Flow resistance in sinuous or irregular channels

The resistance to fully developed turbulent flow at constant depth in an open channel increases as the square of the mean velocity as long as the boundary conditions remain completely unchanged. The presence of the free water surface allows the possibility of departure from the relationship of resistance to the square of the velocity. Experimental evidence is given, which is in quantitative agreement with fluid dynamic theory, that such departure may be abrupt, with a marked increase of resistance. These departures are observed under conditions of boundary and flow which occur commonly in natural rivers.

It is shown that the condition under which this discontinuous increase in resistance occurs is definable by the mean Froude number for the whole flow which may be as small as 0.4. At this initial state, the rate of resistance increase with the square of the velocity may be more than double.

The phenomenon, which is absent in straight uniform channels, is associated with excessive deformations of the free surface due to transverse deflections of the whole or a part of the flow by changes along the channel in the curvature of the flow boundary.

In the simple cases examined the critical Froude number at which the sudden jump occurs depends mainly on the ratio of channel width to mean radius of channel curvature, though the inclination of the banks appears also to have a minor effect

Over the range of values of the above ratio usually to be found in natural rivers, the critical Froude number ranges between 0.4 and 0.55. The possible significance is discussed of the remarkable correspondence between this range of critical Froude number and the range of Froude number within which river flow at bankfull stage appears to be restricted.