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Critical Wavelength For River Meandering, Boyd F. Edwards, D. H. Smith

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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.