Ramification of stream networks Devauchelle, Olivier; Petroff, Alexander P.; Seybold, Hansjörg F. ...
Proceedings of the National Academy of Sciences - PNAS,
12/2012, Letnik:
109, Številka:
51
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The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification—the mechanism of branching by which such networks ...grow—remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2 π /5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km ² groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9° ± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.
Path selection in the growth of rivers Cohen, Yossi; Devauchelle, Olivier; Seybold, Hansjörg F. ...
Proceedings of the National Academy of Sciences - PNAS,
11/2015, Letnik:
112, Številka:
46
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River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion ...for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.
Bifurcation dynamics of natural drainage networks Petroff, Alexander P.; Devauchelle, Olivier; Seybold, Hansjörg ...
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
12/2013, Letnik:
371, Številka:
2004
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As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, ...mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α=2π/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.
Symmetric rearrangement of groundwater-fed streams Yi, Robert; Cohen, Yossi; Devauchelle, Olivier ...
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences,
11/2017, Letnik:
473, Številka:
2207
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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.
On wave-driven propulsion Benham, Graham P.; Devauchelle, Olivier; Thomson, Stuart J.
Journal of fluid mechanics,
05/2024, Letnik:
987
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A theory is presented for wave-driven propulsion of floating bodies driven into oscillation at the fluid interface. By coupling the equations of motion of the body to a quasipotential flow model of ...the fluid, we derive expressions for the drift speed and propulsive thrust of the body which in turn are shown to be consistent with global momentum conservation. We explore the efficacy of our model in describing the motion of SurferBot (Rhee et al., Bioinspir. Biomim., vol. 17, issue 5, 2022), demonstrating close agreement with the experimentally determined drift speed and oscillatory dynamics. The efficiency of wave-driven propulsion is then computed as a function of driving oscillation frequency and the forcing location, revealing optimal values for both of these parameters which await confirmation in experiments. A comparison with other modes of locomotion and applications of our model with competitive water sports is discussed in conclusion.
Sediment load determines the shape of rivers Popović, Predrag; Devauchelle, Olivier; Abramian, Anaïs ...
Proceedings of the National Academy of Sciences - PNAS,
12/2021, Letnik:
118, Številka:
49
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Understanding how rivers adjust to the sediment load they carry is critical to predicting the evolution of landscapes. Presently, however, no physically based model reliably captures the dependence ...of basic river properties, such as its shape or slope, on the discharge of sediment, even in the simple case of laboratory rivers. Here, we show how the balance between fluid stress and gravity acting on the sediment grains, along with cross-stream diffusion of sediment, determines the shape and sediment flux profile of laminar laboratory rivers that carry sediment as bedload. Using this model, which reliably reproduces the experiments without any tuning, we confirm the hypothesis, originally proposed by Parker G. Parker,
89, 127-146 (1978), that rivers are restricted to exist close to the threshold of sediment motion (within about 20%). This limit is set by the fluid-sediment interaction and is independent of the water and sediment load carried by the river. Thus, as the total sediment discharge increases, the intensity of sediment flux (sediment discharge per unit width) in a river saturates, and the river can transport more sediment only by widening. In this large discharge regime, the cross-stream diffusion of momentum in the flow permits sediment transport. Conversely, in the weak transport regime, the transported sediment concentrates around the river center without significantly altering the river shape. If this theory holds for natural rivers, the aspect ratio of a river could become a proxy for sediment discharge-a quantity notoriously difficult to measure in the field.
A fluid flowing over a granular bed can move its superficial grains, and eventually deform it by erosion and deposition. This coupling generates a beautiful variety of patterns, such as ripples, bars ...and streamwise streaks. Here, we investigate the latter, sometimes called ‘sand ridges’ or ‘sand ribbons’. We perturb a sediment bed with sinusoidal streaks, the crests of which are aligned with the flow. We find that, when their wavelength is much larger than the flow depth, bedload diffusion brings mobile grains from troughs, where they are more numerous, to crests. Surprisingly, gravity can only counter this destabilising mechanism when sediment transport is intense enough. Relaxing the long-wavelength approximation, we find that the cross-stream diffusion of momentum mitigates the influence of the bed perturbation on the flow, and even reverses it for short wavelengths. Viscosity thus opposes the diffusion of entrained grains to select the most unstable wavelength. This instability might turn single-thread alluvial rivers into braided channels.
Catchments respond to rainfall by storing and releasing water according to their internal dynamics. Groundwater had long been treated as the slow reservoir in this process, but isotopic measurements ...showed how responsive it can be. Here, we investigate the mechanics of groundwater's contribution to floods. To do so, we monitored over 3 years the shape of the water table in, and the runoff out of, a small tropical catchment. We find that groundwater and runoff respond within minutes of a rainfall event. Using an asymptotic theory inspired by recent laboratory experiments, we suggest that the peak water discharge at the catchment's outlet increases like the rainfall rate to the power of 3/2. This formula consistently predicts the stream's response to the 137 isolated rainfall events recorded during our field survey. In addition, its prefactor yields an estimate of the average groundwater storage.
Plain Language Summary
Rainwater infiltrates into the ground, accumulates in porous rocks, and eventually flows toward a neighboring stream. Although this underground travel often takes millennia, groundwater can contribute quickly to floods. To understand how an underground flow can be so responsive, we have recorded the motion of the groundwater surface in a small tropical catchment during 3 years. We find that groundwater swells within minutes of a rain event and that this deformation directly pushes more water into the stream. The resulting stream‐discharge peak strengthens faster than the rainfall intensity: A threefold increase of the latter causes a fivefold increase of the stream discharge. Including this mechanism into flood‐forecasting models should allow us to better predict the impact of extreme precipitations. Finally, we introduce a method to measure how much water an aquifer stores during a rainfall event, before releasing it—a central parameter for the management of water resources.
Key Points
High‐frequency measurements show that groundwater nonlinearly amplifies the response of a catchment to rainfall events
The stormflow regime of the underground flow consistently predicts the peak runoff
We propose a method to measure the volume of water available in a shallow aquifer based on the hydrograph of the corresponding catchment
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