River‐Bend Bank Protection by Submerged Vanes

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Abstract
It is shown, theoretically and by a physical model, that short, vertical, submerged vanes installed at incidence to the channel axis in the outer half of a river‐bend channel significantly reduce the secondary currents and the attendant undermining and high‐velocity attack of the outer bank. The effect of the vanes on the secondary flow is estimated by a simple torque calculation using the Kutta‐Joukowski theorem. A design relation for the vane spacing is derived by equating the torque, about the channel centroid, produced by the flow curvature to that resulting from the lateral force exerted on the vanes. The relation is verified in an idealized, physical model of a bend of the Sacramento River, California.

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