Symmetric rearrangement of groundwater-fed streams

Abstract

Streams shape landscapes through headward growth and lateral migration. When these streams are primarily fed by groundwater, recent work suggests that their tips advance to maximize the symmetry of the local Laplacian field associated with groundwater flow. We explore the extent to which such forcing is responsible for the lateral migration of streams by studying two features of groundwater-fed streams in Bristol, Florida: their confluence angle near junctions and their curvature. First, we find that, while streams asymptotically form a 72° angle near their tips, they simultaneously exhibit a wide 120° confluence angle within approximately 10 m of their junctions. We show that this wide angle maximizes the symmetry of the groundwater field near the junction. Second, we argue that streams migrate laterally within valleys and present a new spectral analysis method to relate planform curvature to the surrounding groundwater field. Our results suggest that streams migrate laterally in response to fluxes from the surrounding groundwater table, providing evidence of a new mechanism that complements Laplacian growth at their tips.

Shapes of river networks

“…On the local (and smallest) scale, the shape of the groundwater table is not strongly correlated to small fluctuations in the local topographic surface, suggesting that the growth of streams on this scale is dominated by local groundwater flow [24]. It is on this scale that planform geometry can be understood through the groundwater field [17,25,26]. However, on the larger, regional scale, the water table replicates the topography and the resulting flows should follow topographic gradients [19,27].…”

Groundwater erosion of coastal gullies along the Canterbury coast (New Zealand): a rapid and episodic process controlled by rainfall intensity and substrate variability

“…Such studies suggest that the velocity at which channel heads advance is a function of the groundwater flux and the capacity of seepage water to transport sediment from the seepage face (Fox et al, 2006;Howard and McLane, 1988;Abrams et al, 2009;, and that channel head erosion occurs by episodic headwall slumping (Kochel et al, 1985;Howard, 1990). Channels incised by groundwater seepage have been shown to branch at a characteristic angle of 72 • at stream tips, which increases to 120 • near stream junctions (Devauchelle et al, 2012;Yi et al, 2017), whereas growing indentations competing for draining groundwater results in periodically spaced channels (Dunne, 1990;Schorghofer et al, 2004). Channel network geometry appears to be determined by the external groundwater flow field rather than flow within the channels themselves (Devauchelle et al, 2012).…”

Geodesic Loewner paths with varying boundary conditions

“…The asymptotic behaviour of the paths of the slits in this and other geometries has application to patterns formed by groundwater-fed stream networks (e.g. [4,7,21]). Similarly, the growth of symmetric pairs of slits is considered here with the piecewise constant boundary condition (2.3) using a modification of the equations in §3b.…”

“…[8,14,20]). Geometric properties of growing geodesic slits have successfully explained features of Laplacian growth, for example, the properties of stream bifurcations in groundwater-fed drainage systems [7,8,21].…”