold channel model. Many researchers now object to such models as "too simple". This objection often misses the point: "the simple model is wrong because it doesn't produce dynamics that I see". This is the equivalent of objecting to a climate model that doesn't reproduce our daily weather. Here, I address two fallacies that have arisen from such objections. First is that alluvial rivers with threshold banks are incompatible with bank erosion, bar deposition and sediment transport. Second is that extreme events dominate in many places, and that Wolman and Miller are wrong. Parker (1976) recognized that bed-load rivers must have banks that are at threshold in order to have a stable width, but accommodate transport in order to pass an imposed sediment load. He realized that the zeroth-order model for alluvial river geometry needed a higher-order correction: by accounting for a lateral stress gradient due to turbulent mixing, one obtains a channel with threshold banks and transport in the middle. The IPGP group formalized this idea in a stastical physics sense: the threshold channel is the ground state of rivers, and sediment transport represents a perturbation that requires a higher-order correction to the model. As for Wolman and Miller: there is much discussion about the potential importance of extreme events that would violate the idea that there is a peak in the distribution of geomorphic work; yet, there are remarkably few studies that formally compute the distribution of sediment transport events, and those that do find a well defined peak. Here I advance the boring notion that Parker's near-threshold channel formulation is a formal "mean field model" for river channel geometry, and that bankfull discharge corresponds to the peak stress impulse imparted on the bed. A "mean field model" reduces the forces of many interacting components to an effective mean force by averaging appropriately; it's what we all do, for example, when we estimate boundary stress from the law of the wall. I demonstrate convergence to the mean-field model in real rivers, and suggest that behaviors like meandering and sorting are higher-order variations around this mean.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFMEP43B..09J
- Keywords:
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- 1824 Geomorphology: general;
- HYDROLOGY;
- 1825 Geomorphology: fluvial;
- HYDROLOGY;
- 1826 Geomorphology: hillslope;
- HYDROLOGY;
- 1862 Sediment transport;
- HYDROLOGY