Publication

Sculpting of a fractal river basin

1997
Journal Articles

Abstract

The principle of reparametrization invariance is used to derive a dynamical equation for the erosion of the landscape of the drainage basin of river networks. The stationary solutions of the equation are found to have scaling behavior that is consistent with observational data. Our analytic prediction of the main stream profile is confirmed by numerical results and is amenable to direct observational verification.

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1997
Journal Articles

Abstract

Official source

Related concepts (32)

Drainage basin

A drainage basin is an area of land where all flowing surface water converges to a single point, such as a river mouth, or flows into another body of water, such as a lake or ocean. A basin is separated from adjacent basins by a perimeter, the drainage divide, made up of a succession of elevated features, such as ridges and hills. A basin may consist of smaller basins that merge at river confluences, forming a hierarchical pattern. Other terms for a drainage basin are catchment area, catchment basin, drainage area, river basin, water basin, and impluvium.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Stream

A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long, large streams are usually called rivers, while smaller, less voluminous and more intermittent streams are known as streamlets, brooks or creeks. The flow of a stream is controlled by three inputs – surface runoff (from precipitation or meltwater), daylighted subterranean water, and surfaced groundwater (spring water).

Related publications (12)

Sculpting of a fractal river basin

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Experimental and Numerical Investigation of Hydraulic Fracturing in Dry Sandstone

Reimagining River Landscape

Quantifying the effects of rainfall temporal variability on landscape evolution processes