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Constrained Random Walk Meander Generation
Author(s) -
Surkan Alvin J.,
Van Kan Joseph
Publication year - 1969
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr005i006p01343
Subject(s) - meander (mathematics) , curvature , random walk , gaussian , isotropy , mathematics , geometry , mathematical analysis , statistical physics , physics , statistics , optics , quantum mechanics
Analyses of meander data and comparison of models based on von Schelling's theory of random walks for isotropic Gaussian deviations yield constraints satisfactory for simulation of realistic meander paths. Runge‐Kutta solutions of the differential equation for most probable paths modified to ∂ 2 ∅/∂s 2 + σ 2 sin ∂ = 0 exhibit excessive regularity. Calculation of correlation functions, transition probability matrices, and second moments for natural meander data as a function of segment direction reveals important dependency on segment ordering and shows isotropic random walk models to be untenable. Neither the directions, curvatures, nor their changes in natural meanders are Gaussian independent. Necessary constraints on random walk deviations for simulating meanders include a significant positive correlation for adjacent curvatures and directions and often a negative one between the curvature changes. Both result from azimuth dependence in the second moment of the curvature. Empirically, § Δθ (Φrpar; = A + B (Φ − ∂ 0 ) 2 describes the standard deviation of curvature for directions ∂ near the mean direction Φ 0 . The application of this directional property of meander curvatures makes possible (1) simulation of realistic meander paths, (2) statistical determination of flow direction, and (3) numerical evidence of a unidirectional flow origin for any meander‐like path.