Dimensional Analysis Applied to Fluvially Eroded Landforms

Research Article| March 01, 1958 DIMENSIONAL ANALYSIS APPLIED TO FLUVIALLY ERODED LANDFORMS ARTHUR N STRAHLER ARTHUR N STRAHLER DEPARTMENT OF GEOLOGY, COLUMBIA UNIVERSITY, NEW YORK 27, N. Y. Search for other works by this author on: GSW Google Scholar Author and Article Information ARTHUR N STRAHLER DEPARTMENT OF GEOLOGY, COLUMBIA UNIVERSITY, NEW YORK 27, N. Y. Publisher: Geological Society of America First Online: 02 Mar 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Copyright © 1958, The Geological Society of America, Inc. Copyright is not claimed on any material prepared by U.S. government employees within the scope of their employment. GSA Bulletin (1958) 69 (3): 279–300. https://doi.org/10.1130/0016-7606(1958)69279:DAATFE2.0.CO;2 Article history First Online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation ARTHUR N STRAHLER; DIMENSIONAL ANALYSIS APPLIED TO FLUVIALLY ERODED LANDFORMS. GSA Bulletin 1958;; 69 (3): 279–300. doi: https://doi.org/10.1130/0016-7606(1958)69279:DAATFE2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract Dimensional analysis permits quantitative geomorphic studies to be placed on a sound geometrical and mechanical basis Form elements of fluvially dissected landmasses are first analyzed according to dimension. Stream length, relief, length of overland flow, and basin perimeter have the dimension of length L. Drainage density, texture ratio, and curvature of profile have an inverse length dimension L−1. Areal measures and volumes have the dimensions of length squared L2 and length cubed L3, respectively. Dimensionless parameters include stream-order number, stream azimuth, ground-slope angle, and channel gradient. Combinations of dimensional elements produce dimensionless numbers, such as stream-length ratio, basin circularity ratio, ruggedness “number, and hypsometric integral, which provide descriptive indices of the terrain, irrespective of scale.Corrsin's dimension space is a useful graphic device for clarifying the dimensions of physical properties as unique vectors extending from an origin to appropriate points in space with respect to three orthogonal coordinates scaled in integer powers.Application of dimensional analysis and the Pi Theorem to drainage density as a function of runoff intensity, an erosion proportionality factor, relief, fluid density and viscosity, and gravity yields four dimensionless groups: a ruggedness number, an erosion-intensity number (here named the Horton number), a Reynolds number, and a Froude number.Complete geometrical similarity of landforms in two regions exists when all corresponding linear dimensions are in the same scale ratio, and all corresponding dimensionless numbers are the same. As an illustration, approximate similarity in planimetric form, but not in relief and slope, is established between small areas of mountainous terrain in the Verdugo Hills, California, and the Great Smoky Mountains, North Carolina. Examples from the Clinch Mountain area of western Virginia illustrate a case of extremely close similarity in landforms developed on different rock types and a case of striking dissimilarity where structural and lithologic controls are strong.Accelerated land erosion, in which gullying results in badlands, is interpreted as a drainage-density transformation in response to sharp increases in the Horton number. Despite a many-fold increase in drainage density, the geometry number tends to be conserved by reduction of relief and increase of slope. Geometrical similarity is preserved in planimetric aspect but not in vertical aspect. The resultant system reaches a new steady state capable of exporting greatly increased load because of steepened valley-side and channel gradients. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.