Critical wavelength for river meandering.

A fully nonlinear modal analysis identifies a critical centerline wave number q(c) for river meandering that separates long-wavelength bends, which grow to cutoff, from short-wavelength bends, which decay. Exact, numerical, and approximate analytical results for q(c) rely on the Ikeda, Parker, and Sawai [J. Fluid Mech. 112, 363 (1981)] model, supplemented by dynamical equations that govern the river migration and length. Predictions also include upvalley bend migration at long times and a peak in lateral migration rates at intermediate times. Experimental tests are suggested.