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Sedimentology (1980) 27 3 1-46

A physical model for the transport and sorting of fine-grained sediment by turbiditycurrents

D O R R I K A V. S T O W * A N T H O N YJ. B O W E N

Departments o f Geology and Oce anography, Dalhousie University, Ha lifa x,N . S . , Canada

ABSTRACT

Turbidite muds i n cores from the outer Scotian continental margin,off eastern Canada, contain

abundant thin silt laminae. Graded laminated units are recognized in parts of this sequence. Theserepresent single depositional events, and show a regular decrease in modal grain size and thickness ofthe silt laminae through the unit. A similar fining trend is shown by both silt and mud layers overhundreds of kilometres downslope. Textural analysis of individual laminae allows the construction ofa dynamically consistent physical model for transport and sorting in muddy turbidity currents.Hydraulic sorting aggregates finer material to the to p a nd tail regions of a large turbidity flow whichthen overspills its channel banks. Downslope lateral sorting occurs with preferential deposition ofcoarser silt grains and larger mud flocs. Depositional sorting by increased shear in the boundarylayer separates clay flocs from silt grains and results in a regular mud/silt lamination. Estimates canbe made of the physical parameters of the turbidity flows involved. They are a minimum of severalhundreds of metres thick, have low concentrations (of the order of or2500 mg 1 - l , and movedownslope a t velocities of10-20 cm s-I. A 5 mm thick, coarse silt lamina takes abou t10 h to deposit,and the subsequent mud layer ‘blankets’ very rapidly over this.A complete unit is deposited in2-6days which is the time it takes for the turbidity flow to pass a particular point. These thick, dilute,low-velocity flows are significantly different from the ‘classical’ turbidity current. However, there ismounting evidence in support of the new concept from laboratory observations and direct fieldmeasurements.

I N T R O D U C T I O N

Fine-grained sediments (clays and s i l ts) make upmuch of the fill of ocean bas ins and the moderncover of coastal and shelf environments . However,less at tent io n has been paid to the process of t rans-por t an d depos i tion of th i s mate r ia l tha n t o thevolurnetr ical ly less important sands and gravels(McC ave, 1 972; Piper, 1978).A vsriety of mechan-

isms has been proposed for the t ransport of f inesediment into deep water. They include, the set t lingof pelagic, hemipelagic and ice rafted material(Davies Laug hton, 1972); deposi t ion from

* Present address: British NationalOil Corporation,150 St Vincent Street, Glasgow, Scotland

0037-0746/80/0200-0031 $02.00980 International Association of Sedimentologists

iiepheloid layers (Ewing& Thorndike , 1965; Ewinget a / . , 1971); deposi t ion froni bot tom currents(Heeze n, Hollister Ru ddi ma n, 1966; Hollister,1967); and deposition from large-scale turbiditycirrrents (Hesse, 1975; Piper, 1978). Various low-velocity, low-densityflows have also been proposed(Gors l ine , Drake & Barnes, 1968; Moore, 1969;

McCave, 1972; Sheparde t a / . , 1977).Textural analyses of late Wisconsinmuds a n d

si l ts on the outer cont inental marginoff N o v aScotia reveal pronoun ced do wnslo pe t rends in grainsize parameters (Stow, 1976, 1977). These sedi-ments have been shownto be mostly turbidites(Stow, 1979) and probably result from relativelyslow, widespread ‘sheet’ flows caused by largeturbidity c urre nts overtopping their chann el levees.

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32 D . A . V. Stow and A . J . Bowen

A physical model is developed in this paper to explainthe observed sorting, to derive general estimates ofthe flow parameters (Fig. l ) , and to attempt anexplanation of the siIt/rnud lamination.

p+ CURRENT DENSITYU CURRENT VELOCITYh CURRENT THICKNESSN SEDIMENT CONCENTRATlONp(D) GRA IN SIZE DISTRIBUTIONw EFFECTIVE SETTLING VELOCITY0’ SLOPEx DISTANCE DOWNCURRENT

HEIGHTABOVE BED

L

Fig. 1 Development of a fine-grained turbidity current

from a slump, and definition of current parameters.

O B S E R VAT I O N

The late Quaternary geology of the deep watermargin off Nova Scotia (Fig. 2) has been discussedby Piper (1975) and Stow (1975, 1977, 1979).During periods of lowered sea-level much of thewide continental shelf was exposed. A floating iceshelf probably existed in the Laurentian Channel andlarge amounts of sediment were supplied to theupper slope. Slumping of this material resulted in itsdownslope transport via turbidity currents. Coarsesands and gravels were deposited i n deeply incisedchannels while the fine-grained sediment built upthick inter-channel deposits over the Laurentian Fanand adjacent slope and rise. Smaller turbiditycurrentswere also initiated in the heads of submarinecanyons along the shelf-break shore edge. Reworkingof more slowly deposited hemipelagic sediments bythe contour following Western Boundary Under-current was only significant during interstadialperiods and the Holocene.

More than fifty cores and many hundreds of silt,

sand and mud layers have been examined for thepresent study using visual descriptive and X-radiographic techniques. Over 200 size analyses havebeen carried out using the pipette and sieve method(Laughton, Berggren et a/., 1972), and a model TCoulter Counter (Sheldon Parsons, 1967).

The silt laminae vary in thickness between t0.5and 10 mm. Th e thicker ones commonly have sharpbases and sharp or gradational tops; the thinner

ones are less clearly defined. They occur either asdistinct graded laminated units (Piper, 1972)between 1 and 10 cm thick (Fig. 3), or as con-tinuous silt laminated sequences. Size analyses ofgrouped silt laminae are shown in Fig. 4. There maybe several prominent silt laminae showing a slight

decrease in modal size through the unit; or onedistinct, coarser basal lamina overlain by numerousthinner, finer laminae (Fig. 4). The intercalatedmuds are less clearly graded. Total size analysisthrough a single unit (either by proportional sum-mation of separat e analyses or by channel sampling)reveals an even distribution spanning a wide rangeof grain sizes (Fig. 4). Mineralogical and structuralevidence suggests that these graded laminated unitswere deposited as single sedimentation events(Stow, 1977).

A similar fining trend is apparent from size

analyses of the more prominent (basal) laminae fromslope through rise to abyssal plain environments overa distance greater than 1000 km (Fig. 5a). The de-crease in modal size with distance downslope is stillmore pronounced in the interlaminated muds (Fig.5b). A plot of standard deviation versus mean sizeemphasizes the trend in sorting of the fine siltlaminae (Fig. 6). Mean size generally decreasesdownslope and away from channel axes. The finer,more ‘distal’ laminae are less well sorted. This is incontrast to Piper’s (1978) model which suggests aslow process of segregation of silt from clay flocsduring turbidity current transport and, hence,improved sorting in the direction of transport.

S E D I M E N T AT I O N

Clayey sediment flocculates readily in sea water.The most important factors controlling this floc-culation are th e concentration of particles within thesuspending fluid (Migniot, 1971) and the turbulenceintensity (Krone, 1959, 1962; Einstein & Krone,1961; Partheniades, 1965). Over a period of time,continued flocculation results in progressively larger

clay-water aggregates with greater settling velocitiesand lower densities and shear strengths (Krone,1963; Moon, 1972). According to Partheniades(1965) these floc aggregates will reach a maximumequilibrium diameter related to the turbulenceintensity. Kranck (1973) believes that the stablefloc size distributions obtained in sea water aredetermined primarily by the initial size of the indi-vidual grains. The Roc mode is always larger than

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Transpo rt and sorting in fine-grained t urbid ity currents 33

( b )

DIRECT TURBIDITY FLOWS FROM GLACIERSTURBIDITY CURRENTS AND FL OATING ICE SHEL F IN LAURENTIAN CHANNEL.SLUMPS AND FROM CANYONSHEADING IN BEACH ZONE

RARE SLUMPING AND[ TURBIDITY CURRENTS

EASED INFLUENCEOFTERN BOUNDARY

Fig. 2. Summary of sedimentation on Nova Scotian outer continental margin during glacial and non-glacial periods(a) Glaciated margin, Wisconsin; (b) non-glaciated margin, Holocene.

the original grain mode, and the floc settling velocity

is probably of the same order as that for the largestindividual grains present in a suspension (White-house, Jeffrey Debbrecht, 1960; Partheniades,Cross Ayora, 1969; Kranck, 1973).

Deposition of fine-grained sediment occurs whenflocs form strong enough bonds to resist the flow-induced, disruptive shear stress near the bed(Partheniades et a/. 1969). There appears to be acritical velocity above which fine sediment does not

deposit. Values ranging from I5 to 25 cm s-' havebeen given by Einstein & Krone (1962), Krone(1962), Partheniades (1965) and Partheniades et al .(1969). Other work on the deposition of fine sedi-ment is summarized by Partheniades 1 964), Odd &Owen (1972), Krone (1972, 1976), Buller, Green &McManus (1975) and McCave (1970, 1972, 1976).According to these authors, the most importantfactors controlling deposition are: flow turbulence,bed shear stress, and the concentration and settling

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34 D . A . V . S t o w and A . J . BOMWI

Fig. 3. X-radiograph positives of laminated mud facies in Scotian margin cores. Typical, graded laminated units areindicated by the arrow s in4 and C . n D and E these units are less clearly recognized. The widthof the core sectionsis about 4 cm.

veloci ty of the sediment . More minor controls arethe sediment propert ies and composi t ion (s i l t andclay behave very differently), water chemistry, and

the na ture of the d eposi t ional surface.Furthe r informationon th e behaviour of fine sedi-

ment may be derived from studies of erosion(Partheniades & Paaswell, 1968; Migniot, 1968;Einsele et al., 1974; You ng Sou tha rd, 1978).The most important factors affect ing the cr i t icalerosion s tress for mud dy sediments ar e the sedimentnature (clay type, bulk density, consolidation, etc.),the bo t tom topography and the bed shear s t ress .

W h i t e (1970) investigated the plane bed thresholdsof f ine-grained, non-cohesive sediments . H e fou ndthat the absolute value of s t ress for erosion de-

creases slowly as the size decreases below200 p.m(see also dataof Miller, McC ave& Ko ma r, 1977).

CALCULATJONS

Rate of deposition

Although the bulk propert ies ofa turbidity currentmay be descr ibed by an overa l l concent ra t ion N a n d

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Transport and sorting in fine-grained turbidity currents

WHOLE UNITI II

104 MUDS II I I0

GRADEDLAMINATEDUNIT

75 009 118360-368

D ( tical) 1D,(rnode)

Dmax

Fig. 4. Smoothed, weight , grain-size curves fromanalyses of individualsilt layers, mud layers and thewhole graded laminated unit shown as a schematic coresection on the right. The numbers beneath the coresection are the core code and section depth in cm. Thecritical grain diameter( D c ) ,silt mode D,) and maximumsilt size Dmax)are shown. See textfor further discussion.

IDownslope*

Gra in S i z e ( u r n )Fig. 5. Downslope textural trends in silts(A) and muds(B) from Scotian margin cores. The distance betweensample s is of the orde r of100 km.

35

3 0 :n ; ; d ;MEAN SIZE (0)

Fig. 6. Standard deviation versus mean size for Scotianmargin and Sohm Abyssal Plain thin sands and silts.The mean sizealso decreases with distance offshoresothat sorting becomes poorer (ie. standard deviationincreases) downslope.

a typical settling velocityw s Fig. l ) , any detai ledcalculat ion requires fur ther insight into the dis t r ibu-t ion of par t ic le s ize and composi t ion.

McC ave Swift (1976) have suggested tha t thera te of deposition , of sedimen t of settling velocityw , s given by an eq uat ion of the form ,

where C is the concentrat ion of the sediment ofsettling velocity, w and density, ps, in the Row jus tabove the v i scous sub layer o f the b o t tom boundarylayer (note tha tN , above, is th e concentrat ionof allgrain sizes in theentire f low); and P i s the probabil i tyt h a t a given particle will be deposited. Da ta fro mexperiments with fine, non-cohesive silt (White,1970), lead to the suggestion that P i s given by

where 7 is the local bot tom stress ,T,(w) a criticalvalue for the deposi t ion of sediment of settlingvelocity w , a n d p' is a fac tor to account fo r o therinfluences o n the probab ilityof deposi t ion. McCave& Swift (1976) givea plot of r a s a funct ion of w ,based largely o n th e da ta of W hite (1970). This isgenerally in line with experiments on the deposition

of cohesive ma terial, discussed earlier.Fo r muds , thereis n o simple relation ship between

the grain s ize obtained by analysis of the deposi t ,an d t he d ynam ic behaviour of f locculated part iclesin suspension. The relationship between grain-sizedistribution and particle-size distribution has beendiscussed by Kranck (1973, 1975).

Jn t h e case of silts behav ingas indi vidu al particles,the settling velocityw is a well defined function of the

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36 D . A . V. Stow and A . J . B o w m

grain diameter and density. Equations 1 and 2 canbe rewritten as

R ( D ) = p s C ( D ) w ( D )p’ 1 )I (3)for grain diameter D. Any layer deposited in timeT owill be made up of contri butions from the varioussediment sizes (of differing settling velocities) insuspension. If a layer of thickness q is identified in acore, sediment analysis provides both the bulkdensity (volume concentration) of the depositedsediment N s and the proportion of each size com-ponent, the grain-size distribution p s ( D ) .

This was deposited over some unknown period oftime To, where, for any particular size

and fo r the whole layer

From Equations 3 and 4, since C p , ( D ) = l

where

and C ( D )can be re-expressed as Pb(D)Nb where Nbis the total sediment concentration and p b ( D ) thegrain-size distribution in the flow just above theviscous sublayer.

Inferences from silt and mud laminae

There are three unknown quantities in Equation6 : Q , T and C. p s . w and T~ are known or measuredfunctions of grain size provided the sediment

behaves dynamically as individual grains. Of theunknowns, C ( D ) is a function of grain size, repre-senting the distribution of grain sizes in the flowjust above the viscous sublayer, T is a property ofthe flow independent of grain size, Q is a collectionof parameters of which q and Ns can be measured,To is unknown, and p’ might be a function of grainsize. Clearly the values of T, To and p’ are of greatinterest. Can they be estimated?

An important consequence of Equations 3 and 6is that there should be no material deposited of grainsize less than some critical diameter, D,, given by

Inspection of the size distribution of the silty layersin Scotian margin sediments shows a small quantityof very fine material, but a distinct change i n trendat some intermediate grain size (Fig. 4). This pro-vides a first, crude estimate of D, and hence, usingMcCave Swift (1976), of the actual stress, T at thetime of deposition. Implicit in the above assumptionsis that there ar e finer particles in the flow not beingdeposited because T is to o large.

Figure 4 represents typical size analyses of siltlaminae and superjacent mud layers. Inspection ofthe size distribution of the superjacent mud layers

shows that the coarse tail begins to fall off at thesame size interval that the silt curve changes to amarked upward trend. This point, therefore, alsoprovides a crude estimate of 7 . The curve decreasesto zero at a grain size close to that of the modal silt(Fig. 4). This close match between silt and super-jacent mud is, clearly, strong evidence that they weredeposited almost simultaneously from the same flow.The flow is one in which grains are behaving asindividual silt particles during the depositionalphase. Proportional summation of these analyses,or measurement of a continuous sample throughthe couplet, shows a fairly even distribution of grainsizes for the ‘silt+ mud couplet’, in the size rangesbelow the median silt size.

The size distribution of the couplet provides anestimate of the size distribution of the suspensionfrom which first the silt and then the mud aredeposited (Stow Bowen, 1978). C ( D ) may beapproximately constant for the sizes between

and D , or less (Fig. 4). This can be checkedby using Equation 6 for the distribution of the siltlayer, grain size by grain size. For any particularsize Do,

giving a line on a plot of Q / C vs T (Fig. 7) for eachgrain size. As can be seen in Fig. 7, the data for anumber of grain sizes lead to a set of equations thatare all satisfied by a particular value of T and Q/C,given by the point of intersection of the lines. Thisprovides an estimate of actual bottom stress at the

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Transport and sorting in jine-grained turbidity currents 37

1

SAMPLE73 031 12

84C

0 0.4 08

Fig. 7. Estimate ofcritical shear stressT~) rom the m odalsize distribution of a particular silt lamina. UsingEquation 4 Q/C is plotted against7 for each grain sizeinterval D ) ; the confluence of lines giveT~ and A (aparticular valueof Q / C ) .

T dynes)

t ime of deposition.Of course, this gives roughly thesam e resul tas look ing forT~ n either the s i lt o r m udsize distrib ution s. Equ ally significantly, it sugg estsQ/C is not a function of grain size (if i t were thelines in Fig. 7 would no t converge toa single point).

The s imples t assumpt ion f rom the ev idence of thesi l t deposi t ion and the knowledge of the propert ieso f t h e s i l t f m u d c ou pl etis that neither C ( D ) n o r p'are s t rong funct ions of grain s ize.An even distri-but ion of grain s izes in the b ound ary layer (Fig. 8)is m a d e u p o fa coarse si lt m ode an da fine mu d tail .The coarse s i l t set t les into the boundary layer asindividual grains , while the mud probably set t les

233DzYPJEJG

Drnode Rocs) > mode (silt)

an d the effective floc settling velocity is of th e sam eorder as tha t of the silt . The finest silt and thesmaller flocs are left behind in the turb idity curren t.

Model for depositional sorting

Within a fine-grained turbidity current there will be

clay flocs and silt grains having equivalent settlingvelocities, so that th e expected deposi t f roma waningcur ren t would bea graded, s i l ty-mud. I n m ost cases ,however, th e depositional un it is distinctly laminate das well as graded. Such s i l t - laminated muds areavery common deep mar ine fac ies and occur re -peatedly in the geological record.A variety ofmechanisms has been proposed for their origin.These include: current pulsat ions (Lombard, 1963;Sanders , 1960, 1965; Lambert , Kel ts& Marshal l ,1976); mult iple events (Kingma, 1958; Wood&Smith, 1959; Moore, 1969); congregat ional sor t ing(Kuenen, 1966; Piper, 1972) migration of bedform s (Jopling, 1964, 1966, 1967); an d rewo rking bybo tto m cur ren ts (Hollister, 1967).A more comple tereview is given in Stow (1977). The separation ofmud and s il t layers in outer S cot ian marg in sedi-ments is believed to be primarily d ueto deposi t ional

sor t ing in the boundary ,l ayer a t the base o faturbidity current (Fig. 8).

The sediment concentrat ion gradients within theturbidi ty c urrent ar e maintained by turbulent mixing,such tha t the sed iment concent ra t ion fora particularsize fraction p N , in the flow is less than that justabove the boundary layerPo ; the ra t iopo/p beinglargest for large diameter particles (Hjulstrom,1939). How ever, f or sm all particlesw- c m s-')McCave (1970) has shown that the downward

$

c

G R A N SIZE

Fig. 8. Model for shear sorting in the boundary layer of aturbidity current. Depth measured from sea floor in amillimetre logarithmic scale. The boxes on the right showthe probable grain-size distributions at different levelswithin the boundary layer and the measured grain-sizedistribution of the sediment.

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38 D. . V. S t o w and A . J . Bowen

increase in concentration is small for reasonablemixing values. A s a first approximation then, wemay take,

for either clay flocs (diameter, Of) or silt grains(diameter, D . As the particles fall towards the bedthe increased shear in the boundary layer causes theclay floes to break up (Krone, 1962; Partheniadeset a[., 1969). Initially Nb remains constant, whilethe size distribution p o changes due t o deflocculationto a new distribution Pb more nearly representingthe distribution of solid particles (Fig. 8).

Po(Df, D)+Pb(D)

The silt grains settle through the viscous sublayerto form a silt lamina (Fig. 9a and b). As more sedi-ment is supplied to the top of the bounda ry layer themud concentration builds up, and some refloccula-tion may occur (Fig. 9c). At some critical concen-tration the clays are able to form sufficiently largeaggregates that they overcome shear, break-up

Fig. 9. Schematic representation of the stages of silt andmud deposition through the boundary layer of a t u r-bidity current to f o r m silt and mud laminae,

and deposit rapidly through the laminar sublayeras a mud 'blanket' over the coarser silt lamina(Fig. 9d). The cycle of silt and mud deposition isthen repeated for successively finer grain sizes.

While separation of mud and silt in this way doesappear to be a necessary corollary of bounda ry layer

shear, it is not clear why the mud deposits so rapidly.Temporary disturbance of the boundary layerstructu re (by velocity fluctuations, etc.), or the partialdevelopment of a cohesive bed surface as the largestflocs manage to settle through the sublayer, arepossible explanations. The increased mud concen-tration may affect these processes (EinsteinKronp, 1962) or may be sufficient alone to cause mudblanketing. Experimental work with mud slurriesdoes suggest that they deposit more rapidly withincreasing concentration (Migniot, 1968). The factthat the mud does deposit very rapidly is indicated

by the absence of coarse silt particles from the mudlayer.This model suggests that coarse silt layers should

generally be thicker than the subsequent fine siltlayers. As the coarser silts have a higher settlingvelocity, proportionately more coarse silt should bedeposited before the concentration of mud in theviscous sublayer becomes 'critical'. At lower settlingvelocities the silt layers should become finer andthinner, and there will be a higher proportion ofmud relative to silt. Apart from the effects arisingfrom the general slowing of the current, the mudlayers should be of rather constan t thickness.

The graded, Iaminated units clearly show theexpected trends (Fig. 4 . There is even a generalcorrelation between layer thickness and modal siltsize for all cores (Fig. 10). However, the modal sizeis also roughly correlated with the current velocity(Table l ), which could also be a factor in determininglayer thickness.

General eyuations for a turbidity current

In order to test the validity of the deposition model,and also to infer total flow characteristics, we can

look at the dynamic constraints o n the turbiditycurrent itself.The stability of the upper surface of a turbidity

current has been discussed by Ippen Harleman(1952) and Harleman (1961) who define the densi-metric Froud e Number,

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40

LL

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ue

D. . V. Stow and A . J . Boweiz

.0 8

..

loo,

8

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. 0:..I . .0 40 80 120

Fig. 10. Coarse layer thickness versus modal grain size forScotian margin sands and silts. The trend of increasinglayer thickness with increasing grain size is predicted bythe proposed model for depositional sorting.

MODAL GRAIN SIZE urn)

where p t is the mean density of the current, p is thefluid density, h is the depth of the current, and U themean velocity.

Bagnold (1962) has shown that the equation forhe flow of a turbidity current can be expressed as,

( p t ) sh ( U sin p - D cos p = U (10)

where p is the bottom slope. The effective settlingvelocity I? of the suspension is given by

where p is the proportion of the grain-size distribu-tion in suspension with settling velocity w (Bagnold,1956).

Equation 10 reduces to the Chezy equation fre-quently used to describe turbidity currents (Komar,1971, 1973), if w < U tan p. The bottom stress canbe expressed as,

where cf is a dimensionless drag coefficient, and U ,

is the friction velocity. Values of cf can be estimatedfrom McCave (1970) or Daily Harleman (1966)following Komar (1970). Typical values are in therange 2 x to 3 x not a significant variationin terms of the present study. Combining Equations9, 10 and 12 the Frou de Number can be expressed as,

Fo r reasonable values of cf, the values of p, given inTable 1, show that in many cases Fv is considerablygreater than unity unless s a substantial fractionof U tan p. To look at the dynamics of these fine-grained turbidity currents we may therefore need touse Equation 10 in its full form. Th e Chezy equation ,

which would suggest strongly supercritical flows,is probably inadequate.

We can estimate a number of the variables inEquatio n 10 (Table 1). From E quation 7 we have anestimate of T, and using Equation 12 this can beinterpreted as the flow velocity, U . The slope p isknown approximately. The mean density of theflow pt, can be expressed in terms of the totalsediment concentration, N

P t - F P s - P Ps- Ph=- NghN- N g h as p t r P (14)

P t P t F

where N and h remain to be determined. There aresome, very broad , constraints o n the values that canbe assumed for these variables. Bagnold (1962) hassuggested that for the flow to be fully turbulent,the Reynolds Number,

U hRe=->3000

L

where p is the kinematic viscosity, Bagnold (1954)

has also suggested that grain/grain interactionbecomes dominant when,

The size ranges under discussion do not generallymove as bedload. For suspended loads one expectsthe concentration to be relatively low, and todecrease as the current evolves downslope depositingthe coarser silt and leaving the finer materialbehind.

Sedime nt dispersal and current thickne ss

McCave & Swift (1976) extended their idea of localdeposition, leading to Equation 1 to considerthe large scale dispersal pattern due to materialbeing transported away from a source, where theconcentration is C nder uniform flow conditions.Then, following Einstein (1968), the concentrationat a distance x downstream is,

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Transport and sorting in fine-grained turb idity currents 41

C - C o exp [ w 1 - p’ ] (17)As the coarser material is deposited most rapidly,

the concentration distribution becomes more andmore weighted towards the finer material withdistance downstream. Now, combining Equations1 and 17 the deposition rate R , , becomes

R ~f(D) exp [-Xf(D)] (19)

PSCOP’

where

and

is a known function of D for the silts. By differentiat-ing Equation 19 it can easily be shown that thefunction, f(D) exp [ Xf(D)], has a maximum valueof X-le-l at Xf(D,)=l, where D , is the modal

diameter of the deposited silt. Using this solutionwe have,

x is the distance from the source, in this case theshelf break. Knowing x and using values of T ~ ,and U derived from D , of a particular silt lamina,we can solve Equation 20 for h . Estimates of currentthickness derived in this way are given in Table 1.

They range from 580 to 1700 m (with three excep-tions) assuming a value of p’ =l . This gives a maxi-mum thickness as p‘ cannot be greater than 1 and,presumably, may be significantly less than 1 forfiner silt and mud which has more chance of escapingfrom the upper boundary layer. McCave & Swift(1976) use values of p ’ from 0.4 and 1.0. Using avalue of p’=O3 we have thicknesses of 300-850 m.

These estimates of current thickness are of a

comparable order of magnitude to the channeldepths on the main fan, which range from 200 to800 m ; they are somewhat greater than those in theliterature to date, Menard (1964) suggested thatabyssal plain flows are a few tens of metres thick.However, Griggs & Kulm (1970) found evidence for

Holocene turbidity currents in the Cascadia channelof about 120 m in thickness, and Komar (1977)points out that many deep sea fan channels withlevees are up to 300 m deep.

The larger flows on the Laurentian Fan may becapable of topping the seamounts to the southwestof the Gra nd Banks, which Alam Piper (1977)believed were o u t of reach of turbidity currents.The seamounts rise about 1000 m above the sur-rounding ocean floor and are covered, for the mostpart, by a slowly deposited, biogenic-rich, hemi-pelagic mud. However, there are certain intervals of

fine, silt-laminated muds within the cores, whichAlam & Piper supposed resulted from storm re-suspension of material at the shelf break andtransport along a density interface within the watercolumn. They may in fact have been deposited fromthe upper part of thick, dilute turbidity currents,in which case they should be very fine grained,thinly laminated silty muds, perhaps equivalent to amore ‘distal’ (Sohm Abyssal Plain) turbiditesequence.

Time scales and current length

Fro m Equa tion 8 we have,

where Q / C is a constant for any particular siltlamina estimated from the grain-size distribution(Fig. 7). Now, C = p b N b where P b is roughly constant(Fig. 4) and Q is defined by

Thus the time To, or the deposition of any particularlayer is,

We have data on N , from porosity and water contentmeasurements: it generally varies between 0.65 and

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42 D. A . V . S t o w and A . J . Bowett

0.75. As discussed previously, p probably liesbetween 0.4 and 1.0. Values of Q/C deduced f romEquat ion 4 range f rom0.1 for fine silts to 1.0 f o rcoa rse silts. These, together w ith lamina e thicknesses,q , are shown in Table1.

The least known quant i ty in Equat ion 22is Nb,

the concentrat ion of the turbidi ty current . Bagnold( 1962) suggests that the sediment concentrat ionmust be less than 0.09. Komar (1977) estimates therange of densi t ies for turbidi ty curren ts a t between1.05 a n d 1.3 g ~ m - ~ ,hich give concentrationsspanning Bagnold's limit) however, these arefor sandy, turbidi ty currents . Ran do m measurementsof suspended sediment concentrat ions in thenepheloid layer near the deep sea bed show valuesseveral orders of magnitudeless than these values(0.01-0.54 mgI - l , McC ave Swift, 1976, table 4).

A different estimate ofNb can be made by con-

sidering the volumes of s lumps which m ay generateturb id ity cur ren ts. We have , a t a ny po in tx s l u m pvolume mater ial a l ready redeposi ted= to ta lvolume of curren t .

where Vs i s the s lump volume andL , Wa n d h are thelength, width a nd thickness of the turbidi ty curren t .Various est imates of s lump volumes are given inTable 2 (after Morgenstern, 1967); Komar (1969)suggests that the s lump volumes for the largerPleistocene turbidity currents in Monterey channelwere of the o rder o f 108 109 3.

A current thickness oflo3 m , a width of 25 km(channel plus half levee widths) might be reasona bleest imates . The length of the current is of the orderof the mean velocity times the deposition tim eTo.

Table 2. Volume of submarine slumps(after M orgenstern,1967)

~~

Location Volunie(m3)

Magdalena River DeltaMississippi R er Delta 4~ 107

Valdez, Alaska 7.5 x 107Folla Fjord 3 x lo5Orkdals Fjord 10'Sagami Wan 7 x 10'Gran d Banks Slope 10

3 x 10s

Suva, Fiji 1.5 x 10'

L=UTo

The n, following Kom ar (1969)

However, Equat ion 19 also providesa relationshipbetween N b a n d To suggesting

then

Th e present discussion ha s concentrated on thedeposition of only fine-grained material, fo r , thisacont r ibu t ion of the o rder o f 108 m 3 seems of ther ight order. Althougha value of N b T o has beenobtain ed this might represent deposi t ion from fairlyconcentrated f low fora relat ively short t ime o r froma dilute suspension fora muc h longer t ime. Equa t ion22 has therefore been solved forTo fo r a range ofconcent ra t ions f rom to (250-25,000 mg1-l). Th e t imes taken for the deposi t ion of individualsilt laminae are given in T abl e1. F o r Nh=IO-3(2500 mg I- l) , m m of coarse s il to r 1 m m of f inesi lt wil l be deposi ted in a bou t10 h .

Now, while the silt is deposi t ing the mud con-centrat ion bui lds upto some cr i t ical value in theboun dary layer, and then deposi ts very rapidly. I t istherefore suggested tha t the silt deposition essentiallydetermines the t ime scale for the who le uni t , which isthen given by integration of the depositional timesof al l s il t laminae throu gha single uni t . Fo r0.5 c mcoars e si lt a nd0.5 cm fine silt (with perhaps 1-2 cmmud) we havea total deposit ion t ime of ab out 2.25days. A thicker uni t , say 2 cm si l t and 4 cm mud,would take4-6 days t o depos i t ; o r, fo r concentra -tions of t o (250-25,000 mg 1-l) fro mafew hours to 1 or 2 months . I t appears tha t con-

centra t ions of the order of (2500 mgI - I ) givethe mo st reasonable est imatesof depositional times.

A single silt lamina would take several yearstodeposi t f rom a f low wi th the concent ra t ion com-monly reported from deep sea nepheloid layers( M c C a v e& Swift, 1976; Pierce, 197 6; Drak e, 1976).The resul t ing deposi t would be an homogeneoussilty mud, without evidence of relatively rapiddeposi t ion and without dis tinct s il t /mud lamina t ion.

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Transport and sorting in fine-grained turbidity currents 43

Current velocity and grain sizeSeveral other points are evident from the datapresented in Table 1 The current velocities deducedfrom deposition of the silt layers (coarse and fine)lie in a very close range of between 9 and 16 cm s-*.This agrees well with the previous estimates ofcritical depositional velocities for fine-grainedmaterial (Einstein & Krone, 1962; Partheniades,1964, 1965) and emphasizes the fact that clay willdeposit rapidly from flowing water when it is suf-ficiently concentrated and flocculated.

From the discussion of Equation I 3 it is clear thatthe characteristic settling velocity of the flow, $,given by Equation 11 must be of the order of Utan @. cannot readily be estimated from the grain-size as it depends critically on the size distribution ofthe flocculated silt/mud suspension in the body ofthe turbidity current. However, the previous dis-

cussion has emphasized the possible relationshipbetween grain and floc sizes suggested by variousauthors (particularly Kranck, 1973, 1975), as shownin Fig. 8. It was suggested that w D f ) for the mud isof the same order as w(Dm) for the silt. The datain Table 1 and the relationship between @ andU tan (Fig. 11) reinforce this concept. The three

1

\V (Dmode) (Cm/S)

Fig. 11 U tan versus w (mode), the characteristicsettling velocity of the flow. The relationship shows theapproximate equivalence of the two parameters assuggested in the discussion of Equation 10. The anomal-ously high and low values probably represent, respectively,samples from a muddy slump mass and a sandy suprafanchannel.

anomalous points in Fig. 11 may be explained invarious ways. One is from the upper slope and mayrepresent part of a slump mass rather than a turbiditycurrent deposit; another is from the distal end of theLaurentian fan and may be a particularly sandylayer from a suprafan channel. The third perhaps

indicates the order of magnitude of the uncertaintiesinvolved in these various assumptions and calcula-tions.

CONCLUSIONS

A total picture of a turbidity current has beenevolved jn the previous discussion from the sedi-mentary characteristics of the silt-laminated mudson the outer Scotian margin. A new model isproposed for t h e origin of lamination by deposi-tional sorting due to increased shear in the bottom

boundary layer. This mechanism is consistent withprevious work on fine-grained sediment dynamics,in particular, that of Kranck (1972, 1973, 1975) onfloc properties; Kro ne (1962, 1963, 1972, 1976) o nflocculation, deposition and shear destruction in theboundary layer; and others. The discussion of timescales has indicated how rapidly the sediment settlesif the sediment dynamics up to the point where themud is deflocculated in the boundary are determinedprimarily by the mode size of the silt.

The lateral, downslope evolution of sedimentcharacteristics is consistent with the work of McCave(1970, 1972, 1976) and McCave & Swift (1976). Theturbidity current model developed is consistent withthe dynamic restraints discussed by Bagnold (1954,1956, 1962), Ippen Harleman (1952), Harleman(1961), and others. However, the overall system issignificantly different from the picture commonlyenvisaged. The turbidity flows responsible for muddeposition on the outer Scotian margin are of a verylarge scale (up to 1000 m thick), of low concentra-tion (about or 2500 mg l-l), and move down-slope at velocities of 9-16 cm s- . Can such large,dilute slow flows still be considered turbiditycurrents? What evidence is there from other field

measurements to support this concept?There is in fact a growing body of observations

that supports the proposed modification of theturbidity current theory but we have so far been slowto accept the changes implicit in these data. Highvelocities have only rarely been directly inferred forturbidity currents (e.g. the 1929 Grand Banks flow,Kuenen, 1952), although a competent current isclearly required for the transport of gravel down

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44 D. A . V. S t o w a n d A . J . Bowen

deep sea canyons and channels . However, recentcurrent-meter measurements ina variety of subma r-ine canyons haveall pointed to mu ch lower veloci ty(50-150 cm s- l ) turbidi ty cur rents (Gennesseaux,G u i b o u t & Lacombe, 1971; Shepard& Marshal l ,1978, Kel ler Shep ard, 1978; Shep ardet al . , 1977).

Curre nts in fan val leys are usual ly s lower tha n tho sein the canyons. Turbid layer underflows in lakes(No rma rk Dickson , 1976; Lam ber tet al., 1976)have dem onstra ted s ti ll lower veloci ties (max imumof 30 c m s-l).

The levees and inter-channel areas of submarinefans are presumably constructed by turbidi tycurrent overf low of fan channels . Th e depthof thosechannels must therefore give so me indicat ion of f lowthickness. Estimates fr om several tens (Me nar d, 1964)to several h undre ds of metres (Griggs& Kulm , 1970;Ko ma r, 1977) have been m ade, and chan nels on the

Lauren t ian Fan a re upto 800r

deep . Normarkrf al. (1980) have at tem pted t o infer f low character-istics from t he dime nsions of sedime nt waveson t h ebacksides of Monterey Fan Channel levees; theydeduced a flow thicknessof between 100 a n d 800 m .

Mo st est imates of f low concentrat ions have beenfor sandy turbidi ty currents (Komar, 1977) andthese a re on e or tw o orders o f magni tude grea te r thano u r lo-’ (2500 mg I-l) figure. However, directmeasurements of sediment concentrat ion in canyonflows by Dra ke& Gorsl ine (1973) and Dra ke (1974)while Shepard and coworkers were measuringcurrent velocities gave values of2 x0.5-5 mg I - l ) . These low-velocity, down-canyon

surges have been at t r ibutedto s to rm bui ld -up ofshelf water against the coast l ine and to peak r iverdischarge during floods. Shelf nepheloid layershave concentrat ions around 2.5 mg 1-l)according to Pierce (1976). The average suspended-sediment concentrat ion of the world’s twenty ma jorrivers (most of which result in large delta/fan com-plexes) is a b o u t 5 x 10-I 1250 m g I-l), a n d t h a t o f t h enext twenty is about5 x 125 mg 1-l) St rakov,1967; Hole man , 1968). Actual concentrat ions d uringrainy seasonsor t imes of f lood m ay be considerably

higher (Crickmay, 1974).These several l ines of evidence al l support the

concept of low-concentration, slow-rnoving, thickturbidity flows. We believe that theseflows areimportant in carrying large quant i t ies of f ine-grained sediment to the deep-sea f loor, both assepara te sedimentat ion events and in associat ionwith the ‘classical’ higher-velociiy, channelizedturbidity currents.

t o 2 x

ACKNOWLEDGMENTS

We t h a n k D r s D. J. W. Piper and K. K r a n c k f o rmany helpful discussions and their support in thelabora tory analysis. Sediment samples were col lectedo n Bedford Inst i tu te of Oceanography/Dalhousie

Universi ty cruises over the past few years; a ndalsofrom the Laniont-Doherty Geological Observatorycore co llect ion a t Colum bia Univers ity, New Yo rk ;we would l ike to than k th e man y people involved .The Canadian Commonweal th Schola rsh ip andFel lowship Commit tee p rov ided suppor t fo rD.A.V.S. which is grateful ly acknowledged. Theresearch was also supporte d by grants f rom ImperialOi l L td (Ca lgary) and the Nat iona l ResearchCounci l (Canada) toD. J. W. Piper and A. J.Bowen. P. D. K o m a r a n d S. S m i t h a r e t h a n k e d f o rtheir valuable comments and cr i t ical review of themanuscript .

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( M a n u s c r i p t r e c e i v ed 17 M a y 1978; rev ision rece ived 15 February 1979)