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- W3184830364 abstract "The equations and constraints of a general class of models of equilibrium fluvial landscapes are represented as a variational principle (VP). The VP minimizes a functional defined as the sum of (a) the difference between the total kinetic and potential energies of flows over the unchanneled slopes and (b) the sum of the kinetic and potential energies of the channelized flows. When the flows over the slopes are subject to a stability constraint on their magnitude, landscapes that minimize the functional are characterized by: (a) the occurrence on channel boundaries of the minimally stable value of slope runoff; (b) the symmetry of inflows into the channels; (c) the minimal total channel length for rainfall and area ; (d) the minimization of the action of the slopes if and only if they are stable and their slope-discharge relation is monotone-increasing in slope; and (e) the minimization of channel energy if and only if the slope-discharge relation for channels is monotone-decreasing in slope. Applications of the variational theory to first order channels on a linear ridge lead easily to solutions with equal-length, uniformly-spaced channels in symmetrical valleys staggered at the ridge-crests. These solutions minimize the functional of the VP when the equilibrium landscape is in a minimally-stable state and correspond well to numerical solutions to analogous time-dependent models driven to equilbrium. The theory offers a promising approach for investigating the structure of equilibrium channel networks that are stably integrated into equilibrium slopes." @default.
- W3184830364 created "2021-08-02" @default.
- W3184830364 creator A5059870867 @default.
- W3184830364 date "2021-07-28" @default.
- W3184830364 modified "2023-09-27" @default.
- W3184830364 title "A Variational Principle for the Integrated Channels and Slopes of Stable Equilibrium Landscapes" @default.
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- W3184830364 doi "https://doi.org/10.1029/2020jf006014" @default.
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