Statistical characterization of flow field structure in evolving braided gravel beds

Braided rivers quickly vary their geometry, modifying their boundaries and floodplains. Therefore, flooding of a braided stream is typically associated with high hydrologic risk in the surrounding areas or alluvial valleys. A forecast of these morpho-hydrodynamic processes is therefore essential when managing the environmental and economic impact of flood events. A few studies in the past demonstrated that open channels spontaneously tend to establish and maintain an equilibrium state that corresponds to a specific level of cross-sectional velocity entropy. The present study analyses for the first time the relationship between bank-full flow (described by measures of velocity entropy and second-order spatial statistics) and bed topography (described in terms of bed elevation second-order spatial statistics) in gravel-bed braided rivers at cross-sectional scale, in both equilibrium and pre-equilibrium conditions. Based on the outcome of suitable laboratory experiments, we found that, in gravel bed braided rivers, longitudinal equilibrium during floods is associated with a periodic-like spatial minimization of normalized cross-sectional velocity entropy. This periodic-like minimization of cross-sectional velocity entropy (and statistical variance) corresponds to a periodic-like maximization of normalized bed elevation variance, according to general theories on longitudinal river profile evolution. Additionally, bed evolution occurs by both entropy minima/maxima appearance and growth and entropy minima/maxima longitudinal migration