Review Articles

The Meander Paradox—A Topological View

[+] Author and Article Information
Albert Gyr

Institute of Environmental Engineering, Swiss Federal Institute of Technology, CH-8093 Zurich, Switzerlandgyr@ifu.baug.ethz.ch

Appl. Mech. Rev 63(2), 020801 (Jan 14, 2010) (12 pages) doi:10.1115/1.4000725 History: Received September 29, 2008; Revised November 25, 2009; Published January 14, 2010; Online January 14, 2010

Meanders are puzzling phenomena because a meandering river seems to contradict the principle of least action. Different approaches to explain this paradox are outlined by adopting a topological view, which allows for a classification of different types of meanders and to discuss the relevant mechanisms in a rather general manner. It is shown that secondary flows of helical type are the features responsible for the increase in the sediment transport when the slope of rivers decreases due to meandering and that the increase in the discharge is due to a partial Beltramisation of the flow and to a reduction in the friction at the boundary of the helical cells. The review article contains 78 references.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 4

A fragment of a river with alternating sand banks, which are the result of secondary flow depositions. The proper flow pattern is shown (44).

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Figure 5

Behavior of a meander with a one helical flow cell. (a) From a sinusoidal structure of the channel, a skewed wave system develops. (b) The migration velocity as a function of the size of the bends (49).

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Figure 1

A cross-section of a rectangular strait open channel flow with secondary flow starting by a flow toward the corners and propagating toward midchannel by forming quadratic cells of side length H

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Figure 2

Bed patterns associated with various degrees of braiding. The number of braids is m. The dotted regions mark submerged bars (43).

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Figure 3

A secondary flow of aspect ratio 2 (m=1). The top view shows how the surface flow is directed inwards, whereas the one on the bottom outwards compatible with the internal helical flow rollers. The rollers are initiated by the corner flow, which can degenerate when the corner-vortices are moved upwards. The result is an opening of the angle of the sidewalls.

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Figure 7

Sketch of the flow in a bend with two separation zones (A-B) and (C-D), as well as the topology of the flow in two cross-sections P1 and P2. (Explanation in the text).

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Figure 8

Topological sketch of a flow with two secondary cells in a bend with separation. The mechanism is discussed in the text.

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Figure 9

A typical bend and point bar illustrating skewing (49).

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Figure 10

An equal cross-sectional area of a rectangular and triangular form is compared. H of the triangle is 2H of the rectangle. a is the asymmetric shift of the apex.

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Figure 11

Three sketches from Leonardo da Vinci’s notebooks: (a) the question, (b) the experiment, and (c) the observation noted in the Codex Arundel 60 R.

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Figure 6

A cross-section through a river in the apex of a bend. A pair of secondary flow cells (1 and 2) is superimposed on the main flow. A dominant cell lies on the inner and a weaker one on the outer side of the bend. The circulation produces a stagnation in the water surface; all stagnation points lie on the separatrix ss, where the flow separates from the water surface and is reattaching on the separatrix sa. The vortical induction of the rolls on each other is stabilizing them.



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