A Cascade‐Like Energy Dissipation Mechanism Behind the Gradual Achievement of River Equilibrium Sinuosity

Abstract The prediction of river planimetric evolution and related interactions with anthropic activities and public safety is one of the most critical aspects in the planning of a sustainable land‐use. Since the beginning of the past century, a large number of theoretical and experimental studies have focused on the investigation of river meandering dynamics, coming to sometimes contrasting conclusions in the forecast of the associated bend sequence pattern. Drawing inspiration from the phenomenological equivalence between fluid‐dynamic and morpho‐dynamic dispersion within the river floodplain, the present contribution proposes an explicit analytical solution in terms of scale‐dependent and equilibrium sinuosity. Such analytical solution, which reveals the strong dependence of river equilibrium planform on valley bank‐full velocity distribution, is successfully validated on the basis of a field data set provided via a restoration pilot project by Basilicata Region Environment and Energy Department (Italy), and further discussed by related lagrangian simulations. Moreover, the governing equation from which the equilibrium solution originates is shown to be compatible with the interpretation of near‐equilibrium dynamics highlighted by stochastic numerical experiments documented in the literature.