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Initiation of Channel Head Bifurcation by Overland Flow
Author(s) -
Pornprommin Adichai,
Izumi Norihiro,
Parker Gary
Publication year - 2017
Publication title -
journal of geophysical research: earth surface
Language(s) - English
Resource type - Journals
eISSN - 2169-9011
pISSN - 2169-9003
DOI - 10.1002/2016jf003972
Subject(s) - bifurcation , radius , geometry , mechanics , mathematics , channel (broadcasting) , flow (mathematics) , head (geology) , perturbation (astronomy) , saddle node bifurcation , physics , geology , engineering , computer science , telecommunications , nonlinear system , geomorphology , computer security , quantum mechanics
Channel head bifurcation is a key factor for generating complexity of channel networks. Here we investigate incipient channel head bifurcation using linear stability analysis. Channel heads are simplified as circular hollows, toward which surface sheet flow accelerates in the radial direction. Sinusoidal perturbations in the angular direction with different angular wave numbers k are imposed on the bed, and their growth ratesΩ ~ are computed. Because the channel head radiusR ~cis extending over time, the base state (circular hollow in the absence of perturbations) also evolves continuously. With the use of the momentary stability concept, the evolving base state is defined as momentarily unstable to the imposed perturbation if the disturbance is growing faster than the evolution of the base state. It was found that in the range of sufficiently smallR ~c , bifurcation cannot be initiated. AsR ~cincreases, bifurcation starts to be possible with k ≈ 3–5. A higher k implies bifurcation with a narrower channel junction angle ( θ = 2 π / k ). The average junction angle of the Colorado High Plains for the smallest drainage area is about 85° with a standard deviation of 35° (Sólyom and Tucker, 2007). Our predicted angles (75°–120°) agree qualitatively with the observed angles. Finally, we propose a simple criterion to compute the thresholdR ~cfor the onset of bifurcation.