On the Quantification of the Bed Development Time of Alluvial Meandering Streams

This paper concerns the quantitative evaluation of the time of bed development of alluvial meandering streams. In agreement with the prevailing approach, it is assumed that the stream centerline follows a sine-generated curve; the banks are rigid. The flow is turbulent and subcritical, and the flow width is much larger than the flow depth. The movable bed is flat at time $t=0$ ; at $t=T_b$ , the bed reaches its equilibrium or developed state. With the aid of dimensional and physical considerations, an expression is found for the duration of bed development $T_b$ . According to this expression, $T_b$ is proportional to the square of the flow width $B$ and inversely proportional to the specific volumetric bed-load rate corresponding to the channel-averaged flow. The proportionality factor is found to be a function of the initial deflection angle ${\theta }_0$ alone. The form of this function is investigated on the basis of a series of experimental runs carried out by the writers in a sine-generated channel having an intermediate value of ${\theta }_0$ (i.e., an intermediate value of sinuosity), as well as data available in the literature.