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Hydrodynamic interpretation of a boulder berm and associated debris-torrent deposits
Geomorphology, 1 (1987) 53-67
53
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
HYDRODYNAMIC INTERPRETATION OF A BOULDER BERM AND ASSOCIATED DEBRIS-TORRENT DEPOSITS P.A. CARLING Freshwater Biological Association, Windermere Laboratory, The Ferry House, Far Sawrey, Ambleside, Cumbria LA22 OLP (England) ( Revised version accepted March 16, 1987)
Abstract Carling, P.A., 1987. Hydrodynamic interpretation of a boulder berm and associated debris-torrent deposits. Geomorphology, 1: 53-67. The hydrodynamic environment associated with a boulder berm is reconstructed from the geometry and sedimentology of the berm and associated debris-torrent deposits. Berms may result from a variety of hydrodynamic scenarios but in this instance the berm was associated with flow separation downstream of an abrupt change in channel morphology. Sediment fabric analyses are summarized particularly as eigenvalues and these data compared with the fabric of debris flows and clear-water gravel deposits. Although data are few, the eigenvalue results can be interpreted consistently as reflecting a transition between the end members of a sediment fabric continuum. The value of detailed studies of berm geometry and sedimentology is discussed with reference to their hydraulic significance. This latter aspect is important for palaeo-discharge reconstruction of both Newtonian and non-Newtonian flows.
Introduction
A problem in present-day terrestrial sedimentological process studies is the identification of deposits attributable to heavily sediment-laiden flash-floods (debris-torrents of Miles and Kellerhals, 1981) as opposed to debris-flow deposits (Costa, 1984). Debris flows may be strongly non-Newtonian whilst debris torrents tend to be transitional or Newtonian in character, depending on the sediment concentration. Critical concentrations, the nature of the transition between the two types of flow, and the associated mechanics of flow are a matter of some debate. A varied and commonly inconsistent terminology has been applied to deposits of debris 0169-555X/87/$03.50
flows and torrents. In the past especially there has been a propensity to describe depositional features associated with debris torrents in only general terms and to provide only limited sedimentological data. However, debris torrents, heavily charged with coarse material, may deposit distinctive linear features called boulder berms (Stewart and La Marche, 1967; Scott and Gravlee, 1968). These little-studied features are believed to be sedimentologically distinct from "morphologically similar" debrisflow deposits termed lev~es and lobes (Costa, 1984). Berms may develop transverse to and flanking stream channels but the exact mode of formation and hydraulic significance of these structures is unclear as the process cannot be readily observed. In certain instances, berms
© 1987 Elsevier Science Publishers B.V.
54
may be remnants of chute or delta-like deposits, which were subsequently dissected by fhlling-stage discharges to produce a longitudinal ridge topography. An alternative, and by no means exclusive mechanism, is flow separation in plan-view unconnected with incision of flood deposits. For example, some berms occur in regions of the channel or valley where one might expect flow separation and rapid deposition during "catastrophic" discharges. The typical location of gravel deposits on the inside of channel bends described by Shroda et al. (1976) is an example. In this paper, a boulder berm is described and attributed to flow separation. The debris-torrent event responsible for the deposit has been described by Carling (1986) and consisted of a single-peak hydrograph, of a duration no more than two hours, which was heavily charged with fine comminuted peat and coarse gravel. The deposit, although unusual in the sense that it is extremely well formed, is similar to several other berm deposits in the U.K. uplands resulting from flood episodes which also reasonably can be interpreted using the same hydraulic model.
The enL~ironment of deposition The berm was deposited on a valley-side bench in the narrow, steep-sided West Grain valley in the north of England (Figs. 1 and 2). The most important characteristics of the site are that here the valley bends abruptly through an internal angle of 130 ° (Fig. 3) and expands rapidly downstream. The channel gradient also steepens from 0.0728 upstream of the bend to 0.1032 adjacent to and downstream of the berm site. Survey of flood trash-lines indicated a cross-sectional area, immediately upstream of the bend, of 6.00 m 2 whilst downstream the section increased to 14.12 m 2 {Fig. 4). Given the rapid flow expansion with a transition from confined flow to partially unconfined flow, considerable spatial variation in velocity might be expected across the downstream section; high velocities being sustained
in the centre of the channel with more tranquil flow and low velocities in lateral areas. Discharges in the small cobble and boulderbedded channel were usually only a few litres a second and in a three-year period never exceeded 1.2 m :~s ~. In contrast,, the flood peak discharge was estimated to lie between 16 and 22 m 3 s ~and overtopped the valley-side bench. The average peak velocity through the reach cannot be known with certainty but would be at least 2.7 m s ~ and possibly as high as 3.7 m s ~ immediately upstream of the berm site ( Carling, 1986 ).
The morphology of the berm The berm consists primarily of boulders overlying cobble deposits. At the proximal and distal ends, the berm is narrower than at the intermediate section. The crest at the proximal end was aligned with the upstream valley axis, whilst the distal end was aligned with the downstream valley axis. The change in alignment in between was gradational giving an approximate radius of curvature of 114.5 m (Table 1 and Fig. 5). The berm has an overall length of 32 m, a maximum height of 1.10 m and a width varying between 2 and 4 m. The transition from the boulder deposit to the cobble deposits on the leeside of the berm was abrupt. The surface of the cobble deposits enclosed by the berm and the valley walls was essentially flat and up to 4 m wide forming a trough which opened out in a downstream direction through a scoured gap in the berm (Fig. 5).
Flow separation model In the following text, the morphology of the berm is interpreted as representing deposition in a plane half-jet separation vortex. Models of jet-flow have been used by geologists to explain, for example, the distribution of sediments at river mouths and delta fronts (Wright, 1977). Although the physics and mathematical
55
Ireshopeburn
B~p/v
7
L
1Kin
1
/~
Fig. 1. Location map showing site of berm.
Fig. 2. General view of the valley of the West Grain and the reach immediately upstream of the berm, showing over-bank gravel deposits on the left bank and the nature of the catchment. The proximal end of the berm is visible in the lower left of the view. Stream width ca. 7 m.
expression of vortex flow are complex, for most sedimentological applications simplified models have been proven most useful. Abramovich (1963) provides a useful introductory text concerning jet hydraulics whilst Allen (1982) details some specific sedimentological examples of the application of jet and vortex models. In this section the basic hydraulic model is out-
lined ( Fig. 3 ) and this is expanded and justified in following sections. The model is of necessity two-dimensional because the estimated hydraulic data are not suitable to include in a three-dimensional analysis of flow pattern. Nevertheless, the channel curvature might induce a degree of spiral flow throughout the bend; resulting in a transverse velocity component of near-bottom flow directed towards the inner right bank, and a compensating surface flow towards the left outer bank (Allen, 1985). Given the estimated hydraulic and measured geometric conditions (Table 1 ), separation of turbulent flow would be expected to occur at the inflection in the valley alignment (cf. Leeder and Bridges, 1975). The presence of an effective re-entrant in the valley-wall alignment adjacent to the terrace would ensure separation similar to that experienced when an inertia-dominated plane halfjet reattaches to an adjacent parallel boundary (Abramovich, 1963; Allen, 1982, p.l12). The flow in the main channel may be conceptually equated with the zone of no diffusion in separated-flow models. The velocity in this region might be expected to be comparable with
56
TABLE 1 Characteristic d i m e n s i o n s of t h e b e r m a n d s e p a r a t i o n zone Basic m e a s u r e m e n t s L L'
b
=
W
w/2
d H
=
R
z
1) Basic geometric ratios L'/b b/h L/H
= =
H/(W/2)
=
Hydraulic ratios Fr
=
Re
s t r a i g h t line length crest line length b e r m width, p r o x i m a l a n d maximum b e r m h e i g h t average a n d maximum stream width m a x i m u m w i d t h of leeside trough ( valley side to b e r m (:rest) radius of curvature ( H/2 ) + (L~/2H) average d e p t h u p s t r e a m of berm
longitudinal form index (berm) vertical form index ( b e r m ) longitudinal form index (sep. zone ) relative s t r e a m w i d t h index ( sep. zone )
(J/v'~g~ F r o u d e n u m b e r (IDly R e y n o l d ' s n u m b e r
that occurring immediately upstream despite the flow expansion because of inertia and the local steepening of the gradient at this point. The flow in the re-entrant over the bench, however, would be characterized by a large separation vortex with local current vectors in an upstream direction induced by friction and fluid re-entrainment at the border of the mainstream jet. Between the two flow regions a shearflow zone would exist (Fig. 3). In fully turbulent conditions the main jet reattaches at a distance typically 6-8 times the width of the reentrant or step ( e.g. Blatt et al., 1972 ) the exact distance being a function of the relative step height (Allen, 1982, p . l l l ) . Velocities in the recirculating flow would be 20-40% of the freestream velocity (Allen, 1982, p.112 ).
-30m ~32 m ~2m, 4m 4 0 . 7 6 m, t.1 m ~9m ~4.5m ~4m
114.5 m 1.04 m
~ 8.00 ~ 3.64 ~ 7.50 ~ 0.89
~ 0.79-1.33 ~ 10.% 10 ~
Morphological evidence for the model It is hypothesised that the boulder berm was deposited largely within the shear-flow zone downstream of the inflection in valley alignment, whilst the trough area represents the region of reverse flow within the vortex bubble. Basic assumptions are that the sediment supply was unlimited, and sufficient time was available to construct a depositional feature, the geometry of which in part mimics the gross features of the hydraulic pattern. Sedimentological data are discussed below but morphological evidence for geometric equivalence with characteristic dimensions of a hydraulic model is as follows: (1) The general elliptical shape of the chan-
57
Fig. 3. Stylized view of the environment of berm deposition. The figure shows the hypothetical flow separation zone, developed in the valley-wall re-entrant, downstream of an inflection in channel alignment. The shape of the velocity profile and strength of vectors are conjectural but are scaled to represent the estimated main stream velocity. The form of the separation bubble is based on a number of theoretical and observed separated flow structures reported in the literature (e.g. Allen, 1982). Notation related to characteristic dimensions is given in Table 1. S--separation point, X = reattachment point, = the angle of the separation, and A --the upstream sediment sampling point.
Upstreamaection
'!
V
,L\~\
\\\\'\\\'~"
~
BoulderBerm
~
Turf
i
Floodgravels
x\xxx\\"\\
~\~
\\\xx\\\\,
Channellag gravels
\\\\xx\\\\\\>}}~>>>\\\xxx.}>~\ \ \ ' ' '
i
2 Metres
Downstreamsection
L
RIGHT ~ BANK
W *
~ X\\\\\\\%\XN\\X \~\~\XX\X\X
S~I \\X\\\X\x\%\ N X \N\X\N\N%%\\ \\\\\\X\\XX \\\~X~%~\XX \\\\\\\\\~\.. ~\ \ X \ "
\\\\XX\
X
\
~
\\~-
~
BANK
\"
\.
------~--XXX\\\..
Fig. 4. Cross-section surveys of the valley-bottom. Location of sections are given in Fig. 3. Water surface profiles are based upon trashline surveys. Vertical exaggeration × 2.
58 1.2 1.0
A
0-8 .
0'6
~
o.4
,u
0"2 0 10 9 8 7
~6 "t"5
3 2 1 0
0
5
10
15
20
LENGTH
25
30
(M)
Fig. 5. ( A ) Long-section through berm showing variation in height of crest line. ( B ) Plan-view of berm showing relationship of berm to platform deposits and location of scoured area within the trough between berm and valley wall. Small rosediagrams indicate local mean flow direction and mean angular deviation from the azimuth ( see text for explanation). B and C represent downstream sediment sampling points.
nel-side and leeside margins of the berm (Fig. 5B) conforms to the elliptical form of the separation eddy observed in controlled hydraulic investigations concerned with stream flow past abrupt lateral flow expansions (Stevens et al., 1976), negative steps (Allen, 1982) or resulting from angled jets (e.g. Stek and Brandt, 1976; Best and Reid, 1984 ). ( 2 ) For fully turbulent conditions and at high Reynolds' numbers ( typically R >~10 4 ) the form of the flow separation eddy is independent of the main stream velocity but depends on the geometry of the flow expansion (e.g. Abbott and Kline, 1962). Critical ratios are L/H and Hid as defined in Fig. 3 and Table 1. Reattachment typically occurs at a distance of 6-8 H as indicated above. According to Allen (1982) for a relative step height (H/d) of 0.9 as observed here, reattachment should occur at L/H ~- 7.5.
In the case of the berm L/H~_ 7.5 (Table 1 ). (3) The angle (~?) between the local valley wall and the crestline of the berm was determined to be 12-13 c (Figs. 3 and 5). For plane fully turbulent jets the angle of separation from the wall to the jet boundary is a constant 12 ° 24' (Stolzenbach and Harleman, 1971 ); similar to the observed angle. (4) The proximal end of' the deposit is narrow but expands downstream. The steady initial expansion mimics the behaviour of both theoretical and observed shear-flow zones (Allen, 1982, p.121 ). The asymmetrical cross-section of' the berm, with the steepest face towards the inside of the bend (Figs. 4, 5 and 6) is evidence for the role of secondary cross-channel currents enhancing the movement of material into the shear-flow zone (Allen, 1985).
59
Fig. 6. View from point S in Fig. 3 looking downstream along crest line of berm. Feet of figure are at the juncture between the berm and the cobble deposits in the trough area.
Sedimentology of the berm The berm consists primarily of limestone and sandstone boulders with predominantly cobble- and pebble-sized material lodged locally between the boulders. Measurement of the three major axes of the 25 largest clasts yielded the following information; average long axis = 100.7 cm, average intermediate a x i s = 67.7 cm, average short axis = 34.5 cm. Typically, boulders fell just within Zinggs "oblate" shape class (Pettijohn, 1975), although many individual clasts tended to equant dimensions, so that imbrication was weakly developed. There was no downstream change in boulder size, nor was there evidence of a variation in grain size in the vertical section.
As noted above, proximal deposits were very loosely stacked to give a steep face on the leeside of the berm so that the deposit resembled a dry-stone wall (Fig. 6). At this location average slopes down the flanks of the berm were 37 °, similar to the typical angle of residual shear of loose gravel (ca. 35°; Statham, 1974). Elsewhere on the berm the slope of the flanks was on average 29 °; at, or below, the critical angle. The narrow and steeply stacked proximal deposits are interpreted to represent deposition at peak discharge from a highly turbulent flow in which cobbles and small boulders were swept towards the re-entrant by secondary currents. Deposition primarily was restricted at this time to the narrow shear-flow zone so that no boulder-size material was transported laterally into the vortex bubble because of an extremely steep lateral velocity gradient and the presence of a counter-current over the trough. The principal line of flow separation therefore constrained the deposition pattern. The orientation of the plane of maximum projection of well-imbricated discoid clasts on the berm was measured. All of the structures examined were not superficial features but form an integral part of the berm structure. Consequently the results are pertinent to hydraulic conditions at the time of berm construction. Sixty clasts were measured using a Bruntontype compass. Although many more particles would have been preferred these were not available as clearly imbricated structures. The number, however, should be adequate (Andrews and Smith, 1970) for the present purpose. Results are shown graphically on an equal-area Schmidt net (Fig. 7). Long axes tended to be perpendicular to the flow, azimuths therefore represent the intermediate axes and the mean is a resultant of the upstream and downstream valley alignments. The data represent a poorly clustered distribution with a mean orientation of 319 ° and a mean angular deviation (s) of +39.5 °. Dips were steep, averaging 47 ° ( s = + 17 ° ) and only 8% of particles dipped in the downstream direction.
60
N
Fig. 8. Section approximately 60 cm deep through Cobble deposits at site A. A coarse, structureless basal deposit occupies ca. 40 cm thickness and is overlain by ca. 20 cm of a finer pebble deposit. Imbrication is locally weakly developed. Although large clasts appear to be set in a fine matrix in reality all size grades from cobbles to silts are well represented. Lens cap gives scale. Flow left to right.
(e)
:~-: ~;:/(~...
" tf i.j~
I g
-2
~
T •
,
(f)
(h)
Some imbricated clasts had very steep dips up to 90 ° (Fig. 7b ). Very flat discs in particular were frequently "nested" together in groups of two or three against a large equant obstacle clast to form s t o s s - o r leeside deposits. Stoss-side discs were interpreted to have been implaced violently by high current speeds and pressed against the obstacle. Leeside discs presumably bounced or slid over the obstacle to be emplaced by reverse flows in the small-scale separation zone downstream of the obstacle.
Sedimentology of the cobble deposits Stratigraphy
Fig. 7. Sedimentary fabrics represented as equal area Schmidt nets and dip diagrams. Schmidt nets are upper hemisphere projections of the azimuth and dip of the planes of maximum projection of discoidal clasts. Net divisions are at 10° intervals. Closed symbols represent clasts dipping upstream relative to the main streamline, whilst ()pen symbols represent clasts with the reverse attitude. (a) and (b) represent the boulder berm, (c) and (d) site A, (e) and (f) site B and {g) and (h) site C. Broad-headed arrows indicate direction of valley alignment whilst narrow-headed arrows indicate mean fabric azimuths or dips.
Extending across the bench and beneath the boulder berm is a deposit of variable thickness consisting of a contact "framework" of cobblesized material and a "matrix" of pebble- to siltsize debris including turf and rootlet fragments yielding an overall organic content of 6-7 %. The deposit viewed in section was structureless ( Miall's, 1977 Gm facies ) with much open-void space ( Fig. 8). Some clasts were imbricated but it was not possible to sample for azimuth and dip effectively in pit side-walls owing to the unconsolidated and therefore unstable nature
61
of the deposit. Beneath the berm there was no segregation of grain size of the coarse material with depth. These facts, together with the poor sorting (Table 2 ), are interpreted as indicative of rapid deposition from rapid flow. As locally the deposits lie beneath the boulder berm they must represent primarily deposition on the rising limb of the flood hydrograph. Where the cobble deposits are not overlain by the boulder berm, the loosely packed surface deposits are finer, consisting predominantly of pebbles ( Fig. 9 ). This layer is up to 25 cm thick although 10-15 cm is more usual. The percentage of sand ( < 2 mm) and finer sediment throughout the deposits is typically 11-16%. The surface layer grades imperceptibly down into the basal gravels and being finer is interpreted as representing deposition on the falling limb of the hydrograph. The basal deposits are loosely packed. Consequently a rectangular pit was dug into a natural exposure; the weight of sediment removed and the estimated volume of the pit were used to calculate an approximate porosity. The value, 0.45 is close to that given by Allen (1972) for rapid deposition. A value of 0.47 is often quoted as the maximum possible porosity in primary clastic deposits (Blatt et al., 1972). With such a high porosity it might be expected that the finer fractions will be flushed out by heavy
rainfall and compacted down towards the base of the deposit with time. Granulometric curves based on large bulk samples (British Standards, 1982) are given in Fig. 9. The curves may be interpreted simply as representing a truncated log-normal distribution. At the coarse end the distribution is limited by the lack of particles coarser than - 8 0 in the deposit. Coarser particles presumably were mobilized close to the peak discharge and therefore are only found concentrated in the boulder berm. At the fine end of the distribution, material smaller than 2 ¢ was effectively transported through the reach, probably as a washload sustained by the high velocities and high turbulence levels. Only small amounts were entrapped in the interstices of the rapidly deposited gravel. The distribution reflects the fact that materials of a broad size range were deposited largely contemporaneously. Only at the latter stages of the flood were coarse gravels ( > - 6 ¢) unavailable and so are not represented in the surface layer. The grading curves for the basal flood deposits were compared with the grading curve for a bulk sample of source sediments excavated from naturally eroding bluffs of solifluxion deposits close to the channel, 200-300 m upstream of the berm. The curves were similar in form, indicative of little downstream sorting, the only dif-
TABLE 2 Statistical parameters of grain-size distributions representing the platform deposits (values in m m where appropriate) Parameter
Sample location (A) basal
Mean Stand. dev. Skewness d~,,) d~4 d,~, Percent < 2 m m Percent < 63 p m T r a s k coeff.
111.37 69.05 - 0.18 78 138 180 11.02 0.12 1.53
(A) surface
( B ) basal
(C) basal
33.65 35.54 0.91 17 58 95 15.60 0.30 3.37
51.69 37.73 0.09 33 73 96 9.62 0.15 2.26
75.00 46.33 0.21 58 84 180 10.99 0.09 1.67
62
99'99
-
t
99 ¸
95 90
80 70 ¢ ~.
60 SO' 40
~ 30' ~ 20' 10' 5'
0"01
.
. +4
.
. 3
.
. 2
. 1
0
1
,
,
,
,
,
,
2
3
4
5
6
7-
phi
Fig. 9. Cumulative frequency diagram of representative grain-size distributions. Squares: basal gravels at site A; triangles: surface gravels at site A; dots: source materials from bluffs. Vertical scale is normal probability distribution. ference being a larger p e r c e n t a g e of material finer t h a n 2 O in the source sediments; some 5 - 6 % as opposed to only 3 - 4 % in the flood deposits.
Palaeocurrent analysis As s t a t e d above it was n o t possible to measure the o r i e n t a t i o n of clasts in the basal gravel deposits. T h e o r i e n t a t i o n of surface particles is likely to r e p r e s e n t the falling-stage hydraulic climate (e.g. B y r n e , 1963) a n d c o n s e q u e n t l y m a y not reflect m e c h a n i s m s responsible for the deposition of the bulk of the deposit. N e v e r t h e less cobble i m b r i c a t i o n can be used as a sensitive i n d i c a t o r of local changes in s t r e a m flow direction ( K a u f f m a n a n d Ritter, 1981) and it is unlikely t h a t the gross velocity p a t t e r n in
plan-view c h a n g e d s u b s t a n t i a l l y whilst the gravels were deposited. T h e r e f b r e the dip of the p l a n e of m a x i m u m p r o j e c t i o n was m e a s u r e d for large discoidal cobbles in well-imbricated surface structures. As on the b e r m t h e a-axes t e n d e d to be orient a t e d n o r m a l to t h e valley o r i e n t a t i o n . At site A on the left b a n k u p s t r e a m of the b e r m only 22 well-imbricated s t r u c t u r e s were found. T h e s e , however, if i n t e r p r e t e d correctly, reflect the process of m o m e n t u m t r a n s f e r over the c h a n n e l b a n k ( Seltin, 1964; T o e b e s and Sooky, 1967); the m e a n a z i m u t h of flow being 359 ° ( s = + 59 c ) as opposed to the c h a n n e l alignm e n t of 3305. T h e m e a n particle dip was 30 c ( s = +_ 12 c ) and all clasts dipped up-valley ( Fig. 7d). In c o n t r a s t , at site B on the c h a n n e l - s i d e of the berm, the a z i m u t h of well-imbricated particles was close to the c h a n n e l a l i g n m e n t i.e. 288 ° ( s = + 53 ° ) as opposed to 280 ° a n d the average dip was 13.50 ° ( s - + 1 9 ~') in an u p s t r e a m direction. H o w e v e r , a second group of well-imbricated particles had an a z i m u t h of 62.50 ° (s = _+41 ° ) a n d a m e a n dip down-valley of 18 ° ( s = _+12 °). T h e s e d a t a indicate the p r e s e n c e of reverse flows in the vicinity of the b e r m e i t h e r (1) i n d u c e d by the valley wall configuration before the boulder b e r m was deposited, or (2) induced locally by the p r e s e n c e of the b e r m itself in the l a t t e r stage of the hydrograph. At site C the evidence for reverse flow was very strong. Of the particles m e a s u r e d 59% dipped in an up-valley direction (average dip 14 ~, s = _ + 9 ) a n d h a d an a z i m u t h of 273 c (s - + 4 9 ~ ) whilst the r e m a i n i n g 41% dipped down-valley (16 =, .s = -" l l :} with an inferred m e a n a z i m u t h of 73 : I s - :k 56 ). S o m e of the n o r m a l l y dipping clasts were located in the scoured hollow in the t r o u g h area ( Fig. 5 ). Initially the o c c u r r e n c e of this scour was difficult to explain. P r e s u m a b l y the boulder b e r m developed from the p r o x i m a l end in a d o w n s t r e a m direction and a s t r o n g down-valley c u r r e n t on the leeside of the b e r m would have been precluded. T h e delicate u n s t a b l e p r o x i m a l b e r m
63 structure indicated the absence of a strong current flowing over this area. The scour is interpreted as representing a late stage in berm development. As the hydrograph fell rapidly some 12-14 m 3 of water would have been ponded between the berm and the valley wall. Subsequently the berm failed principally in the area of the scour but also at a minor gap in the berm downstream (Fig. 5B ). In order to summarize the spatial information obtained from the particle orientation data, normalized eigenvalues, gl ~ gl > g2 and great-circle girdles, g~ < g2 < g3 (Mardia, 1972, p.225). S u m m a r y ratios of eigenvalues consequently are directly related to fabric shape and strength (see e.g. Woodcock, 1977, for further details). Used with other indicators, eigenvalues may have value in discriminating between environments of deposition. Using this approach, Nelson (1985) attempted to discriminate between a number of sediment sources or depositional environments which included "debris flows" as a category as well as small "sediment flows" associated with glacier snouts. Apparently, alluvial debris-torrent gravels were not included. Nelson's data are reproduced with additional data for comparison (Fig. 10). Additional data represent (1) the boulder berm and associated cobble fabric; (2) pebble orientation data from subaqueous slip-faces on experimental gravel dunes; and (3) cobble-orientation data from a natural stream where the fabric was formed under moderately high flows. Eigenvalues and associated parameters for the debris-torrent deposits are summarized in Table 3. The parameter K represents the gradient of straight lines emanating from the origin in Fig. 10. Girdle distributions plot below a K = I line where 0~
s
/"/ /./// //
v c
•z~/,/"
II
•,.
y•
•
•
• ~•
~
[] zx
•
o o
•D • ~0
o 0
odu
0
D f
•
o
•
~
~,
~
Fig. 10. Logarithmicratio plot of eigenvalueratios for various types of sedimentary deposits. Dots and solid squares represent debris flow and sediment flows respectively as defined by Nelson (1985) from whose Fig. 3 the data are extracted. Additional symbols represent: big open triangles, the boulder berm; small open triangles, the cobble deposits ~data from the present investigation; open squares, coarse sedimentsin a high-velocitystream;circles, slip-face deposits on experimental gravel dunes from the authors unpublished data. The pecked line represents the girdle-cluster transition at K = 1 (see text).
distributions plot near the origin and have a low value of C, and those distributions with a stronger preferred orientation plot farther from the origin.
TABLE 3 Eigenvalues and associated parameters for the berm and platform deposits (see text for details) Sample
g~
g3
K
C
Berm A B C
0.069 0.125 0.087 0.069
0.749 0.522 0.614 0.538
1.47 0.58 0.38 0.18
2.38 1.95 1.43 2.05
K = ln (g2/g~) In (ga/g2)
C=ln (&/g~)
64
Discussion Berm geometry as a palaeo-flow indicator
Published accounts of boulder berms rarely have included hydraulic interpretation of the berm form other than a consideration of the velocities necessary to entrain the largest boulders present. Given that coarse debris is unlikely to compact significantly through time, the crestlines of berms have been used to indicate the probable maximum water depth (Costa, 1984 ). The evidence for maximum depth in the present investigation (Fig. 4) is based on trashline levels and would tend to support Costa's conclusion. Other aspects of berm geometry have not been considered as potential flow indicators although the orientation of the long axes presumably reflect mean or local flow directions. Sedimentary deposits attributable to lateral flow separation of Newtonian flows have been described on a variety of scales (e.g. Karcz, 1972; Werner and Newton, 1975; Leeder and Bridges, 1975; Ferentinos and Collins, 1980; Allen, 1982, p.183). In a similar manner the identification of berm structures related to flow separation is potentially a useful indicator of Newtonian debris-torrent flow vis-a-vis cohesive debrisflow behaviour. Further detailed attention to berm geometry might therefore prove useful. Allen (1971) amongst others proposed relationships between current speed, obstacle dimensions and the dimensions of the wake deposits in fine-grained sediments. However, with respect to coarse flood deposits, only Krumbein (1942) has suggested that a relationship should exist between the size of an obstacle and the magnitude of the wake deposit. Allen's (1971) investigations are particularly pertinent as the ability to reconstruct velocity is especially crucial to palaeo-discharge analysis. However, it should be noted that velocity cannot be obtained from geometric relationships of' separated flows in the fully turbulent phase. The geometry of the separa-
tion zone and hence the associated sediment: deposit is proportional only to the geometry of' the channel re-entrant. Only fbr laminar flows is the geometry of the separation zone proportional to the velocity (e.g. Thomas et al., 1981 ). Flow-separation geometry therefore may not be useful to estimate velocity in turbulent flow but further investigations are required to evaluate the potential value of berm geometry in palaeoflow analysis. Particle imbrication
Particular imbricate structures may be associated with debris torrents but any diagnostic features need to be clearly distinguished from those associated with normal flood gravels. Rust (1984) investigated a coarse largely ungraded gravel deposit he believed accumulated under "clear-water" flows characterized by high velocities. Particles dipped upstream and the mean dip of the a - b plane was 23.4 °. Although Rust's interpretation is representative of a number of studies of' flood gravel fabrics, particle geometry significantly influences imbrication angles so results may be site specific ( e.g. Pettijohn, 1975). Consequently, to aid in the present interpretation, the a - b dip of cobbles was measured at six sites in a gravel-bedded stream sedimentologically similar to the West Grain. The sediments in question had been deposited by rapid velocities associated with an in-channel discharge of unexceptional magnitude. The mean dip of 180 clasts was 2 2 ( s - _+ 12 ~ ) and there was negligible difference between the six sites. A perusal of the literature of which Rust's {1984) paper is one example, supported by the additional field data, suggest that the mean dip of the platform clasts at site A (i.e. 30 ° ) is typical of a high-velocity depositional environment. The lower dips at sites B and C, (i.e. 13.5-18 ~ ) would indicate either reorientation by waning flows or more likely an environment subject to lower velocities at peak flow. The tat-
65 ter interpretation would accord with the presence of a separated flow structure. Very steep dips have been associated with deposition in macro-turbulent environments (e.g. Hendry, 1976), and Jarrett and Costa (1985) indicate that boulders constituting berms have steep imbrication angles, commonly exceeding 60 ° . The data for the West Grain berm support these observations. The mean dip (47 ° ) is steeper than that observed on the platform deposits and represents deposition at high velocities. The transverse orientation of the a-axes of clasts to the flow (as on the West Grain) is common in high-velocity deposits (Rust, 1984; Jarrett and Costa, 1985) but not universal. Krumbein (1942) observed flood gravels with a-axes parallel to the flow azimuth. Rust (1972) notes that orientation is a function of particle size, sediment sorting and modes of transport and deposition as well as particle shape. Consequently a-axis orientation can be expected to be variable and the a-b dip plane is a more reliable palaeo-flow indicator (Johansson, 1965 ).
Eigenvalues as discriminators of the Newtonian character of depositional events The fabrics of the deposits have weakly developed modes aligned principally with the valley orientation. The berm in particular had a boulder fabric tending to a clustered distribution. The platform deposits, however, had more strongly developed fabrics with girdle distributions. The datp collated by Nelson (1985) representing "debris flows" and "sediment flows" may include some "debris-torrent" deposits, but largely represent weak fabrics scattered across the cluster/girdle transition area (Fig. 10). In contrast, the field and experimental data for rapidly deposited pebbles and cobbles in Newtonian streams have stronger fabrics with girdle tendencies. The few data for the present investigation fall in the intermediate area between the two extremes. Although clearly there are insufficient data for the "debris
torrent" class to draw a definite conclusion, inspection of Fig. 10 suggests a transition or continuum may exist between high-viscosity debris-flow deposits with weak fabrics and clustered distributions (e.g. Mills, 1984) to strongly developed fabrics with girdle tendencies representing "flash-flood" or rapidly deposited fluvial sediments. The intermediate area presumably is represented by: (a) more fluid, low-viscosity debris flows where sub-parallel fabrics may be weakly developed (e.g. Lewis, 1984) ; and (b) debris-torrent deposits. The sedimentary fabric of the latter category is poorly defined at present and requires further study. Taking all the available data (Fig. 10) the transition or continuum may be represented by a relatively invariant gffg2 ratio typically less than 1 and a highly variable s2/sl ratio. Conclusions The boulder berm developed under peak flow conditions during a debris-torrent event. The locale for deposition was the shear-flow zone in an area of separated flow downstream of a sudden change in both valley alignment and channel cross-section. The geometry and sedimentology of the berm, and the sedimentary fabric of associated flood deposits, can be interpreted consistently with the presence of a flow separation bubble in the valley re-entrant. Both sediment packing and fabric orientation indicate rapid deposition from a high velocity low-viscosity flood-flow heavily charged with coarse debris. Formed within the re-entrant in the valley wall alignment, the feature has some broad similarities to flow-separation deposits formed at a variety of scales downstream of obstacles. Consequently the geometry of berms and associated hydraulic patterns might usefully be explored further. Although the reconstruction of the "palaeo-velocities" from berm geometry would not seem possible where flows were within the fully turbulent phase, the water depth and azimuth of flows may be reconstructed.
66
Eigenvalues summarizing the strength and pattern of the fabric of the debris-torrent deposits indicate a transitional phase between fabrics associated with debris flows and water floods, respectively. Further investigations of fabrics and particle-size distributions are required, but eigenvalues in conjunction with other independent evidence, may be useful in classifying the deposits associated with heavily sediment-laden flows.
Acknowledgements Mr. M. Glaister and Ms. C. Williams assisted in field work and Mr. M. Glaister drafted the figures. Prof. J.R.L. Allen and two anonymous referees read an earlier version of the manuscript and suggested a number of improvements.
References Abbott, D.E. and Kline, S.J., 1962. Experimental investigation of subsonic turbulent flow over single and double backward facing steps. A.S.M.E. Ser. D, J. Basic Eng., 84: 317-325. Abramovich, G.N., 1963. The Theory of Turbulent Jets. MIT Press, Cambridge, Mass., 671 pp. Allen, J.R.L, 1971. Transverse erosional marks of mud and rock: their physical basis and geological significance. Sediment. Geol., 5: 167-385. Allen, J.R.L., 1972. Intensity of deposition from avalanches and the loose packing of avalanche deposits. Sedimentology, 18: 105-111. Allen, J.R.L., 1982. Sedimentary Structures: Their Character and Physical Basis. Vol. 2. (Developments in Sedimentology, 30B ) Elsevier, Amsterdam 663 pp. Allen, J.R.L., 1985. Loose-boundary hydraulics and fluid mechanics: selected advances since 1961. In: P.J. Brenchley and B.P.J. Williams (Editors), Sedimentology: Recent Developments and Applied Aspects. Blackwell, Oxfl)rd, pp. 7-28. Andrews, J.T. and Smith, D.I., 1970. Statistical analysis of till fabric; methodology, local and regional variability. Geol. Soc. London, Q. J., 125: 503-542. Best, J.L. and Reid, I., 1984. Separation zone at open-channel junctions. J. Hydraul. Eng. ASCE, 110: 1588-1594. Blatt, H., Middleton, R. and Murray, R., 1972. Origin of Sedimentary Rocks. Prentice-Hall, Englewood Cliffs, New Jersey, 634 pp. British Standards, 1982. Draft of the revised standard on bed material sampling. Document 82/30444 (unpublished).
Byrne, J.V., 1963. Variations in fluvial gravel imbrication. J. Sediment. Petrol., 33: 467-482. Carling, P.A., 1986. The Noon Hill flash floods; July 17th 1983. Hydrological and geomorphological aspects of a major formative event in an upland landscape. Trans. Inst. Br. Geogr., 11: 105-118. Costa, J.E., 1984. Physical geomorphology of debris flows. In: J.E. Costa and P.J. Fleisher (Editors), Developments and Applications of Geomorphology. Springer, New York, N.Y., pp. 268-317. Ferentinos, G. and Collins, M., 1980. Effects of shoreline irregularities on a rectilinear tidal current and their significance in sedimentary, processes. J. Sediment. Petrol., 50: 1081-1094. Hendry, H.E., 1976. The orientation of discoidal clasts in resedimented conglomerates, Cambro-Ordovician, Gaspd, Eastern Quebec. J. Sediment. Petrol., 46: 48-55. Jarrett, R.D. and Costa, J.E., 1985. Hydrology, geomorphology, and dam-break modeling of the July 15, 1982, Lawn Lake Dam and Cascade Lake Dam Failures, Larimer County, Colorado, U.S. Geol. Surv., Open-File Rep. 84-612,109 pp. Johansson, C.E., 1965. Structural studies of sedimentary deposits. Geol. FSren. Stockh. FSrh., 87: 3-61. Karcz, I., 1972. Sedimentary structures formed by flash floods in southern Israel. Sediment. Geol., 7: 161-182. Kauffman, M.E. and Ritter, D.F., 1981. Cobble imbrication as a sensitive indicator of subtle local changes in river flow direction. Geology, 9: 299-302. Krumbein, W.C., 1942. Flood deposits of Arroyo Seco, Los Angeles County, California. Bull. Geol. Soc. Am., 53: 1355-1402. Leeder, M.R. and Bridges, P.H., 1975. Flow separation in meander bends. Nature, 253: 338-339. Lewis, D.W., 1984. Practical Sedimentology, Dowden, Hutchinson and Ross, Stroudsburg, Pa., 227 pp. Mardia, K.V., 1972. Statistics of Directional Data. Academic Press, New York, N.Y., 357 pp. Miall, A.D., 1977. A review of the braided river depositional environment. Earth-Sci. Rev., 13: 1-62. Miles, M.J. and Kellerhals, R., 1981. Some engineering aspects of debris torrents. Can. Soc. Civ. Eng. 5th Can. Hydrotech. Conf., New Brunswick, pp. 395-420. Mills, H.H., 1984, Clast orientation in Mount St. Helens debris-flow deposits, North Fork Toutle River, Washington. J. Sediment. Petrol., 54: 626-634. Nelson, F.E., 1985. A preliminary investigation of solifluction macrofabrics. Catena, 12: 23-33. Pettijohn, E.J., 1975. Sedimentary Rocks. Harper and Row, New York, N.Y., 3rd ed., 628 pp. Rust, B.R., 1972. Pebble orientation in fluvial sediments. J. Sediment. Petrol., 42: 384-388. Rust, B.R., 1984. Proximal braidplain deposits in the Middle Devonian Malbaie Formation of Eastern Gasp~, Quebec, Canada. Sedimentology, 31: 675-695. Scott, K.M. and Gravlee, G.C,. 1968. Floodsurge on the
67 Rubicon River, California - hydrology, hydraulics, and boulder transport. U.S. Geol. Surv., Prof. Pap., 422-M: 40 pp. Sellin, R.H.J., 1964. A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche, 7: 793-801. Shroba, R.R., Schmidt, P.W., Crosby, E.J. and Hansen, W.R., 1976. Storm and flood of July 31-August 1, 1976, in the Big Thompson River and Cache la Poudre River basins, Larimer and Weld Counties, Colorado, part B geologic and geomorphic effects in the Big Thompson Canyon area, Larimer County. U.S. Geol. Surv., Prof. Pap., 1115: 87-152. Statham, I., 1974. The relationship of porosity and angle of repose to mixture proportions in assemblages of different size materials. Sedimentology, 21: 149-162. Stek, J.B. and Brandt, H., 1976. Aerodynamic throttling of a two-dimensional flow by a thick jet. Aeronaut. Q., 27: 229-242. Stevens, M.A., Chen, J.H. and Simons, D., 1976. Riverbank recessions for power plant facilities. A.S.C.E. Waterways, Harb. Coastal Eng. Div. 2nd Annu. Symp., Modelling Techniques, 1: 560-574.
Stewart, J.H. and La Marche, V.C., 1967. Erosion and deposition produced by the flood of December 1964 on Coffee Creek, Trinity County, California. U.S. Geol. Surv., Prof. Pap., 422-K. Stolzenbach, K.D. and Harleman, D.R.F., 1971. An analytical and experimental investigation of surface discharges of heated water. M.I.T., Ralph M. Parsons Lab., Water Resources and Hydrodynamics, Dep. Civ. Eng. Rep. 135:212 pp. Thomas, C.E., Morgan, K. and Taylor, C., 1981. A finite element analysis of flow over a backward facing step. Comput. Fluids, 9: 265-278. Toebes, G.H. and Sooky, A.A., 1967. Hydraulics of meandering rivers with flood plains. J. Waterways Harb. Div. A.S.C.E., 93: 213-236. Werner, F. and Newton, R.S., 1975. The pattern of largescale bed forms in the Langeland Belt (Baltic Sea ). Mar. Geol., 19: 29-59. Woodcock, N.H., 1977. Specification of fabric shapes using an eigenvalue method. Geol. Soc. Am. Bull., 88: 1231-1236. Wright, L.D., 1977. Sediment transport and deposition at river mouths: A synthesis. Geol. Soc. Am. Bull., 88: 857-868.
53
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
HYDRODYNAMIC INTERPRETATION OF A BOULDER BERM AND ASSOCIATED DEBRIS-TORRENT DEPOSITS P.A. CARLING Freshwater Biological Association, Windermere Laboratory, The Ferry House, Far Sawrey, Ambleside, Cumbria LA22 OLP (England) ( Revised version accepted March 16, 1987)
Abstract Carling, P.A., 1987. Hydrodynamic interpretation of a boulder berm and associated debris-torrent deposits. Geomorphology, 1: 53-67. The hydrodynamic environment associated with a boulder berm is reconstructed from the geometry and sedimentology of the berm and associated debris-torrent deposits. Berms may result from a variety of hydrodynamic scenarios but in this instance the berm was associated with flow separation downstream of an abrupt change in channel morphology. Sediment fabric analyses are summarized particularly as eigenvalues and these data compared with the fabric of debris flows and clear-water gravel deposits. Although data are few, the eigenvalue results can be interpreted consistently as reflecting a transition between the end members of a sediment fabric continuum. The value of detailed studies of berm geometry and sedimentology is discussed with reference to their hydraulic significance. This latter aspect is important for palaeo-discharge reconstruction of both Newtonian and non-Newtonian flows.
Introduction
A problem in present-day terrestrial sedimentological process studies is the identification of deposits attributable to heavily sediment-laiden flash-floods (debris-torrents of Miles and Kellerhals, 1981) as opposed to debris-flow deposits (Costa, 1984). Debris flows may be strongly non-Newtonian whilst debris torrents tend to be transitional or Newtonian in character, depending on the sediment concentration. Critical concentrations, the nature of the transition between the two types of flow, and the associated mechanics of flow are a matter of some debate. A varied and commonly inconsistent terminology has been applied to deposits of debris 0169-555X/87/$03.50
flows and torrents. In the past especially there has been a propensity to describe depositional features associated with debris torrents in only general terms and to provide only limited sedimentological data. However, debris torrents, heavily charged with coarse material, may deposit distinctive linear features called boulder berms (Stewart and La Marche, 1967; Scott and Gravlee, 1968). These little-studied features are believed to be sedimentologically distinct from "morphologically similar" debrisflow deposits termed lev~es and lobes (Costa, 1984). Berms may develop transverse to and flanking stream channels but the exact mode of formation and hydraulic significance of these structures is unclear as the process cannot be readily observed. In certain instances, berms
© 1987 Elsevier Science Publishers B.V.
54
may be remnants of chute or delta-like deposits, which were subsequently dissected by fhlling-stage discharges to produce a longitudinal ridge topography. An alternative, and by no means exclusive mechanism, is flow separation in plan-view unconnected with incision of flood deposits. For example, some berms occur in regions of the channel or valley where one might expect flow separation and rapid deposition during "catastrophic" discharges. The typical location of gravel deposits on the inside of channel bends described by Shroda et al. (1976) is an example. In this paper, a boulder berm is described and attributed to flow separation. The debris-torrent event responsible for the deposit has been described by Carling (1986) and consisted of a single-peak hydrograph, of a duration no more than two hours, which was heavily charged with fine comminuted peat and coarse gravel. The deposit, although unusual in the sense that it is extremely well formed, is similar to several other berm deposits in the U.K. uplands resulting from flood episodes which also reasonably can be interpreted using the same hydraulic model.
The enL~ironment of deposition The berm was deposited on a valley-side bench in the narrow, steep-sided West Grain valley in the north of England (Figs. 1 and 2). The most important characteristics of the site are that here the valley bends abruptly through an internal angle of 130 ° (Fig. 3) and expands rapidly downstream. The channel gradient also steepens from 0.0728 upstream of the bend to 0.1032 adjacent to and downstream of the berm site. Survey of flood trash-lines indicated a cross-sectional area, immediately upstream of the bend, of 6.00 m 2 whilst downstream the section increased to 14.12 m 2 {Fig. 4). Given the rapid flow expansion with a transition from confined flow to partially unconfined flow, considerable spatial variation in velocity might be expected across the downstream section; high velocities being sustained
in the centre of the channel with more tranquil flow and low velocities in lateral areas. Discharges in the small cobble and boulderbedded channel were usually only a few litres a second and in a three-year period never exceeded 1.2 m :~s ~. In contrast,, the flood peak discharge was estimated to lie between 16 and 22 m 3 s ~and overtopped the valley-side bench. The average peak velocity through the reach cannot be known with certainty but would be at least 2.7 m s ~ and possibly as high as 3.7 m s ~ immediately upstream of the berm site ( Carling, 1986 ).
The morphology of the berm The berm consists primarily of boulders overlying cobble deposits. At the proximal and distal ends, the berm is narrower than at the intermediate section. The crest at the proximal end was aligned with the upstream valley axis, whilst the distal end was aligned with the downstream valley axis. The change in alignment in between was gradational giving an approximate radius of curvature of 114.5 m (Table 1 and Fig. 5). The berm has an overall length of 32 m, a maximum height of 1.10 m and a width varying between 2 and 4 m. The transition from the boulder deposit to the cobble deposits on the leeside of the berm was abrupt. The surface of the cobble deposits enclosed by the berm and the valley walls was essentially flat and up to 4 m wide forming a trough which opened out in a downstream direction through a scoured gap in the berm (Fig. 5).
Flow separation model In the following text, the morphology of the berm is interpreted as representing deposition in a plane half-jet separation vortex. Models of jet-flow have been used by geologists to explain, for example, the distribution of sediments at river mouths and delta fronts (Wright, 1977). Although the physics and mathematical
55
Ireshopeburn
B~p/v
7
L
1Kin
1
/~
Fig. 1. Location map showing site of berm.
Fig. 2. General view of the valley of the West Grain and the reach immediately upstream of the berm, showing over-bank gravel deposits on the left bank and the nature of the catchment. The proximal end of the berm is visible in the lower left of the view. Stream width ca. 7 m.
expression of vortex flow are complex, for most sedimentological applications simplified models have been proven most useful. Abramovich (1963) provides a useful introductory text concerning jet hydraulics whilst Allen (1982) details some specific sedimentological examples of the application of jet and vortex models. In this section the basic hydraulic model is out-
lined ( Fig. 3 ) and this is expanded and justified in following sections. The model is of necessity two-dimensional because the estimated hydraulic data are not suitable to include in a three-dimensional analysis of flow pattern. Nevertheless, the channel curvature might induce a degree of spiral flow throughout the bend; resulting in a transverse velocity component of near-bottom flow directed towards the inner right bank, and a compensating surface flow towards the left outer bank (Allen, 1985). Given the estimated hydraulic and measured geometric conditions (Table 1 ), separation of turbulent flow would be expected to occur at the inflection in the valley alignment (cf. Leeder and Bridges, 1975). The presence of an effective re-entrant in the valley-wall alignment adjacent to the terrace would ensure separation similar to that experienced when an inertia-dominated plane halfjet reattaches to an adjacent parallel boundary (Abramovich, 1963; Allen, 1982, p.l12). The flow in the main channel may be conceptually equated with the zone of no diffusion in separated-flow models. The velocity in this region might be expected to be comparable with
56
TABLE 1 Characteristic d i m e n s i o n s of t h e b e r m a n d s e p a r a t i o n zone Basic m e a s u r e m e n t s L L'
b
=
W
w/2
d H
=
R
z
1) Basic geometric ratios L'/b b/h L/H
= =
H/(W/2)
=
Hydraulic ratios Fr
=
Re
s t r a i g h t line length crest line length b e r m width, p r o x i m a l a n d maximum b e r m h e i g h t average a n d maximum stream width m a x i m u m w i d t h of leeside trough ( valley side to b e r m (:rest) radius of curvature ( H/2 ) + (L~/2H) average d e p t h u p s t r e a m of berm
longitudinal form index (berm) vertical form index ( b e r m ) longitudinal form index (sep. zone ) relative s t r e a m w i d t h index ( sep. zone )
(J/v'~g~ F r o u d e n u m b e r (IDly R e y n o l d ' s n u m b e r
that occurring immediately upstream despite the flow expansion because of inertia and the local steepening of the gradient at this point. The flow in the re-entrant over the bench, however, would be characterized by a large separation vortex with local current vectors in an upstream direction induced by friction and fluid re-entrainment at the border of the mainstream jet. Between the two flow regions a shearflow zone would exist (Fig. 3). In fully turbulent conditions the main jet reattaches at a distance typically 6-8 times the width of the reentrant or step ( e.g. Blatt et al., 1972 ) the exact distance being a function of the relative step height (Allen, 1982, p . l l l ) . Velocities in the recirculating flow would be 20-40% of the freestream velocity (Allen, 1982, p.112 ).
-30m ~32 m ~2m, 4m 4 0 . 7 6 m, t.1 m ~9m ~4.5m ~4m
114.5 m 1.04 m
~ 8.00 ~ 3.64 ~ 7.50 ~ 0.89
~ 0.79-1.33 ~ 10.% 10 ~
Morphological evidence for the model It is hypothesised that the boulder berm was deposited largely within the shear-flow zone downstream of the inflection in valley alignment, whilst the trough area represents the region of reverse flow within the vortex bubble. Basic assumptions are that the sediment supply was unlimited, and sufficient time was available to construct a depositional feature, the geometry of which in part mimics the gross features of the hydraulic pattern. Sedimentological data are discussed below but morphological evidence for geometric equivalence with characteristic dimensions of a hydraulic model is as follows: (1) The general elliptical shape of the chan-
57
Fig. 3. Stylized view of the environment of berm deposition. The figure shows the hypothetical flow separation zone, developed in the valley-wall re-entrant, downstream of an inflection in channel alignment. The shape of the velocity profile and strength of vectors are conjectural but are scaled to represent the estimated main stream velocity. The form of the separation bubble is based on a number of theoretical and observed separated flow structures reported in the literature (e.g. Allen, 1982). Notation related to characteristic dimensions is given in Table 1. S--separation point, X = reattachment point, = the angle of the separation, and A --the upstream sediment sampling point.
Upstreamaection
'!
V
,L\~\
\\\\'\\\'~"
~
BoulderBerm
~
Turf
i
Floodgravels
x\xxx\\"\\
~\~
\\\xx\\\\,
Channellag gravels
\\\\xx\\\\\\>}}~>>>\\\xxx.}>~\ \ \ ' ' '
i
2 Metres
Downstreamsection
L
RIGHT ~ BANK
W *
~ X\\\\\\\%\XN\\X \~\~\XX\X\X
S~I \\X\\\X\x\%\ N X \N\X\N\N%%\\ \\\\\\X\\XX \\\~X~%~\XX \\\\\\\\\~\.. ~\ \ X \ "
\\\\XX\
X
\
~
\\~-
~
BANK
\"
\.
------~--XXX\\\..
Fig. 4. Cross-section surveys of the valley-bottom. Location of sections are given in Fig. 3. Water surface profiles are based upon trashline surveys. Vertical exaggeration × 2.
58 1.2 1.0
A
0-8 .
0'6
~
o.4
,u
0"2 0 10 9 8 7
~6 "t"5
3 2 1 0
0
5
10
15
20
LENGTH
25
30
(M)
Fig. 5. ( A ) Long-section through berm showing variation in height of crest line. ( B ) Plan-view of berm showing relationship of berm to platform deposits and location of scoured area within the trough between berm and valley wall. Small rosediagrams indicate local mean flow direction and mean angular deviation from the azimuth ( see text for explanation). B and C represent downstream sediment sampling points.
nel-side and leeside margins of the berm (Fig. 5B) conforms to the elliptical form of the separation eddy observed in controlled hydraulic investigations concerned with stream flow past abrupt lateral flow expansions (Stevens et al., 1976), negative steps (Allen, 1982) or resulting from angled jets (e.g. Stek and Brandt, 1976; Best and Reid, 1984 ). ( 2 ) For fully turbulent conditions and at high Reynolds' numbers ( typically R >~10 4 ) the form of the flow separation eddy is independent of the main stream velocity but depends on the geometry of the flow expansion (e.g. Abbott and Kline, 1962). Critical ratios are L/H and Hid as defined in Fig. 3 and Table 1. Reattachment typically occurs at a distance of 6-8 H as indicated above. According to Allen (1982) for a relative step height (H/d) of 0.9 as observed here, reattachment should occur at L/H ~- 7.5.
In the case of the berm L/H~_ 7.5 (Table 1 ). (3) The angle (~?) between the local valley wall and the crestline of the berm was determined to be 12-13 c (Figs. 3 and 5). For plane fully turbulent jets the angle of separation from the wall to the jet boundary is a constant 12 ° 24' (Stolzenbach and Harleman, 1971 ); similar to the observed angle. (4) The proximal end of' the deposit is narrow but expands downstream. The steady initial expansion mimics the behaviour of both theoretical and observed shear-flow zones (Allen, 1982, p.121 ). The asymmetrical cross-section of' the berm, with the steepest face towards the inside of the bend (Figs. 4, 5 and 6) is evidence for the role of secondary cross-channel currents enhancing the movement of material into the shear-flow zone (Allen, 1985).
59
Fig. 6. View from point S in Fig. 3 looking downstream along crest line of berm. Feet of figure are at the juncture between the berm and the cobble deposits in the trough area.
Sedimentology of the berm The berm consists primarily of limestone and sandstone boulders with predominantly cobble- and pebble-sized material lodged locally between the boulders. Measurement of the three major axes of the 25 largest clasts yielded the following information; average long axis = 100.7 cm, average intermediate a x i s = 67.7 cm, average short axis = 34.5 cm. Typically, boulders fell just within Zinggs "oblate" shape class (Pettijohn, 1975), although many individual clasts tended to equant dimensions, so that imbrication was weakly developed. There was no downstream change in boulder size, nor was there evidence of a variation in grain size in the vertical section.
As noted above, proximal deposits were very loosely stacked to give a steep face on the leeside of the berm so that the deposit resembled a dry-stone wall (Fig. 6). At this location average slopes down the flanks of the berm were 37 °, similar to the typical angle of residual shear of loose gravel (ca. 35°; Statham, 1974). Elsewhere on the berm the slope of the flanks was on average 29 °; at, or below, the critical angle. The narrow and steeply stacked proximal deposits are interpreted to represent deposition at peak discharge from a highly turbulent flow in which cobbles and small boulders were swept towards the re-entrant by secondary currents. Deposition primarily was restricted at this time to the narrow shear-flow zone so that no boulder-size material was transported laterally into the vortex bubble because of an extremely steep lateral velocity gradient and the presence of a counter-current over the trough. The principal line of flow separation therefore constrained the deposition pattern. The orientation of the plane of maximum projection of well-imbricated discoid clasts on the berm was measured. All of the structures examined were not superficial features but form an integral part of the berm structure. Consequently the results are pertinent to hydraulic conditions at the time of berm construction. Sixty clasts were measured using a Bruntontype compass. Although many more particles would have been preferred these were not available as clearly imbricated structures. The number, however, should be adequate (Andrews and Smith, 1970) for the present purpose. Results are shown graphically on an equal-area Schmidt net (Fig. 7). Long axes tended to be perpendicular to the flow, azimuths therefore represent the intermediate axes and the mean is a resultant of the upstream and downstream valley alignments. The data represent a poorly clustered distribution with a mean orientation of 319 ° and a mean angular deviation (s) of +39.5 °. Dips were steep, averaging 47 ° ( s = + 17 ° ) and only 8% of particles dipped in the downstream direction.
60
N
Fig. 8. Section approximately 60 cm deep through Cobble deposits at site A. A coarse, structureless basal deposit occupies ca. 40 cm thickness and is overlain by ca. 20 cm of a finer pebble deposit. Imbrication is locally weakly developed. Although large clasts appear to be set in a fine matrix in reality all size grades from cobbles to silts are well represented. Lens cap gives scale. Flow left to right.
(e)
:~-: ~;:/(~...
" tf i.j~
I g
-2
~
T •
,
(f)
(h)
Some imbricated clasts had very steep dips up to 90 ° (Fig. 7b ). Very flat discs in particular were frequently "nested" together in groups of two or three against a large equant obstacle clast to form s t o s s - o r leeside deposits. Stoss-side discs were interpreted to have been implaced violently by high current speeds and pressed against the obstacle. Leeside discs presumably bounced or slid over the obstacle to be emplaced by reverse flows in the small-scale separation zone downstream of the obstacle.
Sedimentology of the cobble deposits Stratigraphy
Fig. 7. Sedimentary fabrics represented as equal area Schmidt nets and dip diagrams. Schmidt nets are upper hemisphere projections of the azimuth and dip of the planes of maximum projection of discoidal clasts. Net divisions are at 10° intervals. Closed symbols represent clasts dipping upstream relative to the main streamline, whilst ()pen symbols represent clasts with the reverse attitude. (a) and (b) represent the boulder berm, (c) and (d) site A, (e) and (f) site B and {g) and (h) site C. Broad-headed arrows indicate direction of valley alignment whilst narrow-headed arrows indicate mean fabric azimuths or dips.
Extending across the bench and beneath the boulder berm is a deposit of variable thickness consisting of a contact "framework" of cobblesized material and a "matrix" of pebble- to siltsize debris including turf and rootlet fragments yielding an overall organic content of 6-7 %. The deposit viewed in section was structureless ( Miall's, 1977 Gm facies ) with much open-void space ( Fig. 8). Some clasts were imbricated but it was not possible to sample for azimuth and dip effectively in pit side-walls owing to the unconsolidated and therefore unstable nature
61
of the deposit. Beneath the berm there was no segregation of grain size of the coarse material with depth. These facts, together with the poor sorting (Table 2 ), are interpreted as indicative of rapid deposition from rapid flow. As locally the deposits lie beneath the boulder berm they must represent primarily deposition on the rising limb of the flood hydrograph. Where the cobble deposits are not overlain by the boulder berm, the loosely packed surface deposits are finer, consisting predominantly of pebbles ( Fig. 9 ). This layer is up to 25 cm thick although 10-15 cm is more usual. The percentage of sand ( < 2 mm) and finer sediment throughout the deposits is typically 11-16%. The surface layer grades imperceptibly down into the basal gravels and being finer is interpreted as representing deposition on the falling limb of the hydrograph. The basal deposits are loosely packed. Consequently a rectangular pit was dug into a natural exposure; the weight of sediment removed and the estimated volume of the pit were used to calculate an approximate porosity. The value, 0.45 is close to that given by Allen (1972) for rapid deposition. A value of 0.47 is often quoted as the maximum possible porosity in primary clastic deposits (Blatt et al., 1972). With such a high porosity it might be expected that the finer fractions will be flushed out by heavy
rainfall and compacted down towards the base of the deposit with time. Granulometric curves based on large bulk samples (British Standards, 1982) are given in Fig. 9. The curves may be interpreted simply as representing a truncated log-normal distribution. At the coarse end the distribution is limited by the lack of particles coarser than - 8 0 in the deposit. Coarser particles presumably were mobilized close to the peak discharge and therefore are only found concentrated in the boulder berm. At the fine end of the distribution, material smaller than 2 ¢ was effectively transported through the reach, probably as a washload sustained by the high velocities and high turbulence levels. Only small amounts were entrapped in the interstices of the rapidly deposited gravel. The distribution reflects the fact that materials of a broad size range were deposited largely contemporaneously. Only at the latter stages of the flood were coarse gravels ( > - 6 ¢) unavailable and so are not represented in the surface layer. The grading curves for the basal flood deposits were compared with the grading curve for a bulk sample of source sediments excavated from naturally eroding bluffs of solifluxion deposits close to the channel, 200-300 m upstream of the berm. The curves were similar in form, indicative of little downstream sorting, the only dif-
TABLE 2 Statistical parameters of grain-size distributions representing the platform deposits (values in m m where appropriate) Parameter
Sample location (A) basal
Mean Stand. dev. Skewness d~,,) d~4 d,~, Percent < 2 m m Percent < 63 p m T r a s k coeff.
111.37 69.05 - 0.18 78 138 180 11.02 0.12 1.53
(A) surface
( B ) basal
(C) basal
33.65 35.54 0.91 17 58 95 15.60 0.30 3.37
51.69 37.73 0.09 33 73 96 9.62 0.15 2.26
75.00 46.33 0.21 58 84 180 10.99 0.09 1.67
62
99'99
-
t
99 ¸
95 90
80 70 ¢ ~.
60 SO' 40
~ 30' ~ 20' 10' 5'
0"01
.
. +4
.
. 3
.
. 2
. 1
0
1
,
,
,
,
,
,
2
3
4
5
6
7-
phi
Fig. 9. Cumulative frequency diagram of representative grain-size distributions. Squares: basal gravels at site A; triangles: surface gravels at site A; dots: source materials from bluffs. Vertical scale is normal probability distribution. ference being a larger p e r c e n t a g e of material finer t h a n 2 O in the source sediments; some 5 - 6 % as opposed to only 3 - 4 % in the flood deposits.
Palaeocurrent analysis As s t a t e d above it was n o t possible to measure the o r i e n t a t i o n of clasts in the basal gravel deposits. T h e o r i e n t a t i o n of surface particles is likely to r e p r e s e n t the falling-stage hydraulic climate (e.g. B y r n e , 1963) a n d c o n s e q u e n t l y m a y not reflect m e c h a n i s m s responsible for the deposition of the bulk of the deposit. N e v e r t h e less cobble i m b r i c a t i o n can be used as a sensitive i n d i c a t o r of local changes in s t r e a m flow direction ( K a u f f m a n a n d Ritter, 1981) and it is unlikely t h a t the gross velocity p a t t e r n in
plan-view c h a n g e d s u b s t a n t i a l l y whilst the gravels were deposited. T h e r e f b r e the dip of the p l a n e of m a x i m u m p r o j e c t i o n was m e a s u r e d for large discoidal cobbles in well-imbricated surface structures. As on the b e r m t h e a-axes t e n d e d to be orient a t e d n o r m a l to t h e valley o r i e n t a t i o n . At site A on the left b a n k u p s t r e a m of the b e r m only 22 well-imbricated s t r u c t u r e s were found. T h e s e , however, if i n t e r p r e t e d correctly, reflect the process of m o m e n t u m t r a n s f e r over the c h a n n e l b a n k ( Seltin, 1964; T o e b e s and Sooky, 1967); the m e a n a z i m u t h of flow being 359 ° ( s = + 59 c ) as opposed to the c h a n n e l alignm e n t of 3305. T h e m e a n particle dip was 30 c ( s = +_ 12 c ) and all clasts dipped up-valley ( Fig. 7d). In c o n t r a s t , at site B on the c h a n n e l - s i d e of the berm, the a z i m u t h of well-imbricated particles was close to the c h a n n e l a l i g n m e n t i.e. 288 ° ( s = + 53 ° ) as opposed to 280 ° a n d the average dip was 13.50 ° ( s - + 1 9 ~') in an u p s t r e a m direction. H o w e v e r , a second group of well-imbricated particles had an a z i m u t h of 62.50 ° (s = _+41 ° ) a n d a m e a n dip down-valley of 18 ° ( s = _+12 °). T h e s e d a t a indicate the p r e s e n c e of reverse flows in the vicinity of the b e r m e i t h e r (1) i n d u c e d by the valley wall configuration before the boulder b e r m was deposited, or (2) induced locally by the p r e s e n c e of the b e r m itself in the l a t t e r stage of the hydrograph. At site C the evidence for reverse flow was very strong. Of the particles m e a s u r e d 59% dipped in an up-valley direction (average dip 14 ~, s = _ + 9 ) a n d h a d an a z i m u t h of 273 c (s - + 4 9 ~ ) whilst the r e m a i n i n g 41% dipped down-valley (16 =, .s = -" l l :} with an inferred m e a n a z i m u t h of 73 : I s - :k 56 ). S o m e of the n o r m a l l y dipping clasts were located in the scoured hollow in the t r o u g h area ( Fig. 5 ). Initially the o c c u r r e n c e of this scour was difficult to explain. P r e s u m a b l y the boulder b e r m developed from the p r o x i m a l end in a d o w n s t r e a m direction and a s t r o n g down-valley c u r r e n t on the leeside of the b e r m would have been precluded. T h e delicate u n s t a b l e p r o x i m a l b e r m
63 structure indicated the absence of a strong current flowing over this area. The scour is interpreted as representing a late stage in berm development. As the hydrograph fell rapidly some 12-14 m 3 of water would have been ponded between the berm and the valley wall. Subsequently the berm failed principally in the area of the scour but also at a minor gap in the berm downstream (Fig. 5B ). In order to summarize the spatial information obtained from the particle orientation data, normalized eigenvalues, gl ~
s
/"/ /./// //
v c
•z~/,/"
II
•,.
y•
•
•
• ~•
~
[] zx
•
o o
•D • ~0
o 0
odu
0
D f
•
o
•
~
~,
~
Fig. 10. Logarithmicratio plot of eigenvalueratios for various types of sedimentary deposits. Dots and solid squares represent debris flow and sediment flows respectively as defined by Nelson (1985) from whose Fig. 3 the data are extracted. Additional symbols represent: big open triangles, the boulder berm; small open triangles, the cobble deposits ~data from the present investigation; open squares, coarse sedimentsin a high-velocitystream;circles, slip-face deposits on experimental gravel dunes from the authors unpublished data. The pecked line represents the girdle-cluster transition at K = 1 (see text).
distributions plot near the origin and have a low value of C, and those distributions with a stronger preferred orientation plot farther from the origin.
TABLE 3 Eigenvalues and associated parameters for the berm and platform deposits (see text for details) Sample
g~
g3
K
C
Berm A B C
0.069 0.125 0.087 0.069
0.749 0.522 0.614 0.538
1.47 0.58 0.38 0.18
2.38 1.95 1.43 2.05
K = ln (g2/g~) In (ga/g2)
C=ln (&/g~)
64
Discussion Berm geometry as a palaeo-flow indicator
Published accounts of boulder berms rarely have included hydraulic interpretation of the berm form other than a consideration of the velocities necessary to entrain the largest boulders present. Given that coarse debris is unlikely to compact significantly through time, the crestlines of berms have been used to indicate the probable maximum water depth (Costa, 1984 ). The evidence for maximum depth in the present investigation (Fig. 4) is based on trashline levels and would tend to support Costa's conclusion. Other aspects of berm geometry have not been considered as potential flow indicators although the orientation of the long axes presumably reflect mean or local flow directions. Sedimentary deposits attributable to lateral flow separation of Newtonian flows have been described on a variety of scales (e.g. Karcz, 1972; Werner and Newton, 1975; Leeder and Bridges, 1975; Ferentinos and Collins, 1980; Allen, 1982, p.183). In a similar manner the identification of berm structures related to flow separation is potentially a useful indicator of Newtonian debris-torrent flow vis-a-vis cohesive debrisflow behaviour. Further detailed attention to berm geometry might therefore prove useful. Allen (1971) amongst others proposed relationships between current speed, obstacle dimensions and the dimensions of the wake deposits in fine-grained sediments. However, with respect to coarse flood deposits, only Krumbein (1942) has suggested that a relationship should exist between the size of an obstacle and the magnitude of the wake deposit. Allen's (1971) investigations are particularly pertinent as the ability to reconstruct velocity is especially crucial to palaeo-discharge analysis. However, it should be noted that velocity cannot be obtained from geometric relationships of' separated flows in the fully turbulent phase. The geometry of the separa-
tion zone and hence the associated sediment: deposit is proportional only to the geometry of' the channel re-entrant. Only fbr laminar flows is the geometry of the separation zone proportional to the velocity (e.g. Thomas et al., 1981 ). Flow-separation geometry therefore may not be useful to estimate velocity in turbulent flow but further investigations are required to evaluate the potential value of berm geometry in palaeoflow analysis. Particle imbrication
Particular imbricate structures may be associated with debris torrents but any diagnostic features need to be clearly distinguished from those associated with normal flood gravels. Rust (1984) investigated a coarse largely ungraded gravel deposit he believed accumulated under "clear-water" flows characterized by high velocities. Particles dipped upstream and the mean dip of the a - b plane was 23.4 °. Although Rust's interpretation is representative of a number of studies of' flood gravel fabrics, particle geometry significantly influences imbrication angles so results may be site specific ( e.g. Pettijohn, 1975). Consequently, to aid in the present interpretation, the a - b dip of cobbles was measured at six sites in a gravel-bedded stream sedimentologically similar to the West Grain. The sediments in question had been deposited by rapid velocities associated with an in-channel discharge of unexceptional magnitude. The mean dip of 180 clasts was 2 2 ( s - _+ 12 ~ ) and there was negligible difference between the six sites. A perusal of the literature of which Rust's {1984) paper is one example, supported by the additional field data, suggest that the mean dip of the platform clasts at site A (i.e. 30 ° ) is typical of a high-velocity depositional environment. The lower dips at sites B and C, (i.e. 13.5-18 ~ ) would indicate either reorientation by waning flows or more likely an environment subject to lower velocities at peak flow. The tat-
65 ter interpretation would accord with the presence of a separated flow structure. Very steep dips have been associated with deposition in macro-turbulent environments (e.g. Hendry, 1976), and Jarrett and Costa (1985) indicate that boulders constituting berms have steep imbrication angles, commonly exceeding 60 ° . The data for the West Grain berm support these observations. The mean dip (47 ° ) is steeper than that observed on the platform deposits and represents deposition at high velocities. The transverse orientation of the a-axes of clasts to the flow (as on the West Grain) is common in high-velocity deposits (Rust, 1984; Jarrett and Costa, 1985) but not universal. Krumbein (1942) observed flood gravels with a-axes parallel to the flow azimuth. Rust (1972) notes that orientation is a function of particle size, sediment sorting and modes of transport and deposition as well as particle shape. Consequently a-axis orientation can be expected to be variable and the a-b dip plane is a more reliable palaeo-flow indicator (Johansson, 1965 ).
Eigenvalues as discriminators of the Newtonian character of depositional events The fabrics of the deposits have weakly developed modes aligned principally with the valley orientation. The berm in particular had a boulder fabric tending to a clustered distribution. The platform deposits, however, had more strongly developed fabrics with girdle distributions. The datp collated by Nelson (1985) representing "debris flows" and "sediment flows" may include some "debris-torrent" deposits, but largely represent weak fabrics scattered across the cluster/girdle transition area (Fig. 10). In contrast, the field and experimental data for rapidly deposited pebbles and cobbles in Newtonian streams have stronger fabrics with girdle tendencies. The few data for the present investigation fall in the intermediate area between the two extremes. Although clearly there are insufficient data for the "debris
torrent" class to draw a definite conclusion, inspection of Fig. 10 suggests a transition or continuum may exist between high-viscosity debris-flow deposits with weak fabrics and clustered distributions (e.g. Mills, 1984) to strongly developed fabrics with girdle tendencies representing "flash-flood" or rapidly deposited fluvial sediments. The intermediate area presumably is represented by: (a) more fluid, low-viscosity debris flows where sub-parallel fabrics may be weakly developed (e.g. Lewis, 1984) ; and (b) debris-torrent deposits. The sedimentary fabric of the latter category is poorly defined at present and requires further study. Taking all the available data (Fig. 10) the transition or continuum may be represented by a relatively invariant gffg2 ratio typically less than 1 and a highly variable s2/sl ratio. Conclusions The boulder berm developed under peak flow conditions during a debris-torrent event. The locale for deposition was the shear-flow zone in an area of separated flow downstream of a sudden change in both valley alignment and channel cross-section. The geometry and sedimentology of the berm, and the sedimentary fabric of associated flood deposits, can be interpreted consistently with the presence of a flow separation bubble in the valley re-entrant. Both sediment packing and fabric orientation indicate rapid deposition from a high velocity low-viscosity flood-flow heavily charged with coarse debris. Formed within the re-entrant in the valley wall alignment, the feature has some broad similarities to flow-separation deposits formed at a variety of scales downstream of obstacles. Consequently the geometry of berms and associated hydraulic patterns might usefully be explored further. Although the reconstruction of the "palaeo-velocities" from berm geometry would not seem possible where flows were within the fully turbulent phase, the water depth and azimuth of flows may be reconstructed.
66
Eigenvalues summarizing the strength and pattern of the fabric of the debris-torrent deposits indicate a transitional phase between fabrics associated with debris flows and water floods, respectively. Further investigations of fabrics and particle-size distributions are required, but eigenvalues in conjunction with other independent evidence, may be useful in classifying the deposits associated with heavily sediment-laden flows.
Acknowledgements Mr. M. Glaister and Ms. C. Williams assisted in field work and Mr. M. Glaister drafted the figures. Prof. J.R.L. Allen and two anonymous referees read an earlier version of the manuscript and suggested a number of improvements.
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67 Rubicon River, California - hydrology, hydraulics, and boulder transport. U.S. Geol. Surv., Prof. Pap., 422-M: 40 pp. Sellin, R.H.J., 1964. A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche, 7: 793-801. Shroba, R.R., Schmidt, P.W., Crosby, E.J. and Hansen, W.R., 1976. Storm and flood of July 31-August 1, 1976, in the Big Thompson River and Cache la Poudre River basins, Larimer and Weld Counties, Colorado, part B geologic and geomorphic effects in the Big Thompson Canyon area, Larimer County. U.S. Geol. Surv., Prof. Pap., 1115: 87-152. Statham, I., 1974. The relationship of porosity and angle of repose to mixture proportions in assemblages of different size materials. Sedimentology, 21: 149-162. Stek, J.B. and Brandt, H., 1976. Aerodynamic throttling of a two-dimensional flow by a thick jet. Aeronaut. Q., 27: 229-242. Stevens, M.A., Chen, J.H. and Simons, D., 1976. Riverbank recessions for power plant facilities. A.S.C.E. Waterways, Harb. Coastal Eng. Div. 2nd Annu. Symp., Modelling Techniques, 1: 560-574.
Stewart, J.H. and La Marche, V.C., 1967. Erosion and deposition produced by the flood of December 1964 on Coffee Creek, Trinity County, California. U.S. Geol. Surv., Prof. Pap., 422-K. Stolzenbach, K.D. and Harleman, D.R.F., 1971. An analytical and experimental investigation of surface discharges of heated water. M.I.T., Ralph M. Parsons Lab., Water Resources and Hydrodynamics, Dep. Civ. Eng. Rep. 135:212 pp. Thomas, C.E., Morgan, K. and Taylor, C., 1981. A finite element analysis of flow over a backward facing step. Comput. Fluids, 9: 265-278. Toebes, G.H. and Sooky, A.A., 1967. Hydraulics of meandering rivers with flood plains. J. Waterways Harb. Div. A.S.C.E., 93: 213-236. Werner, F. and Newton, R.S., 1975. The pattern of largescale bed forms in the Langeland Belt (Baltic Sea ). Mar. Geol., 19: 29-59. Woodcock, N.H., 1977. Specification of fabric shapes using an eigenvalue method. Geol. Soc. Am. Bull., 88: 1231-1236. Wright, L.D., 1977. Sediment transport and deposition at river mouths: A synthesis. Geol. Soc. Am. Bull., 88: 857-868.