Numerical Simulations of Confined Braided River Morphodynamics: Display of Deterministic Chaos and Characterization Through Turbulence Theory

Abstract

AbstractIn this paper, we utilize a numerical morphological simulation approach to study braiding channel dynamics under steady flow. We conduct 11 different runs in a laboratory configuration, with each initial condition featuring a unique small‐amplitude perturbation pattern of the bed topography. From these infinitesimal initial differences, braided channels evolve into patterns that are macroscopically different and unique to each run, thus showing sensitive dependence on the initial condition and hence a chaotic behavior. Leveraging the analogy of braiding and fluid turbulence put forward by Paola (1996), by introducing a Reynolds‐type decomposition of bed elevations into a reference and a fluctuating component we characterize braided channel dynamics through statistics of bed fluctuations. We observe that, over the simulation time frame, braiding is not statistically homogeneous, but is stationary in a spatially averaged sense. We prove that braiding is anisotropic and extract two distinct length scales associated with the correlations of bed fluctuations in the streamwise and cross‐channel direction. We observe that, under the time averaging window that yields stationary braiding, braiding shows hints of ergodic behavior, as the time statistics of one run converge to the ensemble statistics computed across all the other runs.