Multiquadric interpolation of fluid speeds in a natural river channel

Abstract

An electromagnetic current meter was used to obtain fluid speeds in a meander of the Nottawasaga River, Ontario. The meter was placed at 3 m increments of width and at 0.10–0.45 m increments of depth in 13 cross-sections of the meander. Hardy's multiquadric method of interpolation, using a cone model, was implemented to estimate and map speeds more fully for each cross-section. The multiquadric system of equations was evaluated for a range of about 7–11 ( × 10 3) locations in each of nine shallow cross-sections in the upstream limb of the meander and for about 22–63( × 10 3) locations in each of four deeper sections in the downstream limb. These evaluated speeds were grouped into colour-coded classes and plotted to show the distribution of speeds in each cross-section. In all but two sections, there was one concentration of higher speeds which shifted towards the outer bank of the meander. The other two sections had double concentrations of high speeds. One section had a cluster at the surface, midstream and another at the bed, close to the outer bank. In the second section, one cluster was at the surface close to the outer bank and the other was near the bed midstream, confirming the action of helical flow in the meander. The mapping showed horizontal gradients of speed just as clearly as vertical and oblique gradients, especially where the talweg was close to the outer bank.