Stream-power model of meander cutoff in gravel beds

In the present study we propose a one-dimensional model for the prediction of the large-time evolution of river meanders (pre-cutoff conditions) characterized by gravel bed and negligible suspended load. Due to its relatively simple structure, it may be a fast and easy tool to forecast the time evolution of a bend when the symptoms of an incipient instability suggest quantifying the time left for river exploitation as a naturalistic or a commercial resource and timely planning, if needed, the site management and restoration. Most of the previous research on meandering rivers focused on linearized theories that apply to very small bend amplitudes and very large radii of curvature. The dynamics of meander growth and cutoff was typically afforded by case-sensitive numerical simulations or by descriptive methods aimed at deriving purely empirical laws relating the hydraulics to some geomorphological parameters. The present approach combines the immediacy of a general analytical model with the accuracy of a fluid-mechanical background. The model focuses on energetic principles and interprets the mechanism of meander cutoff as the achievement of limit conditions in terms of river stream power. The corresponding analytical solution, which consists in a 1-D deterministic integro-differential equation governing the meander pre-cutoff phase, accounts for the influence of the morphological and sedimentological parameters by the downstream migration rate and the radius of the meander osculating circle. The results, expressed in terms of instable meander lifetime, are in good agreement with the data obtained from a number of field surveys documented in literature. Additionally, the proposed fluid-mechanical model allows identifying the physical mechanisms responsible for some peculiarities of large-time meander evolution like the decreasing skewness and asymmetry.