Determination of channel curvature in the map forecast model
 of river meandering

Abstract

The article is a development of the author's previous work aimed at predicting channel displacements during the meandering of lowland rivers. The hypothesis about the instability of a straight river bed is accepted as the main hypothesis about the causes of meandering. To construct a meandering model, a statement is used according to which the river bed shifts from its current position along the normal to the dynamic axis of the flow in the direction from the center of its curvature in proportion to the value of the curvature of the channel in a given section, and the proportionality coefficient is unknown in advance and must be determined in the process of cartographic (hydrological) monitoring. Since the curvature of a river channel is ex-pressed through the second derivative of a curve that approximates the outline of the bank, the important question is how to accurately calculate this curvature from the coordinates of bank points. A way to do that is proposed in the article. This way is based on approximating the coast-line with a 2nd order spline in the form of a circle most closely adjacent to the coastline. Since hydrological monitoring makes it possible to find normal channel displacements over a certain period of time, then knowing the curvature of the coastline in all sections of the channel, it is possible to calculate the unknown coefficient of proportionality of this displacement to the cur-vature. The obtained values of the coefficient of proportionality are proposed to be used for pre-dictive mapping of channel dynamics for future time intervals.