Matlab code to generate Artificial fractal riverbeds.
datasetposted on 21.10.2019 by Anzy Lee
Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.
The self-similarity of fractals is indicated by the power-law relationship between their power spectral density and wave number, e.g. |X(k)|=Ck^(-b) where X(k) is the Fourier transform of surface elevation at wave number k and C and b are positive constants. b is often expressed as a Hurst exponent, H: b = 2H+1. 1) fractal_riverbed_4TU.m A Matlab script code to generate artificial fractal riverbeds with specified variables (e.g. Hurst Exponent, domain length, number of points, mininum wavenumber, roll-off wavenumber, ...) 2) artificial_surf1d_phaseC_4TU.m A Matlab function code to generate a power spectrum density and phase shift of a fractal riverbed. Input variables are Cq0 (maximum spectral density), H (Hurst Exponent), Lx (domain length), q0 (minimum wavenumber), qr (roll-off wavenumber1), qS (roll-off wavenumber2), qC (maximum wavenumber). 3) PSD_4TU.mat Power spectra of measured data (Martin, R. L., and D. J. Jerolmack (2013), Origin of hysteresis in bed form response to unsteady flows, Water Resour. Res., 49, 1314–1333, doi:10.1002/wrcr.20093.): qx (wavelength, 1/m), Cq (spectral density, m^3), phase