Nature of deformation of sandy bed forms

We explore a stochastic component of topographic evolution of sandy river beds and its relationship to bed material flux. The behavior of trains of mobile bed forms can be decomposed into two independent constituents, translation and deformation. Translation is the mean downstream migration of the bed at velocity that defines the Lagrangian reference frame of the bed. Deformation is the sum of all changes to the bed's topographic profile measured from within the bed's moving reference frame. The occurrence of deformation leads to exponential decorrelation of bed topography that is in dynamic equilibrium with flow conditions. For the field and laboratory data sets used, correlation decays to 0.5 by the time the bed translates 40% and 360% of the mean bed form length, respectively. Proportions of bed material flux responsible for translation and deformation can be straightforwardly calculated. Translation flux is measured using the traditional bed form‐bed load equation. Deformation flux is determined by excess topographic change scaled by the ratio of horizontal sediment velocity to fall velocity. Deformation represents the sediment exchanged between bed load and suspended load. Because deformation is a stochastic process with zero mean, the apparent rate of deformation decreases as a function of time interval between bed surveys. For the field case, deformation accounts for 40% of bed material flux while it is only 1% of the flux in the laboratory.