MEANDERING CHANNELS IN SWITZERLAND

J. ZELLER(*)

S U M M A R Y

The distribution of meander channels in Switzerland is discussed with reference lo four examples of such channels in alluvial material, solid rock, glacier ice and limestone lapiès. The ranges of the main hydraulic particulars of such channels are set out in a Table, with comments. In a diagram representing over all regression curves for meander length and meander width the discussed meander types (ranges) are demonstrated. A point of special interest is that meanders are found in both the snbcritical and supei-critical ranges, with and without bed-load transportation, and with Reynolds' numbers ranging from very small to very large.

RÉSUMÉ

On peut illustrer la formation des méandres en Suisse à l'aide de 4 exemples fournis par des cours d'eau s'écoulant dans des alluvions, du rocher, de la glace et des lapiès calcaires. Une table récapitule les ordres de grandeur des données hydrauliques les plus importantes de ces différents cours d'eau. Diagramme donnant les courbes de régression des longueurs et amplitudes des méandres en fonction de la largeur de la rivière (valeurs moyennes pour les exemples cités). Il est à noter qu'il y a formation de méandres bien aussi dans le domaine d'écoulement tranquille que torrentiel, avec ou sans charriage de matérieux soiides et pour des nombres de Reynold très variables.

Switzerland is a very diversified country, notably in topographical and geological respects. This very fact almost rules out the likelihood of finding well-developed meanders. Even so, an attempt was made to classify to some degree the winding channels and examine their morphometric patterns. Besides the various alluvial types of meander (free, restricted, incised, disturbed, undercalibrated meanders) and the types incised in rock, Switzerland also has examples of the less known meanders of meltwater streams in glacier ice and furrows (rinnenkarre) in limestone areas.

The object here is to describe, as far as it is possible on the data available, the following four types of meader, viz.:

— alluvia! meanders; — rock meanders; — ice meanders; — furrow meanders in limestone;

with reference to an example in each case. This will be followed in conclusion by a summary of the main hydraulic data typifying Swiss conditions.

I. FREE MEANDERS IN RIVER ALLUVIA, EXEMPLIFIED BY RIVER THUR

The River Thur is a tributary of the Rhine (see fig, 1), with a total catchment area of 1,724 km'3 and a length of 128 km. The upper reach of its main course has a moun­tainous character comprising longish stretches of alluvium interrupted by short stretches of rock (Molasse: sandstone, pudding stone, marl). The alluvium in the lower-reach (river kilometres 20 to 65) is meandering, in parts even braided. Hydro logically, the whole catchment area is fairly homogeneous. Flood-water may arise at any time

(*) Civil engineer, Versuchsanstait fiir Wasserbau und Erdbau (VAWE), Zurich, Switzerland.

174

of the year. The morphometric data were represented in the form of regression curves (regime theory) (fig. 2). The mean sinuosity increases from w = ].1(*) in the upper reaches to m = I .6 in the middle and lower reaches, with the associated valley gradients of JT — 10 p. th. and LI p th. respectively. Diagrams D and £ of fig. 2 show the known fact that the meander-dimensions increas with increasing water discharge (in downstream direction). The exponent of the regime equation for meander length (**> agrees with the empirical values gathered in other areas, while that for meander with (ampIitude)A differs sharply from the empirical standard. (Oddly, though.it agrees with data from Russia I1). The individual values for I and A show marked scatter, due to extraneous disturbances (tributaries, sharp variation in erosion resistance of alluvial material, etc.) and the coarse grain of the bed—load material(***)).

Fig. 1 —• Small-scale hydrographical map of Switzerland, showing areas with meanders (dotted patches), the Rivers Thur and Saane described as examples, and the research areas of Morteratsch Glacier and Silbern.

2. ROCK MEANDERS, EXEMPLIFIED BY RIVER SAANE

The River Saane, a tributary of the River Aare (see figs. 1 and 3), is deeply cut into the Molasse stratum (sandstone and marl) over a length of some 50 km. The valley has a U-shaped section, with partly abutting rock for flanks and fluvial rubble for the floor (ranging from gravelsand to large stones). This stretch meanders with a mean sinuosity of to = 1.85 and a mean gradient of the riverbed / s = 3.9 p . th. The catch­ment area, at river kilometre 62 (head of meander), is about 800 km2 and has a recorded maximum discharge of about 550m3/sec. The respective values for river kilometre 12 are about 1,400 km2 and about 780m3/sec. The individual meanders are very different in shape, which is due to the many disturbances caused by deflecting banks. Even so, the relation A = / ( g ) (see fig. 3) emerges clearly, while A = f(Q) is doubtful. The exponents of these regime equations for X and A are greater than in the case of free meanders. (a)

*) All data relate to the channel axis. **) A critical review about alluvial meanders can be found in (s).

(***) to — channel length divided by meander length.

175

Fig. 2 — Morpliometric diagrams of River Thur : A: Catchment area with tributaries and river kilometres; B: Maximum measured flood discharge Qmax and lone-period daily mean discharge

Qm along entire course. The probability of discharge (in years) is stated directly above and below the confluence with the River Glatt;

C: Maximum measured discharge Qma\ = Qsn correlated with catchment area; D: Regression curve for meander length A; E: Regression curve for meander width A ; (2, and A were measured for the channel axis).

176

\ 1 •j bedrock

I

'4

Fig. 3 — Morphom _ River Saane between Pont la Ville and Klein-bôsingen: A: Measured and interpolated maximum discharge along examined river stretch

for the period 1910-1966; B: Catchment area correlated with river kilometres; C: Meander length A along examined river stretch; D: Meander width A along examined river stretch; E: Regression curve for meander length X plotted against Qmax; F: Regression curve for meander width A plotted against Qmax.

© 2000

Ï500

1200

1000

aoo

eoo 500

400

300

200

•

" 1

1%.

•d$'

—

T \ i i

] ;

too

1000

300

( ? ) 1000 r—-

eoo aoo looo

SOO

500

400

300

—

—

r>/

-

» -

V

—+-

*

•

a

f

„

t

h '?

-

400 soo aoo looo peak flood discharge

0 m m ' / sec

1200

moo

_ soo

: soo

'• 400

—

1

1 s ~~m — ~

1 i

1—,

i

% i

~~~ .i

i %

©

0 10 20 30 40 50 . SO 70 30 *m

1SO0

1200

300

600

0

1400

1200

moo

soo

soo

400

200

'0

1000

300

eoo

400

200

0

'~~:

L

_

- ^

J

®

10 20 30 40 50 SO 70 30 km

\ 1

-À v

'

I

U-

W-n

ÎA

n, i $

1

1

i

j

I

©

0 10 20 30 40 50 SO 70 80 km

î'Vk I

t V

! i i i

i

4KD

P hF, _J

V -\ \ î

*

®

0 10 20 30 4 0 5 0 8 0 70 30 Km

river lengthen km

Fig. 3 b

(text see Fig. 3}

3- ICE MEANDERS, EXEMPLIFIED BY MORTERATSCH GLACIER

The melt-water streams examined are small channels with diminutive catchment areas ranging from 0.002 to 0.050 km2. Heavily influenced by the progress of the par-licular glaciers, the seasons and the weather, the channels change from year to year,

178

and the discharge is almost entirely dependent on the melting of the galcier ice in the catchment area. The channel respresented in figure 4 belongs to the tongue of the Morieratsch Glacier (fig. 1) and is at 2,000 to 2,100 metres above sea level. The ice was coarse-grained and, near the surface, had relatively little resistance to mechanical load. With the discharge encouniered at the time, the channel width at gauge level was 0.25 to 0.30 metre, the mean flow rate about 2.0 to 3.0 metre/sec., and the mean valley gradient JT = 75 to 85 p. th. No correlation of A and A with the distance covered was found, as the meandering stretch was too short (discharge practically unchanged over entire length). On average, % = 2.5 to 2.7 metres, A = 0.8 to 0.95 metre, and sinuosity » = 1.25 to 1.30. The flow rate was so great (supercritical) and the radius of meander curvature so small that the water overshot itself at the outside of the bends, but without noticeably disturbing the flow movement (E), <4).

Fig. 4 —Example of a swift (supercritical-flow) melt water stream of Morteratsch Gla­cier, taken in late summer 1964. The ice—pick shown is 80 cm long. Strong wave motion due to water tumbling over itself at outside of bends.

179

4. FURROW MEANDERS, EXEMPLIFIED BY THE SILBERN REGION

This furrow region is, in the area examined, at about 1,900 metres above sea level, is practically devoid of vegetation and intersected by a large number of furrows running more or less parallel. Furrow length is in general between 2 and 20 metres, and the lower ends usually disappear in clefts or fissures. Their gradients correspond to the dip oFthe banked limestone. The meandering of these miniature channels only occurs in certain ranges of gradient, so thai large areas of this furrow region, notably the steep tracts, only have straight furrows. Such channels can hardly be said to have a catchment area, their formation being chiefly due to melting snow. The discharge is extremely small. Judging by the regular shapes of meanders and migration, the discharge is fairly constant over long periods.

Fig. 5 — Example of sluggish (subctitical—flow) melt—water stream of Morteratsch Giacier, taken in late summer 1964. The sand traces on the channel bed do not move.

The channel surface in the dry state is smooth to slightly rough. No loose material or even traces suggesting a bed-load transport are to be found.

The furrow meander of figure 6 is a channel cut about 6 cm into the rock, with a mean width of 3.0 cm and a mean water depth of 0.2 to 0.3 cm (determined on traces a long banks and by experiments). Thevalley gradient J y is 260 p. th., the channel gradient Js 91 p. th. The meandering is intensive (to = 2.84). Meander length and amplitude, measured for the channel axis, are in the mean A = 5.8 and A = 6.6 cm.

It is striking how regular the large majority of these meander channels are in formation, although size and cross-section of the channels very widely. This is illustrated by figure 7, which shows a section of a channel directly adjacent lo the one in figure 6; it is a typical canyon such as even a large river could not have formed more perfectly. (*)

(*) no usefull informations (references) about furrow meanders are available till today.

180

" • * . \

^Rft^W^l "ft • l U i . J-1

Fig. 6 — Meandering furrows of Silbern area (scales graduated in cm).

Fig. 7 — Detail of a „ large" meandering furrow. Sinuosity about 3.5, channel width 3 cm, depth of „canyon" 30cm (scales graduated in cm).

181

5. CLASSIFICATION OF THESE MEANDERS FROM HYDRAULIC ASPECTS

For the assessment of such meanders from hydraulic aspects, the emphasis is on the data concerning the flow process. Besides the geometric data of the channel, they mainly comprise discharge and sediment transportation (see Table 1). It must be pointed out here that these data represent the natural formations encountered in Switzerland and so do not necessarily define physical patterns outside which meanders cannot occur. (a), (s), (7). Nor are the values given freely combinable, buth rather call for an interpretation following the physical laws. Those patterns in which most meanders are found are specially marked out in the Table.

6. SUMMARY AND SOME CONCLUSIONS

The various examples show that meandering rivers also occur in mountainous countries, i.e. in countries with relatively recent valley formations. If actual conditions are greatly simplified, the following conclusions may be drawn for Switzerland:

Meander distribution

Meanders can be found in channels ranging from the largest to the smallest. Thus, given suitable alluvial materials, they are independent of river size. They are found under the most varied conditions, though there are certain particularly favourable boundary conditions under which meander frequency is greatest. Despite comparatively large valley gradients, coarse graining and "mobility" ofthe alluvial materials, the meander s show the typical rhythmic windings. The resultant regime equations (regression curves) for A and A also hold good for the Alpine region. However, the individual alues tend to have a wide scatter, and another reservation is that these equations greatly depend o n local conditions, thus on account losing their general validity of free transferability.

Meander channels in glacier ice are found in the most varied glacial areas of Switzerland. They frequently show a striking regularity in the meander shapes and seem to depend relatively little on valley gradient, as they occur on glacier slopes ranging from fiat to very steep.

As regards the distribution of meander channels in lapiès areas, nothing definite can be said, as only those of the Silbern region mentioned are known to the author. However, there is no reason to doubt that furrow meanders are perfectly normal phenomena in lapies areas, given similar geological and hydrological conditions.

Channel geometry

The geometry of the four channel-types shows the same basic character and is first of all probably indépendant of the type of bed-material (fig. 8(*)). Indeed, these seam to be analogies to serpentining density currents in standing water.

Bed-had transport

There are obviously various meander mechanisms. While the bed-load transport is an essential condition for alluvial meanders, it appears not to be necessary for meanders in ice and furrows. Nor did the latter show any signs of forcible deflection of the flow

(*) Because of unsufficient datas concerning the water discharge, the meander leometry in figure 8 is based on the channel width, taken from Swiss maps 1 : 25 000 .This is only allowable for rough estimations).

182

o

•a

I I

«

2

.1=

-

ce

S! •a c

l«ï a. S

s ê,s.

V

fi

•s .g

.

*1 *s .«

I TJ

C

A. •

=;

* «k «i

2 C

«

fi

js.sg £§-e 5

*3

o S A

o

-a' 1

iv

i o

o o

OO

„

Sç>

fi"~

—

fiO

A^ I"

o o o

*as

S

311 A

A\

1 S

|

5ï

O

f O

O*

i 1

o

+

11

<N

O

<n o

O

O

ri

o o -15

H

o o

3 S

3

lu s

S

o I I S*S

O

fi -

noo i.

fi raw

I i 1 «3 S

c S

..Isa o

o,S

«

si s S

ls8

5 5

11 II 1

q>

T3

C

d fi s o T

3 seu

-a

1 al reache •ren

-£•

S

M

0.

s'a s « "

i" •14

-^

« fi

|S -u

.st

ier, taken of Silbem

.3 2

F*

fi

-.

•

M

S3

a ter depl matic vis

3 u

a I IÏII1

111 >1

PlflP

Il life

11 fi

p_ ci

HJ

HT

J

S a

.«: rA

Ss^^Jl

^

M m

rr m 45 r- #

#

183

channel width'b in m

Fig. S ~ Regression curves of meander length A and meander width A (average values): 1. Furrow meanders (Silbern) from 24 different meander reaches; 2. Ice meanders (Morteratsch—Glacier), 14 reaches; 2a. Ice meanders (East—Greenland), 12 readies (private communications); 3. Alluvial meanders (VA WE—model -tests), 5 different tests in sand; 4. Meanders of Swiss Rivers, over 50 reaches; 5. Alluvial meanders, Leopold and Wolman's (3) (additional data), 46 reaches; 6. Meandering flow of „ density currents" in a storage basin of River Reuss (basin

width ca. 2A), model tests; 7. Meandering flow of the Gulf—stream (Leopold and Wolman) (3) ;

Till today it is not known if 6. and 7. belong to the same family of meanders as 1. to 5.

184

as the cause of the meandering. As regards ice meanders, it is possible at the beginning of the channel formation (early summer) io find some transport ofice grains. But this solid transport disappears very soon, so that, considering the quick changeability of such channels, it can hardly have any major influence on meandering. (The traces of sand occasionally found in such channels are so slight in quantity as to have no effect on the channel formation).

Migration

This can be observed i n all types of meander described. But the rate of migration varies considerably.

In ice and furrows, the downward migration is often associated with intensive depth erosion, resulting in overhanging banks. The shape of both the meander and the cross-section of the channel remain perfectly preserved. Such effects would also be expected in the case of river meanders cut into the solid rock. However, owing to the great time required for such overhangs to develop through weathering and rock-mechanical processes, such phenomena have till today remained rarities.

Influence of extraneous disturbances

In fairly stable channels, the meanders are found to be quite resistant to extraneous disturbances, provided that the conditions are favourable for meandering- And while disturbances may affect the shape and mechanism of some succeeding meander loops, regeneration to normal is relatively fast.

Hydraulic aspects

The well-developed meander formations are almost exclusively encountered: — in alluvial material, with subcritical flow; — in glacier ice, with supercritical flow; — in limestone furrows, with supercritical flow.

Meanders in alluvial channels in the supercritical range and such in ice channels in the subcritical range are infrequent in Switzerland, In furrow areas, the subcriticai range is entirely wanting, although the meander formations there are so pronounced as to suggest meandering alluvial channels of the subcritical range.

When Reynolds' number is used as a standard for turbulence (based on mean water depth), all meanders with the exception of furrow meanders are found to occupy the range from medium to strong turbulence. By contrast, the flows in the furrow meanders are in the low—turbulence range, occasionally even in the laminar—turbulent transitio­nal range. This observation sugests that the secondary currents determining the mean­dering are not necessarily correlated with turbulence, as is occasionally assumed.

Viewed in this context, the meandering alluvium river is obviously merely a special case within the large family of meander channels.

The genesis of meanders is still much in doubt, especially as it seems likely that, as mentioned, various causes may give rise to meandering or that various boudary con­ditions may encourage or at any rate allow meandering.

REFERENCES

O KONDRATIEV, N.E. , (1959) : River flow and river channel formation. Translated by National Science Foundation, Washington DC (1962) (U.S. Dept. of Commerce, Office of Technical Services).

(2) ZELLER, J., (Î967) : Flussmorphologische Studie uber das Maanderproblem, Geo-grapkica Helvetica, Band XXII. pp. 57-95

J85

(3) LEOPOLD, L. B., WOLMAN, M.G. , (I960) : « River Meanders» Bulletin of the Geo­logical Society of America, Vol. 71, pp. 769-794,

(4) NOBLES, L.H., (1960) : Glaciological investigations, Nunatarssuaq Ice Ramp, Nortliwestern Greenland. US. Army Snow lee and Permafrost Research Estab­lishment, Corps of Engineers, Wilmette/Ill, Tech». Report, 66.

(5) LANE, E.W., (1957) : A study of the shape of channels formed by natural streams flowing in erodible material. U.S. Army Engineer Division, Missouri River, Corps of Engineers, Omaha/Nebraska, M.R.D. Sediment Series, No, 9,

(8) LEOPOLD, L.B., WOLMAN, M.G., (1957) : River channel patterns; braided mean­dering and straight, U.S. Geo!. Surrey Professional Paper, 282-B,

(7) ACKERS, P., (1964) : Experiments on small streams in alluvion. Proc. Am. Soc. Civil Engineers, HY 4, paper 3959, (figs. 7-9).

186