TY - JOUR
T1 - Initiation of Channel Head Bifurcation by Overland Flow
AU - Pornprommin, Adichai
AU - Izumi, Norihiro
AU - Parker, Gary
N1 - The authors thank Editor John Buffington, Associate Editor, reviewer Riccardo Vesipa, and two anonymous reviewers for their constructive reviews that helped to improve the manuscript greatly. Pornprommin was supported by the Japan Society for the Promotion of Science Invitation Fellowship Program (grant-in-aid L-14542) and the Kasetsart University Research and Development Institute (KURDI) (grant 2555/19.55). The participation of Parker was made possible in part by a grant from the U.S. National Science Foundation (grant EAR-1124482). In addition, Parker gratefully acknowledges his award of an Invited Professorship of Hokkaido University in the summer of 2015. The full derivation of the present linear stability analysis is provided as supporting information.
PY - 2017/12
Y1 - 2017/12
N2 - 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 rates Ω are computed. Because the channel head radius Rc is 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 small Rc, bifurcation cannot be initiated. As Rc increases, bifurcation starts to be possible with k≈ 3–5. A higher k implies bifurcation with a narrower channel junction angle (θ = 2π/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 threshold Rc for the onset of bifurcation.
AB - 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 rates Ω are computed. Because the channel head radius Rc is 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 small Rc, bifurcation cannot be initiated. As Rc increases, bifurcation starts to be possible with k≈ 3–5. A higher k implies bifurcation with a narrower channel junction angle (θ = 2π/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 threshold Rc for the onset of bifurcation.
KW - bifurcation
KW - erosion
KW - stability analysis
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U2 - 10.1002/2016JF003972
DO - 10.1002/2016JF003972
M3 - Article
AN - SCOPUS:85040721321
SN - 2169-9003
VL - 122
SP - 2348
EP - 2369
JO - Journal of Geophysical Research: Earth Surface
JF - Journal of Geophysical Research: Earth Surface
IS - 12
ER -