TY - JOUR
T1 - Inception of Regular Valley Spacing in Fluvial Landscapes
T2 - A Linear Stability Analysis
AU - Anand, Shashank Kumar
AU - Bonetti, Sara
AU - Camporeale, Carlo
AU - Porporato, Amilcare
N1 - Funding Information:
The authors acknowledge support from the US National Science Foundation (NSF) Grants EAR‐1331846 and EAR‐1338694, Innovation Award ‐ Moore Science‐to‐Action Fund, and BP through the Carbon Mitigation Initiative (CMI) at Princeton University. S.K.A. and A.P. acknowledge the support from the High Meadows Environmental Institute (HMEI). S.K.A. also acknowledges the support through the Mary and Randall Hack '69 Research Fund. We thank Matteo Bertagni for helpful discussions on the theory of stability analysis and pattern formation. We thank the associate editor Liran Goren and reviewers Stefan Hergarten, Stefano Orlandini, and Eric Deal for their insightful and valuable critique of the manuscript. The numerical simulations in this article were performed on computational resources provided by Princeton Research Computing, a consortium of groups including the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology's High Performance Computing Center and Visualization Laboratory at Princeton University.
Funding Information:
The authors acknowledge support from the US National Science Foundation (NSF) Grants EAR-1331846 and EAR-1338694, Innovation Award - Moore Science-to-Action Fund, and BP through the Carbon Mitigation Initiative (CMI) at Princeton University. S.K.A. and A.P. acknowledge the support from the High Meadows Environmental Institute (HMEI). S.K.A. also acknowledges the support through the Mary and Randall Hack '69 Research Fund. We thank Matteo Bertagni for helpful discussions on the theory of stability analysis and pattern formation. We thank the associate editor Liran Goren and reviewers Stefan Hergarten, Stefano Orlandini, and Eric Deal for their insightful and valuable critique of the manuscript. The numerical simulations in this article were performed on computational resources provided by Princeton Research Computing, a consortium of groups including the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology's High Performance Computing Center and Visualization Laboratory at Princeton University.
Publisher Copyright:
© 2022. American Geophysical Union. All Rights Reserved.
PY - 2022/11
Y1 - 2022/11
N2 - Incipient valley formation in mountainous landscapes is often associated with their presence at a regular spacing under diverse hydroclimatic forcings. Here we provide a formal linear stability theory for a landscape evolution model representing the action of tectonic uplift, diffusive soil creep, and detachment-limited fluvial erosion. For configurations dominated by only one horizontal length scale, a single dimensionless quantity characterizes the overall system dynamics based on model parameters and boundary conditions. The stability analysis is conducted for smooth and symmetric hillslopes along a long mountain ridge to study the impact of the erosion law form on regular first-order valley formation. The results provide the critical condition when smooth landscapes become unstable and give rise to a characteristic length scale for incipient valleys, which is related to the scaling exponents that couple fluvial erosion to the specific drainage area and the local slope. The valley spacing at first instability is uniquely related to the ratio of the scaling exponents and widens with an increase in this ratio. We find compelling evidence of sediment transport by diffusive creep and fluvial erosion coupled with the specific drainage area equation as a sufficient mechanism for first-order valley formation. We finally show that the predictions of the linear stability analysis conform with the results of numerical simulations for different degrees of nonlinearity in the erosion law and agree well with topographic data from a natural landscape.
AB - Incipient valley formation in mountainous landscapes is often associated with their presence at a regular spacing under diverse hydroclimatic forcings. Here we provide a formal linear stability theory for a landscape evolution model representing the action of tectonic uplift, diffusive soil creep, and detachment-limited fluvial erosion. For configurations dominated by only one horizontal length scale, a single dimensionless quantity characterizes the overall system dynamics based on model parameters and boundary conditions. The stability analysis is conducted for smooth and symmetric hillslopes along a long mountain ridge to study the impact of the erosion law form on regular first-order valley formation. The results provide the critical condition when smooth landscapes become unstable and give rise to a characteristic length scale for incipient valleys, which is related to the scaling exponents that couple fluvial erosion to the specific drainage area and the local slope. The valley spacing at first instability is uniquely related to the ratio of the scaling exponents and widens with an increase in this ratio. We find compelling evidence of sediment transport by diffusive creep and fluvial erosion coupled with the specific drainage area equation as a sufficient mechanism for first-order valley formation. We finally show that the predictions of the linear stability analysis conform with the results of numerical simulations for different degrees of nonlinearity in the erosion law and agree well with topographic data from a natural landscape.
KW - channel formation
KW - fluvial erosion
KW - landscape evolution
KW - linear stability analysis
KW - numerical modeling
KW - spectral method
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U2 - 10.1029/2022JF006716
DO - 10.1029/2022JF006716
M3 - Article
AN - SCOPUS:85142891502
VL - 127
JO - Journal of Geophysical Research: Earth Surface
JF - Journal of Geophysical Research: Earth Surface
SN - 2169-9003
IS - 11
M1 - e2022JF006716
ER -