<P> Various mathematical formulae relate the variables of the meander geometry . As it turns out some numerical parameters can be established, which appear in the formulae . The waveform depends ultimately on the characteristics of the flow but the parameters are independent of it and apparently are caused by geologic factors . In general the meander length is 10--14 times, with an average 11 times, the fullbank channel width and 3 to 5 times, with an average of 4.7 times, the radius of curvature at the apex . This radius is 2--3 times the channel width . </P> <P> A meander has a depth pattern as well . The cross-overs are marked by riffles, or shallow beds, while at the apices are pools . In a pool direction of flow is downward, scouring the bed material . The major volume, however, flows more slowly on the inside of the bend where, due to decreased velocity, it deposits sediment . </P> <P> The line of maximum depth, or channel, is the thalweg or thalweg line . It is typically designated the borderline when rivers are used as political borders . The thalweg hugs the outer banks and returns to center over the riffles . The meander arc length is the distance along the thalweg over one meander . The river length is the length along the centerline . </P> <P> Meander formation is a result of natural factors and processes . The waveform configuration of a stream is constantly changing . Fluid flows around a bend in a vortex . Once a channel begins to follow a sinusoidal path, the amplitude and concavity of the loops increase dramatically due to the effect of helical flow sweeping dense eroded material towards the inside of the bend, and leaving the outside of the bend unprotected and therefore vulnerable to accelerated erosion, forming a positive feedback loop . In the words of Elizabeth A. Wood: </P>

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