Where does meander collide?

In geomorphology, a meander is the looping, snaking course a river carves across a floodplain, where the flow erodes the outer bank of each bend and deposits sediment on the inner bank, so the bends migrate and tighten until a loop is cut off as an oxbow. Leopold and Wolman's 1960 River meanders showed that meander wavelength scales regularly with channel width and discharge across rivers of very different sizes, making the pattern a predictable property of flowing water rather than an accident. The referent is a channel planform and its self-shaping dynamics, measured by sinuosity and meander wavelength, and it is a different construct from the abstract winding curve that mathematicians count under the same name.[1]

Unit

The sinuosity and meander wavelength of a river channel

Recovery means

Not applicable

Measured by

Measured by sinuosity (channel length over valley length), meander wavelength and amplitude, and rates of bend migration from maps and imagery

In combinatorics, a meander is a configuration of a single closed loop that crosses a fixed line a given number of times without touching itself, and the central problem is to count how many distinct such configurations exist for each number of crossings. Di Francesco, Golinelli, and Guitter's 1996 Meanders: a direct enumeration approach attacked this hard enumeration problem, which connects to loop models in statistical physics and to the Temperley–Lieb algebra. The referent is a discrete topological object and its counting sequence, defined purely by crossing number and non-self-intersection, and it borrows the river's name only as a picture; it carries none of the erosion or flow of an actual meandering stream.[2]

Unit

The meander number: how many distinct loop configurations cross a line n times

Recovery means

Not applicable

Measured by

Studied by exact enumeration, generating functions, and asymptotic growth exponents for the number of meanders of given order