Spontaneous channelization in permeable ground: theory, experiment, and observation

Abstract

Landscapes that are rhythmically dissected by natural drainage channels exist in various geologic and climatic settings. Such landscapes are characterized by a length-scale for the lateral spacing between channels. We observe a small-scale version of this process in the form of beach rills and reproduce channelization in a table-top seepage experiment. On the beach as well as in the experiments, channels are spontaneously incised by surface flow, but once initiated, they grow due to water emerging from underground. Field observation and experiment suggest the process can be described in terms of flow through a homogeneous porous medium with a freely shaped water table. According to this theory, small deformations of the underground water table amplify the flux into the channel and lead to further growth, a phenomenon we call "Wentworth instability". Piracy of groundwater can occur over distances much larger than the channel width. Channel spacing coarsens with time, until channels reach their maximum length.

Bifurcation dynamics of natural drainage networks

“…We consider only the case in which water flows in a network of streams as opposed to forming swamps and pools. We note that the dynamics of sediment transport often lead to a channellized surficial flow [20]. The water table therefore intersects the network at the elevation of the streams.…”

Shape and dynamics of seepage erosion in a horizontal granular bed

“…In the inclined case, the initial bed slope is the parameter determining the mechanical stability of the sediment [14]. For the flat bed considered here, an analogous parameter may correspond to the ratio between the largest depth of granular material above the water table and the maximum length of the channel and corresponds to the minimum slope inside the channel.…”

“…Seepage erosion is said to shape many examples of valleys, canyons and river networks and assumed to produce amphitheater-headed valleys [4,5,[7][8][9], although recent field reports [10,11] suggest that some of these examples can be attributed to overland flow as well. At smaller and more rapid scales, seepage erosion has been considered in the formation of channels on the beach during outgoing tide [5,[12][13][14], where capillary cohesion between grains can be also important. The spatial distribution of the groundwater flow when brought from a far away reservoir as opposed to being fed by local precipitation can be crucial to the shape of the channels.…”

Evolution of Porosity and Channelization of an Erosive Medium Driven by Fluid Flow

“…Significant work examining erosion and network growth at the surface of an erodible bed due to runoffs and seepage flow has been reported [12][13][14][15]. While these studies provide valuable perspective, the overland flow dynamics can be rather different from those within the subsurface.…”