Spectral Analysis of Sand Waves

The techniques of autocorrelation and spectral density analysis of random processes were applied to the problem of describing and predicting bed profiles of a sequence of dunes in sand-bed channels. The data analyzed were from three sources, a 0.4-ft wide flume, an 8-ft wide flume, and a conveyance channel of the Rio Grande near Bernardo, New Mexico. From the computed covariance and spectral density functions, it was determined that the process could be represented approximately by a Markov second-order linear model. The first three values of the covariance functions, which were found sufficient for computing the approximate models and two other parameters which describe the goodness of fit of the models, are shown to be functions of the simple flow parameter, unit discharge.