Winding, curving channels are a universal landscape pattern, from the Amazonian floodplains to the Aeolis Planum–a ridged region of Mars. Wriggling groves are cut into the bedrock of Utah and the volcanic valleys of the lunar surface.
Despite their ubiquity, few researchers have asked why this pattern is ubiquitous, and what determines how curvy, or sinuous, a channel will be. Eli Lazarus and José Antonio Constantine, both of the Environmental Dynamics Laboratory at Cardiff University in the UK, provide an answer in a paper published April 22 in PNAS Early Edition.
By comparing sinuosity, floodplain slope, and flow resistance (“roughness” due to vegetation or topography) the pair suggest a general theory for river shape: curviness is primarily driven by the ratio of flow-resistance variance (or patchy roughness) to slope. Holding resistance constant, steeper slopes mean straighter channels. Holding slope constant, more resistant landscapes lead to wider river wanderings.
The findings highlight the control the floodplain, or landscape surface, holds over river morphology. While the work exists essentially in the world of theory, the Lazarus and Constantine believe it has possible management applications.
“We argue that the Sacramento River may have straightened out–gone from more sinuous to less sinuous–as a result of historical land-use changes on its floodplain. Cut down all the natural riparian vegetation and replant the floodplain with orchards, and you’ve effectively reduced the floodplain roughness without changing the floodplain slope.”
One problem with rivers is that they can move–straightening themselves out, or adding extra curves as the landscape dictates. Land managers seeking to restore riparian habitat or minimize flood risk, can boost channel ‘sinuosity’ by maintaining or promoting landscape ‘resistance.’
“Even a channel engineered to be sinuous will tend to straighten,” write the authors, “if the R/S (resistance to slope) ratio of its floodplain is suppressed or inherently low and if overbank flows are allowed to mobilize the floodplain surface.”
However, increasing resistance–by promoting log jams or woody masses of debris in a forest, for example–can boost sinuousness. The right management, the authors suggest “might foster a channel more sinuous than extant hydraulic geometry may predict.”
Lazarus became interested in modeling sinuosity during regular drives near Portland, Maine, where he lived prior to moving to Cardiff. Outside the city “there’s a mudflat with a highly sinuous channel you can see from the highway. I drove by that channel a few times a week for about three years–and eventually I noticed that in all that time, despite a large tidal range, hard winters, and other coastal weather events, and despite its high sinuosity, the channel platform hadn’t changed.”
Curiosity aroused, Lazarus began experimenting with simulated channels after arriving in Cardiff. He found by manipulating two variables, slope and resistance, he could dramatically change channel form.
“José saw potential in this little model I’d been tinkering with, and was keen to think about it in terms of why rivers take the shapes they do. I liked that the more we pushed […] the more interesting the results seemed to get.”
The earth scientists created a flow-routing model, running 40,000 simulations through it. The model features a grid of cells, assigned a certain slope. Each cell holds a random resistance factor, corresponding in real life to the resistance a liquid would encounter on its meandering. Beginning from a corner cell, a fluid finds a path through the grid, flowing into whichever neighboring cell holds the lowest resistance value.
The dynamics of river meandering, Lazarus says, has already been described by fluvial geomorphology. “We’re not supplanting that in any way, shape, or form. Rather, that theory focuses primarily on flow inside a channel. In our work here, we effectively start outside the channel. It’s a consideration of the same system from a different perspective.”