2000 GSA Annual Meeting -- Reno, Nevada

Abstract 50661

EVALUATION OF THE CYCLOID AS A FUNCTION FOR DESCRIBING LONGITUDINAL STREAM PROFILE

Presented by Nandi, Arpita
Authors:
      Sasowsky, Ira D.,
      Steer, David N.,
      Szabo, John P.,
      Gross, Laura K..

Key words: cycloid, Red-River, Mississippi-River, Arkansas-River, profiles

In Session 9     Quaternary Geology and Geomorphology (Posters) Monday, November 13, 2000 AM in Room: Hall C at 08:00 AM for .

Abstract: We evaluated the cycloid function as a theoretical ideal for stream longitudinal profiles, using measured stream profiles and discharges for the Red, Arkansas, and Mississippi Rivers. The cycloid is the solution (Bernoulli, 1697) to the brachistochrone problem, whereby the path of quickest time between two points in the absence of friction is found. First, an analytical comparison (energy basis) was made between natural stream systems and the parameters defining the brachistochrone problem. Then, slope-discharge analyses for stream reaches were completed to evaluate the state of equilibrium for selected streams. Elevation profiles were extracted from digital data, and goodness-of-fit for the generated profiles was measured by regression (elevation vs. distance). The longitudinal profiles of streams are a result of the underlying rock, climate, and history of a region. Where certain conditions are met, streams may adopt a smooth, concave upwards profile which may be considered 'at grade' or in dynamic equilibrium. It has been reported that most profiles lie between a condition of equal work and least work. Quantification of stream profiles for geomorphic studies has been conducted by other workers using linear, exponential, logarithmic, and power functions. The involute of 1/2 arch of the cycloid has a theoretical basis for serving as an end-member, high-efficiency profile for streams. Over the full length of a stream the major condition that may not be met is constancy of total energy (through both addition of mass from tributaries and frictional loss). Nevertheless, depending upon conditions within a given reach of stream, the cycloid may provide a suitable match, and one with a potentially greater theoretical basis than other functions that have been used.

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