transport and at mouths: A synthesis

L. D. WRIGHT Coastal Studies Unit, Department of Geography, The University of Sydney, Sydney, N.S.W., Australia 2006

ABSTRACT Yoshida (1967, 1969, 1971), Waldrop and Farmer (1973), Scruton (1956, 1960), Komar (1973), Garvine (1974,1975), Wright (1970, River-mouth process studies and comparisons of river-mouth 1971), Wright and Coleman (1971, 1972, 1973, 1974), and forms from contrasting environments suggest that sediment disper- Wright and others (1973). Synthesis of the above studies suggests sal and accumulation patterns are governed by three basic that river-mouth variability can best be understood by considering forces and by - or wave-induced processes. Neglecting river-mouth systems as the resultants of varying contributions from modifications by or waves, effluent behavior and consequent a few primary and modifying forces. The primary river-mouth depositional patterns depend on the relative dominance of (1) out- forces are related directly to the interactions between effluent and flow inertia, (2) turbulent bed seaward of the mouth, and basin , and they rely on the river outflow for their driving (3) outflow buoyancy. Inertia-dominated are charac- energy. These primary forces and their depositional products are terized by fully turbulent jet diffusion, exhibit low lateral spreading modified to varying degrees by tides and waves. angles and progressive lateral and longitudinal deceleration, and produce narrow river-mouth bars. Under most natural circum- PRIMARY PROCESSES AND FORMS stances, inertial effects are equaled or exceeded by either turbulent bed friction or effluent buoyancy. When the tidal range and incident wave power of the receiving Shallow depths immediately basinward of a enhance basin are negligible or small relative to the strength of river out- the effects of bed friction, causing more rapid deceleration and flow, river-dominated configurations result (Wright and Coleman, lateral expansion. Triangular "middle-ground" bars and frequent 1972, 1973). River-dominant situations characterize river mouths bifurcation result. Low tidal ranges, fine-grained sediment in microtidal , , enclosed or semi-enclosed , or loads, and deep outlets favor strong density stratification within the regions fronted by offshore slopes which attenuate wave lower reaches of the channels. Under such circumstances, effluents power. In such cases, one or more of three primary forces will are dominated by the effects of buoyancy for at least part of the dominate: (1) inertia and associated turbulent diffusion; (2) turbu- year. Buoyant effluents produce narrow mouth bars, lent bed friction; or (3) buoyancy. The associated effluent processes elongate with parallel banks, and few bifurcations. are illustrated in Figures 1 through 3. The role played by each In macrotidal environments where tidal currents are stronger force depends on factors such as the rate and outflow than river flow, bidirectional currents redistribute river , velocity of the , depths in and seaward of the river producing -filled, funnel-shaped distributaries and causing mouths, the amount and of the sediment load, and the linear tidal ridges to replace the distributary mouth . Powerful sharpness of density contrasts between the river and basin waters. waves promote rapid effluent diffusion and decleration and pro- High outflow velocities, small density contrasts, and deep water duce constricted or deflected river mouths. immediately seaward of the mouth permit inertial forces to domi- nate, causing the effluent to behave as a fully turbulent jet (Fig. 1). INTRODUCTION When bed-load transport is large and water depths seaward of the mouth are shallow, turbulent diffusion becomes restricted to the River mouths are the dynamic dispersal points of river-derived horizontal while bottom friction increases deceleration and expan- sediments which contribute to delta formation. They are con- sion rates (Fig. 2). Where the river mouth is deep relative to the sequently the most fundamental elements of deltaic systems. riverine discharge, water enters the mouth as a salt wedge, and River-mouth processes involve a variety of interactions between the buoyancy of the lighter river water becomes dominant; the riverine and marine waters. These processes acting in combination effluent then spreads and thins as a relatively discrete layer (Fig. 3). determine the patterns by which effluents from river mouths Bates (1953) referred to outflows from river mouths having neglig- spread, decelerate, and deposit their sediment load. The geometries ible density contrasts as "homopycnal," whereas the term of river-mouth sediment accumulations, together with the as- "hypopycnal" was applied to buoyant effluents. In addition, Bates sociated distributions of grain size and primary sedimentary struc- distinguished a third effluent type, "hyperpycnal" outflows, in tures, reflect these effluent diffusion patterns. which the issuing water is denser than and plunges beneath the The depositional morphologies and sedimentary sequences of basin water. Field data on the last type are sparse. river-mouth systems are among the most varied of all coastal ac- cumulation forms. Multivariate analysis of 34 major deltaic sys- Dynamic Conditions tems (Wright and others, 1974) suggests the existence of a finite number of river-mouth types. In addition, there have been numer- For homopycnal effluents (that is, negligible buoyancy), the jet ous theoretical, laboratory, and field investigations of river-mouth structure depends on the ratio of the inertial to viscous forces as processes, including studies by Credner (1878), Gilbert (1884), indexed by the R„ at the outlet: Samoilov (1956), Bates (1953), Crickmay and Bates (1955), Axel- son (1967), Bonham-Carter and Sutherland (1963), Borichansky Ro = Uo [bo (b0l2)]l I v (1) and Mikhailov (1966), Mikhailov (1966, 1971), Jopling (1963),

Takano (1954a, 1954b, 1955), Bondar (1970), Kashiwamura and where Un is the mean outlet velocity, h0 and b„ are respectively the

Geological Society of America Bulletin, v. 88, p. 857-868, 8 figs., June 1977, Doc. no. 70614.


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& 6 n 0 ^ 9 (o * (b 0 -Q -0 mou ® d Uo fully turbulent & U max'

ö ö ^ 6 0 effluent 3 s & & r _ â 6 a ó ^ channeîannel 2 <5 ® fi a ® ® 6 bank \ SSSSi zone of ¡ji&ii-iëiiii ^>5flow establishment?:

Plan view

U max

Longitudinal cross section

Figure 1. Spreading, diffusion, and deceleration pattern of fully turbulent axial river-mouth jet.

FRICTION -DOMINATED EFFLUENT(plane turbulent ¡et with pronounced turbulent bed shear) ...¿xgggambi ënt SiSSíí^ water wï?

rapid seaward deceleration

Figure 2. Spreading, dif- Plan view fusion, and deceleration pattern of a plane turbulent jet with pronounced turbu- lent bed friction.

mouth Uo

Longitudinal cross section

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EFFLUENTreloHv. supero« on of lighter effluent S / drives secondary flows

laterally homogeneous effluent -u- (fresh water)

Transverse cross section

U max U max .. I approximately constant dece'erates — »

F1 < 1

^JSsältS^ ^fwedge^ intrusion

Longitudinal cross section

Figure 3. Spreading, mixing, deceleration, and secondary flow patterns of buoyant river-mouth effluents.

depth and width of the outlet, and v is the kinematic viscosity. crease in importance as F' exceeds 1. Hayashi and Shuto (1967, Pearce (1966) found that the jet becomes fully turbulent when R0 1968) found that fully turbulent effluent diffusion occurs when F' exceeds 3,000. In controlled laboratory situations, at the mouths of equals or exceeds 16.1 very small, tranquil , or at the mouths of which are supersaturated with suspended fine sediments (for example, the Inertia-Dominated Effluents: Turbulent Jets Hwang Ho), outflows may be viscous; however, at most large river mouths, R0> 3,000, and homopycnal outflows should be fully tur- Gilbert's (1884) classic discussion on deltaic is bulent. based implicitly on the concept of turbulent jet diffusion. The ideal The boundary layers at most natural nonstratified river mouths model of a fully turbulent, homopycnal outflow with negligible are turbulent, and the vertical flux of momentum is dominated interference from the bottom is probably the simplest and rarest largely by Reynolds stresses. When the mouth is fronted by shallow river-mouth model. This type of effluent is normally associated water and when bed shear stress r0 is large, turbulent bed friction with steep gradient streams entering deep fresh-water lakes, exerts a pronounced influence on effluent expansion and decelera- although it may occasionally prevail initially at newly created river tion patterns. mouths along the open . The theory of turbulent jets is dis- In the case of hypopycnal outflows from highly stratified river cussed in detail by Albertson and others, (1950), Schlichting mouths, buoyancy inhibits turbulence. In addition, the underlying (1968), Abramovich (1963), and Stolzenbach and Harleman salt water isolates the boundary layer of the outflow from the bed, (1971). The first systematic attempt to apply the theory to river- minimizing the effects of turbulent bed friction. mouth sedimentation was made by Bates (1953). Kashiwamura The degree to which the effluent is turbulent or buoyant will and Yoshida (1967, 1969) found that effluent diffusion must be of depend on the densimetric Froude number F' given by: the homopcynal type in order to approximate the turbulent-jet model. F' = 17 / V ygb' (2) Turbulent eddies generated at the free boundaries of the fully turbulent jet cause fluid and momentum exchange between the where U is the mean outflow velocity of the upper layer (in the case effluent and basin waters (Fig. 1). This diffusion is responsible for of stratified flows); y is the density ratio the expansion, mixing, and deceleration of the effluent. The trans- porting capacities of the effluent are diminished, and sediment is y = I - (P/'PS) deposited in a pattern reflecting the effluent spreading. The turbu-

where p, and ps are respectively the densities of fresh water and sea lent effluent expands laterally by progressive seaward growth of the water, g is the acceleration of gravity, and h' is the depth of the turbulent region. Stolzenbach and Harleman (1971) found that for density interface. Low values of F' suggest dominance of the fully turbulent jets the expansion rate was constant and that the buoyant forces; high values indicate inertia dominance. Inertia and spreading angle (the angle between the effluent center line and the turbulence are suppressed when F' is near or less than 1 but in- effluent boundaries) was low, with a value of 12°24' (Fig. 1).

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Turbulent jets consist of two zones: (1) a zone of flow establish- scends more steeply over the seaward front roughly in accordance ment characterized by a seaward-diminishing core of constant ve- with the pattern shown in Figure 4. Laboratory experiments con- locity and (2) a zone of established flow within which turbulent ducted by Jopling (1963) confirmed the development of a similar eddies dominate the entire width of the effluent, and centerline flow bar profile (that is, flat platform, steep bar front) under conditions undergoes a progressive seaward deceleration. Transverse to the of turbulent, homopycnal outflow into a deep basin. However, effluent within the zone of established flow, the time-averaged Jopling's experiments probably did not dynamically duplicate the speeds decrease from a maximum (Umax) at the centerline to zero at "frictionless" turbulent jet. the effluent boundaries; the velocity profile conforms to a Gaussian distribution in the ideal case (Fig. 1). Bed Friction The idealized depositional pattern resulting from inertia- dominated effluents is shown in Figure 4. Because of the low Effluents dominated purely by inertia and the ideal bar type just spreading angles, the lateral dispersion of sediments is confined to a described are rare. The continued deposition of sediment seaward narrow zone, at least in the region immediately seaward of the of the mouth eventually causes a substantial decrease in water outlet. The coarsest material is initially deposited at the end and depth, thereby increasing the relative influence of turbulent bed along the lateral margins of the core of constant velocity. This friction. Under most natural conditions, basin depths just seaward results in the formation of the narrow lunate-type bar originally of the outlet are seldom much greater than the outlet depth and are described by Bates (1953). This lunate form is quite subtle and is commonly shallower. If, under these conditions, outflow velocities largely distinguished by sediment-sorting patterns. Bonham-Carter and bed shear stresses are high, turbulent bed friction will become and Sutherland (1968) conducted computer simulation studies on dominant. Friction acting in combination with lateral turbulent jet the sediment transport and deposition patterns produced by turbu- diffusion (that is, plane jet diffusion), causes the rates of effluent lent jet diffusion. Their results indicated the development of a nar- spreading and deceleration to increase substantially. Borichansky row platform which ascends very gradually seaward but then de- and Mikhailov (1966) and Mikhailov (1971) concluded from a


/ /


/ / / / / y /


/ y / y / / /y coarsest / - '•' finer sands / / Plan view

mouth _

The 'Gilbert type' profile channel flat to gently ascending bar crest bar hnr|-^___

steeper bar front "'••..; • :'."•••.••'" ''•'::-.fore sets ; ''••'•.•..•'. •';•••... •''.'•••'•.•.

Longitudinal profile •—'•

Figure 4. Idealized depositional pattern related to intertia-dominated effluent diffusion.

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series of laboratory experiments that deceleration and lateral ex- shallow interdistributary . Because of the shallow depth, the pansion increase as depths seaward of the outlet decrease. Since combination of increased bed friction and plane turbulent jet diffu- friction is accompanied by plane turbulent jet diffusion, the trans- sion causes rapid effluent expansion and deceleration. This process verse velocity distribution is Gaussian in the early phases of bar initially produces a broad, radial bar; however, as deposition pro- development (Borichansky and Mikhailov, 1966). ceeds, subaqueous develop beneath the lateral boundaries of The depositional response to plane-jet diffusion initiates a short- the effluent, inhibiting further expansion of the effluent. As the bar lived sequence of positive feedback; shoaling seaward of the mouth grows upward, channelization takes place adjacent to the incipient causes an increase in the friction-induced deceleration and effluent levees, creating a bifurcating channel with a triangular spreading, which in turn increases the shoaling rate. Stability is separating the diverging channel arms. A study by Welder (1959) ultimately regained by the establishment of divergent bifurcating of the evolution of Cubits Gap, a major crevasse of the Mississippi channels along the margins of the effluent. Reconcentration of out- Delta, showed that within a few years after the initiation of the flow into channels reduces the frictional effects and minimizes the crevasse in the 1860's a rapidly shoaling radial bar had been re- total work done by the outflow. These channels are separated by a placed by a middle-ground bar flanked by abruptly divergent chan- triangular "middle ground" shoal over which bed shear stresses nels. and turbulent friction effects are relatively low. The overall result The forms of middle-ground bars and associated sediment dis- of this process is the formation of a pattern similar to that shown in tribution are consistent with the pattern shown in Figure 5. The Figure 5. The crevasse-splay "subdeltas" of the modern Mississippi bed ascends abruptly to the bar crest which is situated at the ex- Delta (Welder, 1959), Coleman and Gagliano, 1964, Coleman and treme upstream end of the bar and usually at a very short distance others, 1969; Arndorfer, 1971) are examples of friction-dominated from the outlet. The coarser bed-load material accumulates at the river-mouth deposition. Friction influences also appear to be re- bar crest and along the flanks of the middle-ground shoal as natural sponsible for the morphology of -tide deltas formed - subaqueous levees. Finer material accumulates in the more tranquil ward of tidal (Wright and Sonu, 1975). environment over the middle portion of the shoal (Coleman and In the case of the Mississippi subdeltas, deposition begins when a others, 1964; Arndorfer, 1971, 1973). Mikhailov (1966) found crevasse breaks through the of a major distributary into a that the distance from the outlet to the bar crest decreases and the


ee .s W.

-r-ïjiÀ" • • . v;.;^^ ..-.•.yo-" -' — . _• _ 111 M 11 j 111 ..^vvC ' '. '•'•••.. — '••. - - subaerial 11 M i 11 M 11 - • ••» . \ — •-— : -

1 channel • 'middle ground V- bar . • . • . ''Ml|| subaerila l levee - \ :.•••. . I I I I II I I 111I I I1 IM M i Iu I ^ 'jjfsl- coarsest sands

• . .'•'••• finer sands . ' . • v.*». ••••••• • 2-1- silt and

Plan view "2J interbedded sands • —• and silts



Longitudinal profile

Figure 5. Bifurcating channel and middle-ground bar patterns associated with friction-dominated river-mouth effluents.

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bifurcation angle increases as the depth-width ratio of the mouth Garvine, 1973). As the effluent expands laterally, it thins vertically decreases. in order to maintain its volume, as seaward-flow velocities remain The depositional patterns just described occur at river mouths approximately constant, at least in the initial region of expansion which prograde across flat, shallow offshore slopes and which ex- just seaward of the mouth (that is, from the outlet to x = 4 to 6b0). perience high outflow velocities and high bed-load transport for at In the initial expansion region, mixing is minimal, and the least part of the year. On a larger scale, deltas which developed maximum velocity remains nearly constant. However, the pro- under this type of river-mouth environment tend to exhibit multi- gressive seaward decrease in effluent thickness, h', causes F' to ple channel bifurcations with numerous middle-ground . increase to supercritical values. This leads to the generation and seaward intensification of internal waves. Recent field observations Buoyancy within the South Pass effluent (Wiseman and others, 1976) reveal that these shear-generated internal waves have periods on the order The significant rivers of the world fresh water into salt of 15 to 30 sec (near the observed Brunt-Vaisala frequency). In the water basins. However, vertical density contrasts are often subdued region between 4 and 6 channel widths seaward where F' attains either by tide-and-friction-induced mixing or by the fact that ex- maximum values, pronounced internal waves cause intense salt- ceptionally powerful river outflow forces the saline sea water sea- water entrainment and vertical mixing. Rapid deceleration and de- ward beyond the bar crest. The latter situation prevails at the position of the coarser sediments over the bar crest result. Farther mouth of the Amazon (Gibbs, 1970). Under both circumstances, seaward, the lowered flow velocities allow the densimetric Froude the densimetric Froude number at the outlet is large, and inertia number to drop to subcritical levels and the effluent continues to and turbulent friction dominate over buoyancy. spread as it transports the fine silt fractions and clays seaward to be At many river mouths, however, conditions allow strong vertical deposited over the distal bar and prodelta. During river flood, the density gradients to develop within and seaward of the mouth, salt-water—fresh-water interface is pushed seaward to a position causing the outlet densimetric Froude number F'0 to maintain val- just outside the bar crest. is then transported to the bar ues equal to or slightly less than unity. The outflow will then spread crest where it accumulates as the flood outflow abruptly decelerates as a buoyant plume above the underlying salt water, and a and separates from the bed upon encountering the pycnocline buoyancy-dominated depositional pattern will commonly occur. (Wright and Coleman, 1974). This requires that the discharge of fresh water exceed the tidal Secondary flow associated with buoyant effluent expansion plays prism but not be sufficiently strong to flush completely the sea an important role in controlling the geometry of the river-mouth water from the lower reaches of the channel. A distinct salt wedge deposits. Flow divergence near the surface of the effluent, com- may then intrude into the channel, and the depth of the associated bined with salt-water entrainment, causes a weak secondary con- pycnocline will coadjust with outflow velocity so as to maintain F'0 vergence near the bottom of the effluent and immediately beneath it = 1 (Ippen and Keulegan, 1965; Pritchard, 1952, 1955; Wright, (Wright and Coleman, 1974; Waldrop and Farmer, 1973). The 1971). Salt-wedge intrusion is best developed at river mouths dual helical cells shown in Figure 3 result. Transverse flow con- which are deep relative to the discharge rate, experience low tidal vergence near the accreting bed inhibits the lateral spread of ranges, and are fronted by moderately deep water. Development of coarser sediments. the requisite high river-mouth depth-width ratios is promoted by The buoyancy-dominated depositional pattern is shown in Fig- fine-grained sediment loads. ure 6. Flow convergence near the bed is responsible for the devel- Salt-wedge intrusion and buoyant effluent expansion prevail at opment of subaqueous levees which undergo minimal divergence as the mouths of several of the major distributaries of the Mississippi the channel progrades. This leads to the development of straight, (Wright, 1970; 1971; Wright and Coleman, 1971, 1974), the digitate distributaries with comparatively high depth-width ratios Danube (Bondar, 1963, 1967, 1970), the Po (Nelson, 1970) and and few bifurcations. The major distributaries of the Mississippi, the Ishikari River of Japan (Kashiwamura and Yoshida, 1967, notably South Pass, Southwest Pass, and Southeast Pass, exhibit 1969), as well as at the mouths of numerous smaller streams. In this type of progradational pattern in contrast to the friction- addition, many river mouths which are inertia or friction domi- influenced crevasse subdeltas discussed previously. Seaward of the nated for much of the year may exhibit buoyant effluents for short outlet, the coarsest material accumulates on the distributary-mouth periods. bar crest which is situated approximately 4 to 6 channel widths The expansion, deceleration, and secondary circulation patterns seaward. Again owing to near-bed lateral convergence, the coarsest of buoyant effluents are illustrated in Figure 3. The higher order bar deposits are narrow. Continued of these laterally theory of buoyant jets has been presented by Stolzenbach and restricted bar sands is responsible for the development of the Harleman (1971) and by Waldrop and Farmer (1973, 1974). Ob- "bar-finger sands" described by Fisk (1961). Beyond the bar crest, servations at the mouth of South Pass, (Wright sediments fine progressively seaward, whereas the lateral extent and Coleman, 1971,1974) and the Danube (Bondar, 1970) suggest and continuity of the deposits increases as the result of the expand- that the effects of turbulent diffusion are subdued relative to ing effluent. Over the bar front, sediment redistribution and sorting buoyancy and that observed patterns of effluent expansion and is related more to tidal currents and landward return flows than to thinning can be explained to a first-order approximation by a sim- bed shear from effluent processes. The bar front grades seaward ple buoyant model. In accordance with this model, the effluent in into the distal bar which consists predominantly of silt. The pro- the region between the mouth and about 4 to 6 channel widths (B0 delta clays deposited from suspension in the slow-moving outer in Fig. 3) seaward expands as a relatively homogeneous layer, in extremities of the effluent constitute the ubiquitous basal unit of response to the lateral hydrostatic pressure gradient created by the the delta. buoyant super-elevation of the fresh outflow. The expansion rate is greater than that of a fully turbulent jet but less than that of most MARINE INFLUENCES friction-dominated effluents. As long as the salt wedge remains in the channel, and F'0 — 1, the effluent behaves as shown in Figure 3 In low-energy microtidal coastal environments, the primary except when strong wave or tidal activity promote mixing. Distinct river-mouth processes often dominate, and marine influences are fronts characterize the lateral convergence between effluent and minimal. At many river mouths, however, the roles of marine ambient waters (Wright, 1970; Wright and Coleman, 1971, 1974; forces, particularly tides and waves, are far from negligible. These

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Figure 7. Sand-filled, bell-shaped channel and linear tidal ridges associated with macrotidal river mouths.

marine forces act in combination with the primary processes, tional sediment transport; and (3) the range of positions of the modifying the latter and their products to varying degrees. The land-sea interface and of the zone of marine-riverine interactions is marine forces exert two basic types of influence: (1) they directly greatly extended, both vertically and horizontally. modify the outflow processes by promoting more rapid mixing and The depositional morphology of numerous macrotidal river momentum exchange between effluent and ambient waters and by mouths exhibit many common attributes and conform in general to redirecting the sediment-transporting flows, and (2) they redistri- observations at the macrotidal mouth of the Ord River (Wright and bute and remold the river-mouth deposits following their initial others, 1973, 1975) and to data on other river mouths in similar deposition. Modifying marine processes include tides, waves, coas- environments (Wright and others, 1974; Coleman and Wright, tal currents, various frequencies of internal waves, biologic and 1975). At river mouths of this type, strong tidal currents over the chemical processes, and (in the case of Arctic river mouths) sea ice delta front and within the lower reaches of the river channels are and thermal processes. Only the effects of tides and waves are appreciably stronger than the river flow. In the lower Ord, for considered here. example, where tide range averages about 6 m, the tidal prism exceeds the mean river discharge by nearly 3,000 times, and Effects of Tides bidirectional flood-and-ebb currents exceed 3 m sec~'. Marine salinities prevail at the mouth, and the Ord is well mixed Many rivers empty into macrotidal environments. At the mouths throughout. The sediments introduced by the river during flood are of these rivers, one or more of the primary effluent processes can be transported by the tidal currents and rapidly remolded into tide- expected to play its role; however, the depositional patterns are produced configurations. strongly influenced by tidal processes which often overwhelm It has been shown that, where strong tidal currents cause pro- riverine forces. Notable examples of tide-dominated river mouths nounced bidirectional transport of sediment, flood- and ebb- include the mouths of the Ord (Australia), Klang (Malaya), Shat- dominated bed-load migrations follow adjacent but mutually eva- tal-Arab (Iraq), Colorado (North America), -Kiang sive paths (Ludwick, 1970; Price, 1963). Bidirectional sediment (China), and -Brahmaputra (Bangladesh). transport parallel to the direction of river outflow forms linear Strong tides have three basic effects: (1) tidal mixing obliterates subaqueous ridges in and seaward of the mouth (Fig. 7). These vertical density gradients, subduing the effects of buoyancy; (2) for ridges appear to be formed by the lateral convergence of ebb- and at least part of the year, tides account for a greater fraction of the flood-dominated sediment transport (Wright and others, 1975). sediment-transporting energy than does the river, causing bidirec- The ridges replace the more continuous distributary-

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Figure 8. Depositional patterns characteristic of river mouths influenced by strong wave activity. A. Normal wave incidence. B. Oblique wave in- cidence.

forms typical of lower tide range environments and are separated sents an equilibrium configuration in which tidal modifications and by deep channels. Near the mouth of the Ord, tidal ridges exhibit channel deposition have coadjusted to produce an equal distribu- reliefs of 10 to 22 m (Wright and others, 1975). Similar ridges are tion of work at the channel bed and to maintain a quarter-cycle present at the mouths of the Klang, Ganges-Brahmaputra and standing tide wave over the distance from the mouth to the limit of Shattal-Arab Rivers and have been described at the mouth of the tidal influences (Wright and others, 1973). by Meckel (1975). They were originally described Another distinction between macrotidal and microtidal river by Off (1963). mouths involves deformation of the tide wave within the lower Tidal dominance normally creates bell- or funnel-shaped chan- channel. In tide-dominated river channels, the ratio of tidal nels with a region of intense meandering near the upper limit of amplitude to channel depth is high, and the river tide behaves as a tidal influence. The Ord, for example, is 100 times wider at its finite amplitude wave. This causes the flood phase to shorten in mouth than at the upstream limit of the tide. The rates of seaward duration, whereas the ebb phase is extended. Tidal asymmetry in- widening vary considerably between individual rivers and may be creases upstream, and flood velocities increasingly exceed ebb vel- either linear or exponential, although the latter as shown in Figure ocities (Wright and others, 1973). Consequently, there is appreci- 7 appears to be the more common. The lower Ord offers an ideal able upstream transport of bed load except at times of river flood; example of an exponentially convergent channel. This form repre- in the lower Ord, the largest and most prominent bed forms are

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Dominant Dynamic Ideal river-mouth Basic mechanisms causing Effluent behavior Depositional and morphologic force conditions environment expansion and deceleration patterns

Inertia F'o » 1 High outflow velo- Turbulent diffusion of ef- Constant, low spreading The ideal "Gilbert-type" deposi- r0 = moderate cities; negligible out- fluent with ambient (basin) angle (12.5° for fully tur- tional pattern. Progressive longi- to large let stratification; water causes expansion and bulent jets); progressive tudinal deposition and basinward deep outlet; deep deceleration lateral and longitudinal fining; lateral fining away from ef- water basinward of deceleration; Gaussian fluent centerline; narrow lunate outlet; small to mod- lateral velocity distribution bar with a flat or gently ascending erate bed load back; progradation produces the classic bottomset-foreset-topset sequence

Turbulent F'0>>1 Moderate to high Lateral turbulent diffusion Rapid lateral expansion Rapid shoaling and abrupt deposi- bed t0 = very outflow velocities; enhanced by basinward- (high spreading angle); tion of coarser fractions basinward friction large negligible outlet increasing frictional resis- progressive and rapid from outlet; radial bar develops stratification; shal- tance deceleration into "middle ground" - type shoal low outlet; shallow separating bifurcating incipient water basinward channels of outlet; high bed load

Buoyancy F'o= 1 Intermediate outflow Lateral spreading and verti- Intermediate lateral ex- Progressive seaward shoaling from T0 = low velocities; strong cal thinning induced by the pansion rate accompanied moüth to bar crest; progressive outflow density stra- relative superelevation of by vertical thinning; ex- seaward fining beyond bar crest; tification; deep out- the lighter effluent; decera- pansion and thinning rates bar crest and minimum water let; moderate water tion induced primarily by decrease seaward; ef- depths situated between 4 and 6 depths basinward of entrainment and high-fre- fluent velocity initially near channel widths seaward of the out- outlet (relative to out- quency internal waves at the constant, undergoes rapid let; subaqueous levees prograde flow width); fine- pycnocline (salt-water - deceleration in the region with minimal divergence and grained sediment fresh-water "interface") from 4 to 6 channel widths maintain high depth/width ratios load; low bed load; seaward; lateral-flow con- at outlet small tidal range vergence near base of effluent

flood oriented. Upstream sediment transport by flood currents is Waves directly modify the expansion and deceleration patterns balanced by ebb-dominated sediment transport in deeper channels of river-mouth effluents. Outflow from river mouths refracts and where flow becomes concentrated during falling tide. Extensive steepens incident waves in such a way as to concentrate power on accumulations of sand within the channels and bidirectional the effluent and to cause breaking in water depths greater than the crossbedding result. normally breaking depth. The resultant wave-induced setup op- In less extreme cases, patterns intermediate between the tide- poses the outflow, while wave-breaking enhances the mixing and dominated and purely river-dominated situations should be ex- momentum exchange between the effluent and ambient waters. pected. The mouth of the Chao Phraya of Thailand (NEDECO, The effect is to cause very rapid deceleration and loss of sediment 1965) offers an instructive example. Spring tide range at the mouth transporting ability within short distances from the outlet. Buoyant of the Chao Phraya is less than one-half that of the Ord, averaging effluents are precluded by intense wave-induced vertical mixing; 2 to 4 m. The mean annual discharge, on the other hand, is five Wright (1970) found a statistically significant tendency for vertical times as great as that of the Ord. Like the lower Ord, the lower mixing and deceleration rates to increase when seas are rough. reaches of the Chao Phraya exhibit an exponential bell shape; but Recent observations at the wave-dominated mouth of the Shoalha- the rate and extent of seaward widening are far less than those of ven River on the high-energy southeast coast of Australia (Wright, the Ord. Seaward of the mouth, the deposits have the form of a 1977) show that during low flow considerable wave-induced mix- broad radial bar. However, this bar is surmounted by a series of ing between fresh and salt water takes place within the mouth. linear tidal ridges similar to those which occur at the mouth of the During flood, sea water is completely flushed from the outlet, and Ord. outflow velocities exceed 2 m sec"1. However, breaking waves im- mediately mix the outflowing fresh water with salt water, and over Effects of Waves a distance of two channel widths (about 600 m), seaward velocities drop to values as low as 30 cm sec-1. River mouths located in relatively protected environments or Figure 8A shows the morphology of a typical wave-dominated fronted by flat offshore slopes may experience minimal wave ef- river mouth with normal wave incidence. Increased deceleration fects. However, many river mouths are attacked by powerful causes rapid deposition, and the crest of the crescentic river-mouth waves. Wright and Coleman (1972, 1973) have shown that river- bar forms at short distances from the mouth. Along the lateral dominated deltas such as the Mississippi or Danube are associated flanks of the effluent, steep velocity gradients cause deposition of with extremely flat offshore slopes which substantially reduce the bed load, forming pronounced subaqueous levees which assume power of waves which reach the river mouth or delta shoreline. the form of broad shoals. Contemporaneous with initial deposi- Similarly, broad intertidal and subtidal flats at tide-dominated river tion, shoaling waves create bars which migrate shoreward mouths dissipate wave forces. On the other hand, river mouths over the levee-shoals. The shoreward return of sediments constricts fronted by steep nearshore slopes in high wave-energy environ- the river mouth until outflow becomes sufficiently concentrated to ments are profoundly influenced by waves. maintain the outlet. Constrictions similar to those shown in Figure

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Modifying River-mouth environ- of modifications Behavior of modified Postdepositional modi- Depositional and force ment in which force to effluent effluent fications to river-mouth morphologic patterns most likely to be deposits dominant Tides High tide range, usually Intense mixing by tidal Strong outflow and in- Bidirectional sediment Bell- or funnel-shaped associated with semi- currents destroys vertical flow at mouth related to transport by tidal cur- lower river courses are sand enclosed or shallow seas, stratification; tidal flow tides rather than river rents, causes significant filled with flared mouths; deeply indented gulfs, overwhelms river out- input except during river upstream return of sedi- large tidal ridges aligned or flow, causing currents at ; tidal flow sustains ment into channel; mutu- parallel to flow constitute mouth to reverse with swift currents to con- ally evasive flood- and major bar form. tidal phase; strong bed siderable distances from ebb-dominated sediment shear from tidal currents outlet transports in and sea- ward of the mouth con- verge to form linear elon- gate ridges Waves Direct exposure to open Wave refraction by issu- Rapid seaward decelera- Wave reworking causes Constricted mouth fronted ; relatively steep ing currents causes local tion; effects by buoyancy shoreward return of sand by subaqueous deposits offshore profile concentration of power subdued by destruction over subaqueous levees similar to the ebb-tide around effluent; wave of stratification; effluent as swash bars; mouth be- deltas of tidal inlets; broad, breaking promotes narrowed by lateral con- comes constricted; re- shoal-like subaqueous abrupt mixing and dece- vergence of wave forces working may also trans- levees capped by swash bars leration of effluent; wave- form bar crest into swash converge slightly seaward; induced setup inhibits bar during low flow; regular, crescentic river- outflow shoreward return of sand mouth bar located at short may occasionally seal distance seaward of outlet mouth

8A are a fundamental characteristic of wave-dominated river University of Sydney and the Australian Research Grants Commit- mouths: notable examples include the San Francisco, Senegal, and tee. the Shoalhaven. Where discharge is perennially high, outflow and Much of the original research was conducted in collaboration wave forces achieve a balance, and the outlet is maintained. How- with J. M. Coleman, Director, Coastal Studies Institute. Investiga- ever, if wave power is very high and discharge is seasonal, the tions in the Ord River were conducted in collaboration with J. M. mouth may be temporarily sealed (for example, the Shoalhaven). Coleman and B. G. Thom. Wave-dominated river-mouth depositional patterns are very similar to the ebb-tide deltas seaward of tidal inlets as described by REFERENCES CITED Hayes and others (1970), Oertel (1972), and Wright and Sonu (1975). The subaqueous levees and crescentic bars are respectively Abramovich, G. N., 1963, The theory of turbulent jets: Cambridge, analogous to the ramp-margin shoals and distal lobes of ebb-tide Mass., Massachusetts Inst. Technology Press. deltas (Oertel, 1972). Albertson, M. L., Dai, Y. B., Jensen, R. A., and Rouse, H., 1950, Diffusion When wave incidence is persistently oblique to the river mouth, of submerged jets: Am. Soc. Civil Engineers Trans., v. 115, p. 639- the same basic processes are operative. However, littoral drift redi- 697. rects the sediment downdrift along the adjacent coast, causing a Arndorfer, D., 1971, Process and parameter interaction in Rattlesnake Cre- laterally deflected river mouth similar to that shown in Figure 8B. vasse, Mississippi [Ph.D. dissert.]: Baton Rouge, The mouths of the Senegal (Africa) and Jequitinhonha (Brazil) are Louisiana State Univ. 1973, Discharge patterns in two crevasses of the Mississippi River typical examples. Delta: Marine , v. 15, p. 269-287. Axelson, V., 1956, Laitaure Delta: Geog. Annaler, v. 49, p. 1 — 127. CONCLUSIONS Bates, C. C., 1963, Rational theory of delta formation: Am. Assoc. Petro- leum Geologists Bull., v. 37, p. 2119-2161. River-mouth morphologies and depositional patterns comprise a Bondar, C., 1963, Data concerning marine water penetration into the broad spectrum of types. The position of any individual river mouth of the Sulina Channel: Studii Hidraulica, v. 9, no. 1, p. 293- mouth within this spectrum depends on the relative intensity and 335 [in Romanian]. mutual interactions of each of the primary and modifying forces. 1967, Contact of fluvial and sea waters at the Danube River mouths in the Black Sea: Studii Hidrologie, v. 19, p. 153-164 [in Romanian]. Tables 1 and 2 summarize the process-form associations charac- 1968, Hydraulic and hydrological conditions of the Black Sea waters teristic of five extreme situations in which one of the determinant penetration into the Danube mouths: Studii Hidrologie, v. 25, p. forces in dominant. Many river mouths are intermediate between 103-120 [in Romanian]. these various extremes. In addition, significant roles are played by 1970, Considerations theoretiques sur la dispersion d'un courant liq- forces other than those discussed herein. uide de densite redruite et a niveau libre, dans un bassin contenant un liquide d'une plus grande densite: Symposium on the Hydrology of ACKNOWLEDGMENTS Deltas, UNESCO, v. 11, p. 246-256. Bonhan-Carter, G. F., and Sutherland, A. J., 1968, Diffusion and settling of sediments at river mouths: A computer simulation model: Coast The research on which this synthesis is largely based was sup- Assoc. Geol. Socs. Trans., v. 17, p. 326—338. ported by the Coastal Studies Institute, Louisiana State University, Borichansky, L. S., and Mikhailov, V. N., 1966, Interaction of river and sea under Contract N00014-69-A-0211-0003, Project NR388 002 water in the absence of tides, in Scientific problems of the humid tropi- with the Geography Programs of the Office of Naval Research. In- cal deltas and their implications: UNESCO, p. 175-180. vestigations at the mouth of the Shoalhaven are supported by The Bowden, K. F., 1967, Circulation and diffusion, in Lauff, G. H., ed., Es-

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/88/6/857/3429515/i0016-7606-88-6-857.pdf by guest on 01 October 2021 868 L. D. WRIGHT

tuaries: Am. Assoc. Adv. Sei. Pub. 83, p. 15-36. rica), CSIR Rept. MEG 475. Coleman, J. M., and Wright, L. D,, 1971, Analysis of major river systems Price, W. A., 1963, Patterns of flow and channeling in tidal inlets: Jour. and their deltas, procedures and rationale, with two examples: Sed. Petrology, v. 33, p. 279-290. Louisiana State Univ. Coastal Studies Inst. Tech. Rept. 95, 125 p. Pritchard, D. W., 1952, Estuarine hydrography, in Landsberg, H. E., ed., 1975, Modern river deltas: Variability of process and sand bodies, in Advances in geophysics, Vol. 1: London, Academic Press, p. 243- Broussard, M. L., ed., Deltas: Models for exploration: Houston Geol. 280. Soc., p. 99-149. 1955, Estuarine circulation patterns: Am. Soc. Civil Engineers, Proc. 8, Coleman, J. M., Gagliano, S. M., and Webb, J. E., 1964, Minor sedimen- no. 717, p. 717/1-717/11. tary structures in a prograding distributary: Marine Geology, v. 1, p. Schlichting, H., 1968, Boundary layer theory: New York, McGraw-Hill, 240-258. 747 p. Credner, G. R., 1878, Die deltas, ihre morphologie, geographische Ver- Scruton, P. C., 1956, Oceanography of Mississippi Delta sedimentary envi- breitung, und entstehungs bedingungen: Petermanns Geog. Mitt. (Er- ronments: Am. Assoc. Petroleum Geologists Bull., v. 40, p. 2864- gänzungsband), v. 12, p. 1-74. 2952. Crickmay, C. H., and Bates, C. C., 1955, Discussion of delta formation: 1960, Delta building and the deltaic sequence, in Shepard, F. P., Am. Assoc. Petroleum Geologists Bull., v. 39, p. 107-114. Phleger, F. B., and van Andel, T. H., eds., Recent sediments, northwest Fisk, H. N., 1961, Bar finger sands of the Mississippi Delta, in Geometry of Gulf of Mexico: Tulsa, Am. Assoc. Petroleum Geologists, p. 82-102. sandstone bodies: Am. Assoc. Petroleum Geologists, p. 29-52. Stolzenbach, K. D., and Harleman, D.R.F., 1971, An analytical experimen- Garvine, R. W., 1974, Physical features of the Connecticut River outflow tal investigation of surface discharges of heated water: Massachusetts during high discharge: Jour. Geophys. Research, v. 79, p. 831-846. Inst. Technology, Ralph M. Parsons Lab., Water Resources and Hy- 1975, The distribution of salinity and temperature in the Connecticut drodynamics, Dept. Civil Engineering Rept. 135, 212 p. River estuary: Jour. Geophys. Research, v. 80, p. 1176-1183. Takano, K., 1954a, On the velocity distribution off the mouth of a river: Gibbs, R. J., 1970, Circulation in the estuary and adjacent Oceanog. Soc. Japan Jour., v. 10, p. 60-64. Atlantic Ocean: Jour. Marine Research, v. 28, p. 113-123. 1954b, On the salinity and velocity distributions off the mouth of a Gilbert, G. K., 1884, The topographical features of shores: U.S. Geol. river: Oceanog. Soc. Japan Jour., v. 10, p. 92-98. Survey Ann. Rept. 5, p. 104-108. 1955, A complementary note on the diffusion of the seaward flow off Hayashi, J., and Shuto, N., 1967, Diffusion of warm water jets discharged the mouth of a river: Oceanog. Soc. Japan Jour., v. 11, p. 1-3. horizontally at the water surface: Internat. Assoc. Hydraulic Research, Waldrop, W. R., and Farmer, R. C., 1973, Three-dimensional flow and sed- 12th Cong., Proc. 4, p. 47-59. iment transport at river mouths: Louisiana State Univ. Coastal Studies 1968, Diffusion of warm cooling water discharged from a power Inst. Tech. Rept. 150, 137 p. plant: 11th Conf., Council Wave Research. 1974, Three-dimensional computation of buoyant river plumes: Jour. Hayes, M. O., Goldsmith, W., and Hobbs, C. H., 1970, Offset coastal in- Geophys. Research, v. 79, p. 1269-1276. lets: 12th Coastal Engineering Conf., Proc., Washington, D.C., Welder, F. A., 1959, Processes of deltaic sedimentation in the lower Missis- p. 1187-1200. sippi River: Louisiana State Univ. Coastal Studies Inst. Tech. Rept. 12, Ippen, A. T., and Keulegan, G. B., 1965, Salinity intrusions in estuaries, in 90 p. Wicker, C. F., ed., Evaluation of present state of knowledge of factors Wiseman, W. J., Wright, L. D., Rouse, L. J., and Coleman, J. M., 1976, affecting tidal hydraulics and related phenomena: U.S. Army Corps Periodic phenomena at the mouth of the Mississippi River: Contr. Engineers, Comm. on Tidal Hydraulics, chap. 4. Marine Sci., v. 20, p. 11-32. Jopling, H., 1963, Hydraulic studies on the origins of bedding: Sedimentol- Wright, L. D., 1970, Circulation, effluent diffusion, and sediment trans- ogy, v. 2, p. 115-121. port, mouth of South Pass, Mississippi River Delta: Louisiana State Kashiwamura, M., and Yoshida, D., 1967, Outflow pattern of fresh water Univ. Coastal Studies Inst. Tech. Rept. 84, 56 p. issued from a river mouth: Coastal Engineering in Japan, v. 10, 1971, Hydrography of South Pass, Mississippi River Delta: Am. Soc. p. 109-115. Civil Engineers; Waterways, Harbours and Coastal Engineering Div. 1969, Flow pattern of density at a river mouth: Internat. As- Jour., Proc., no. 97, p. 491-504. soc. Hydraul. Research, 13th Cong., Proc. 3, p. 181-190. 1977, Morphodynamics of a wave-dominated river mouth: 15th Coas- 1971, Transient acceleration of surface flow at a river mouth: Coastal tal Engineering Conf., Proc., Honolulu, Hawaii (in press). Engineering in Japan, v. 14, p. 135-142. Wright, L. D., and Coleman, J. M., 1971, Effluent expansion and interfacial Komar, P. D., 1973, Computer models of delta growth due to sediment mixing in the presence of a salt wedge, Mississippi River delta: Jour. input from rivers and longshore transport: Geol. Soc. America Bull., Geophys. Research, v. 76, no. 36, p. 8649-8661. v. 84, p. 2217-2226. 1972, River delta morphology: Wave climate and the role of the sub- Ludwick, J. L., 1970, Sand waves and tidal channels in the entrance to aqueous profile: Science, v. 176, p. 282-284. Chesapeake Bay: Old Dominion Univ. Inst. Oceanography Tech. 1973, Variations in morphology of major river deltas as functions of Rept. 1, 79 p. ocean wave and river discharge regimes: Am. Assoc. Petroleum Meckel, L. D., 1975, Holocene sand bodies in the Colorado Delta area, Geologists Bull., v. 57, no. 2, p. 370-398. northern , in Broussard, M. L., ed., Deltas: Models 1974, Mississippi River mouth processes: Effluent dynamics and for exploration: Houston Geol. Soc., p. 237-265. morphologic development: Jour. Geology, v. 82, p. 751-778. Mikhailov, V. N., 1966, Hydrology and formation of river mouth bars, in Wright, L. D., and Sonu, C. J., 1975, Processes of sediment transport and Scientific problems of the humid tropical zone deltas and their implica- tidal delta development in a stratified tidal , in Cronin, L. E., ed., tions: UNESCO, p. 59-64. Estuarine research, Vol. 2: New York, Academic Press, p. 63—76. 1971, Dynamics of the flow and the bed in nontidal river mouths: Wright, L. D., Coleman, J. M., and Thom, B. G., 1973, Processes of chan- Moscow, Div. Hydrology, 258 p. nel development in a high-tide-range environment: Cambridge Gulf Nedeco, 1965, Siltation of the Bankok Port Channel, Vols. I and II: Ord River Delta: Jour. Geology, v. 81, p. 15-41. Amsterdam, North Holland Publ. Co. Wright, L. D., Coleman, J. M., and Erickson, M. W., 1974, Analysis of Nelson, B. W., 1970, Hydrography, sediment dispersal, and recent histori- major river systems and their deltas: Morphologic and process com- cal development of the Po River Delta, Italy, in Morgan, J. P., ed., parisons: Louisiana State Univ. Coastal Studies Inst. Tech. Rept. 156, Deltaic sedimentation: Modern and ancient: Soc. Econ. Paleon- 114 p. tologists and Mineralogists, p. 152-184. Wright, L. D., Coleman, J. M,, and Thom, B. G., 1975, Sediment transport Oertel, G. F., 1972, Sediment transport of estuary entrance shoals and the and deposition in a macrotidal river channel, Ord River, Western Au- formation of swash platforms: Jour. Sed. Petrology, v. 42, p. 858- stralia, in Cronin, L. E., ed., Estuarine research, Vol. 2: New York, 863. Academic Press, p. 309-322. Off, J., 1963, Rhythmic linear sand bodies caused by tidal currents: Am. Assoc. Petroleum Geologists Bull., v. 47, no. 2, p. 324-341. Pearce, A. F., 1966, Critical Reynolds number for fully-developed turbu- MANUSCRIPT RECEIVED BY THE SOCIETY NOVEMBER 24, 1975 lence in circular submerged water jets: Nat Mech. Engineering Re- REVISED MANUSCRIPT RECEIVED JUNE 15, 1976 search Inst., Council for Sei. and Indus. Research (Pretoria, South Af- MANUSCRIPT ACCEPTED SEPTEMBER 24, 1976 Printed in U.S.A.

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