Transportation of Sediment in the Sea

Settling Velocity. Sedimentary debris which has been transported to the sea settles through the water and is at the same time carried laterally by currents of different types. The settling velocity of a sedimentary particle depends upon its specific gravity, size, and shape, and upon the specific gravity and viscosity of the water. Before considering the settling velocity of particles in the sea it is necessary to examine the simplest case, where it is assumed that only spheres are involved. The classical equation for the settling velocity of a sphere is that developed by Stokes:

where W is the settling velocity, ρ₁ and ρ₂ are the densities of the sphere and the liquid respectively, g is the acceleration of gravity, r is the radius of the sphere, and μ is the dynamic viscosity of the liquid. All values are in the c.g.s. system. Stokes’ law has been tested and found to be valid for spherical particles settling in a uniform medium of relatively large extent. If the settling velocity is great—as may be the case if the spheres are large, the density difference large, or the viscosity small—turbulent motion is set up and the relationship is no longer valid. Since we are concerned with settling velocities in water and with a relatively constant difference in density, it means that the relationship does not hold for large spheres. Krumbein and Pettijohn (1938) have reviewed the various expressions which have been developed either theoretically or empirically to express the relationship between the settling velocity and the size of larger spheres. The semiempirical relationship developed by Wadell covers the range with which we are concerned. This may be expressed as a correction to be applied to Stokes’ law and can be given in the following form (Krumbein and Pettijohn, 1938, p. 105): where r_s is the radius according to Stokes’ law and r_a is the actual radius, and v_a is the actual settling velocity. In table 105 are shown the terms applied to particles of various diameters and the settling velocity of quartz spheres (density = 2.65) in distilled water at 20°C (μ = 0.0101) of the indicated dimensions according to Stokes’ law and for certain of the larger particles according to Wadell's equation. It is readily seen that the effect of turbulence is to reduce the rate of fall. Stokes’ law can be considered valid for spheres of diameters up to 62.5 microns. Individual sedimentary particles are of course far from spherical in shape, but if their settling velocities are measured their size can be expressed as equivalent radii or equivalent diameters where these terms indicate the dimensions of quartz spheres having the same settling velocity.

---

---

When mechanical analyses are made (see p. 969), the size-grade composition of a sediment is determined by sieving and by determining the settling velocity of the smaller particles. In such an analysis it is customary to employ certain physical and chemical methods for separating the individual particles which in the original sample may be cemented together or held somewhat more loosely by electrostatic or physical forces. This is particularly true of the clay and colloid material which is said to be coagulated or flocculated. Although the coarser material larger than about 15 microns may not be flocculated and will therefore settle with approximately the computed velocity, this is not true for the finer particles. Little is known concerning the state of aggregation of the clay and the colloid particles that are in suspension in the sea; however, studies by Gripenberg (1934) have shown that fine-grained material when mixed with sea water tends to flocculate into units which settle with velocity equivalent to those of quartz spheres between about 5 and 15 microns in diameter, that is, they settle between 1 m and 20 m per day. The flocculation is related to the composition of the clay minerals, particularly with respect to the exchangeable bases (p. 988) and also to the salt concentration of the water. It is probable that the flocculation is much retarded when the suspension of particles is extremely dilute. Studies of clay minerals have shown that the coagulation tends to increase the size of the units, hence to increase their settling velocity, but at the same time the coagulated particles carry with them a certain amount of the water, which reduces their effective density and therefore tends to slow them down.

A certain amount of this extremely fine-grained material may be formed in the sea, but probably most of it comes from the land, where the agencies of mechanical and chemical weathering are much more effective. If this material did not find its way to the sea floor it is obvious that the oceans would ultimately become turbid with suspended particles. Measurements of the penetration of light in the sea show that finely suspended material is present everywhere in the surface layer of the sea (p. 88), but it does not seem reasonable that the average turbidity of the water is changing. Therefore, the rate of supply of material must equal the rate of deposition. Some of the problems of submarine geology are to determine the rate of deposition, the quantity of sedimentary

---

material in suspension in various areas of the sea, the settling velocity of this material, and the changes which it may undergo in the water or after it has reached the sea bottom.

Transportation of Settling Particles by Ocean Currents. The effective settling velocities of sedimentary particles probably range from less than one meter per day to many thousand meters per day. Coarse material which is brought to the sea near shore or which is released from icebergs or remains of plants at great distances from the coast will sink so fast that it is immediately deposited, but fine material with small settling velocities may be carried for considerable distances by currents. A particle 4 microns in diameter settles at a rate of about one meter per day (table 105), hence, may be carried about for many years before reaching the bottom. Such fine material may be introduced by rivers, may arise from wave action in shallow water, or may be derived from the remains of planktonic organisms. The distance to which particles can be carried depends upon their settling velocity, the velocity of the current, and in some instances upon the turbulence associated with the motion. The turbulence will lead to high values of the vertical diffusion (p. 93). This great diffusion will have no effect on the settling of very small particles if they are distributed in such a manner that the net vertical transport by diffusion is zero but, depending upon the change of concentration and the change of eddy diffusion with depth, the diffusion may lead to a net upward or downward transport of particles which may decrease or increase downward transport by settling. So far, no data are available for examination of these conditions.

Another important characteristic of the ocean currents is the presence of horizontal eddies which lead to large-scale horizontal mixing, which can be expressed as horizontal diffusion (p. 92). The horizontal diffusion is of importance near coasts where fine material is brought into the sea by rivers, wave action, wind, or other agencies. In coastal waters the great supply of fine material leads to a high concentration of suspended particles which by horizontal diffusion may be carried to considerable distances from the coast. In a steady state the amount of suspended material transported away from the coast by diffusion through a vertical plane parallel to the coast must equal the amount supplied to the water between the coast and the vertical plane minus what is deposited on the bottom inside of the vertical plane. On the basis of such considerations, Revelle and Shepard (1939) have shown how the finer material may be carried away from shore by the large-scale horizontal eddies which occur off the southern California coast. They introduced a settling velocity of 15 m per day which they consider to be that of “thoroughly coagulated suspensions.”

Transportation of Particles along the Sea Bottom. Material that settles toward the bottom is by no means always permanently

---

deposited where it first reaches the bottom, but may be carried along over great distances before it comes permanently to rest. Deposition is therefore the excess of material reaching any area on the bottom over that carried away along the bottom. This is of importance to bear in mind, because the presence of certain types of sediment in any given locality does not always indicate that the sediment of this type is being deposited. There may be no net deposition; erosion may even take place. In. each instance the factors operating in transporting material along the bottom have to be considered. These factors are primarily (1) mass movement of unconsolidated sediments by mud flows and slides on submarine slopes, (2) sliding, rolling, or saltation caused by the tractive force of bottom currents, and (3) the effect of the turbulence, which will place fine material in suspension such that it can be distributed laterally by diffusion or currents.

Mud flows represent movement of unconsolidated material that has accumulated on a slope and are not necessarily associated with any movement of the overlying water. Owing to instability or to a stimulus such as may be caused by seismic activity, the material begins to slide down the slope. There is some evidence that mud flows are relatively common on steep slopes and it has been suggested that they are of importance as an agency which removes accumulated sediments from submarine canyons. They are most likely to occur in areas where sediments are accumulating rapidly on relatively steep slopes, hence they may occur on the continental slope and on insular slopes. The angle of repose of unconsolidated marine sediments is not known. It is thought that mud flows can take place where the slope is only about one degree, but this does not imply that slopes of greater angle are always devoid of unconsolidated material.

Transportation by mud flows tends to break down stratification that may have developed in the deposit, and may result in the accumulation of rather coarse and unsorted material in deep water. Furthermore, mud flows may carry organisms and their skeletal remains into environments where they could not have developed, thereby leading to complications in interpretation of the environmental conditions from the study of the organic constituents of a deposit. There is very little direct evidence of the occurrence of mud flows in the seas, consequently it is as yet impossible to determine their importance as transporting agencies. The status of present knowledge is discussed by Twenhofel (1939).

In rivers the motion of individual particles along the bottom is described as sliding, rolling, and saltation (Hjulström, 1939). Sliding does not often take place, but rolling and saltation (which is a jumping motion) are common forms of transportation. Nothing is known about the extent to which such transportation takes place along the sea bottom, but certain indications can be obtained by application of results of river

---

studies. Hjulström has prepared a diagram (fig. 251) in which is indicated the manner in which, under certain specified conditions, erosion, transportation, and deposition are related to the average velocity across a transverse profile of a river and the particle size. The part of Hjulström's diagram relating to particles smaller than 0.01 mm will not be considered because such fine particles will be carried mainly in suspension (p. 965). The curve marked A follows the minimum average velocities which are required for eroding uniform material of the various particle sizes and represents therefore a limiting velocity which is called the eroding velocity. Similarly, the curve marked B follows the minimum average velocities which are required for transporting uniform material of the various particle sizes. The diagram brings out the fact that material of particle size about 0.5 mm (medium sand) is the easiest to erode, requiring an eroding velocity of less than 20 cm/sec. The eroding velocity increases rapidly for larger particle size, reaching 100 cm/sec for a size of about 8 mm. The eroding velocity also increases for smaller particles, reaching 60 cm/sec for a size of 0.01 mm (10 microns). Particles of size 0.5 mm (medium sand) are transported at velocities between 4 cm/sec and 20 cm/sec and particles of size 10 mm are transported at velocities between 70 cm/sec and 110 cm/sec.

---

Applying these results from rivers to the problem of transportation along the sea bottom by sliding, rolling, and saltation, it must be borne in mind that in fig. 251 the velocity represents the average velocity across a transverse profile of a river and that the velocity at the bottom is smaller. It may perhaps be assumed that the “average velocities” correspond to those occurring a few meters above the sea bottom. Taking into account the fact that high velocities near the sea bottom are common in shallow water only, it can be considered probable that eroding velocities and transportation along the bottom of coarser material, say, particles with diameters greater than 2 to 3 mm, occur only in shallow water, but that in regions of deep currents similar transportation of fine sand and silty sand may occur at depths of several thousand meters. Sediment collections made by the E. W. Scripps off the coast of California and in the Gulf of California appear to bear out such contentions except where coarse material has been found in the bottom of submarine canyons and on banks. The latter occurrence may be related to former emergence.

It should be added that on a slope alternating currents will lead to net downward transport of sediments because gravity will facilitate a downward and counteract an upward transport.

Transportation of particles in suspension near the bottom is often considered together with sliding, rolling, and saltation because the transition from one form to another is probably a gradual one. The essential difference is that material in suspension can be carried in a short time over much longer distances.

Nothing is known as to the amount or character of material in suspension near the bottom under varying conditions, but an approach to the problem can be made by application of results from laboratory studies on the characteristics of turbulent flow. Such results have been applied to the problem of transportation in rivers (Rouse, 1938), but certain modifications are necessary when dealing with transportation near the sea bottom. The basic concept is that where turbulence exists a current can carry a load of suspended particles that is determined by the condition that the downward transport by settling must equal the upward transport by eddy diffusion. The downward transport by settling equals WS where W is the settling velocity and S is the concentration of suspended particles expressed as mass per unit volume of water. The upwards transport by eddy diffusion equals [Equation] (see p. 116) where D is the coefficient of eddy diffusion and dS/dz is the concentration gradient (z is measured positive upwards). The concentration of suspended particles is therefore determined by the equation

---

If the stability of the stratification is very small it may be assumed that near the bottom the eddy diffusion equals the kinematic eddy viscosity, that is, D = A/ρ where A is the dynamic eddy viscosity (p. 483). When dealing with currents near the sea bottom it can furthermore be assumed that in the lowest layers of the water the shearing stress is independent of the distance from the bottom and equals the stress against the bottom. This stress is (p. 479)

Therefore, Substituting this value one obtains the equation which, integrated, gives where the factor 2.303 enters so that base-10 logarithms can be used instead of natural logarithms.

In order to make use of this general formula, specific assumptions must be made as to the variation of the eddy viscosity with increasing distance from the bottom and as to the value of the velocity at the bottom, z₀. Before doing so it is necessary, however, to point out one principal difficulty that is encountered when attacking the problem in this manner, namely, that the theoretical approach leads only to relative values of the concentration of particles in suspension and not to absolute values. Actually, the mechanism which brings the particles into suspension is not clearly understood. It appears that if laminar flow exists along the bottom, that is, if the bottom is hydrodynamically smooth (p. 479), no forces are present which can thrust particles upwards. Upward thrusts probably occur only if the turbulence reaches to the very bottom, as is the case if the bottom is hydrodynamically rough. Where laminar flow is found over a smooth bottom, the velocity is always zero at the bottom and the stress exerted on the bottom varies in time only if the velocity gradient in the laminar boundary layer varies. If, on the other

---

hand, the surface is rough and the flow is turbulent along the bottom, the level at which the average velocity is zero is a fictitious level generally assumed to pass through the deeper or deepest depressions in the bottom. At any distance above this level a certain average velocity is found depending upon the state of turbulence, but this average velocity is subject to great local variations and the instantaneous velocity gradients are subject to similar great variations. Jeffreys (in Cornish, 1934) has pointed out that where the velocity decreases in a horizontal direction the pressure will be greatest, according to Bernoulli's theorem, where the velocity is small in proportion to the velocity gradient. Hence, small particles may be lifted by the upward thrust beneath them and may either immediately drop back, in which case saltation takes place, or may remain in suspension for a long time. However, the absolute amount of material in suspension at any depth cannot be estimated on a theoretical basis.

Some idea as to the size or the equivalent diameter of particles in suspension can be obtained by assuming that the bottom is hydrodynamically rough. In this case (p. 479),

where k₀ = 0.4 is a numerical constant (von K´rm´n's constant), and where z₀ is the “roughness length” of the surface which, according to Prandtl (1932), may be about 1/30 of the vertical dimension of the irregularities of the bottom. Furthermore, and therefore, If the friction velocity, [Equation], is introduced the formula takes the simpler form In fig. 252 are shown two series of curves, one giving the distributions of suspended particles of different diameters at a velocity of 10 cm/sec at 2 m above the bottom, assuming the roughness length of the bottom to be 0.2 cm; the other giving corresponding distributions, assuming the roughness length of the bottom to be 2 cm.

---

If these results are applicable to conditions near the sea bottom, one should expect that (1) very fine sand, silt, and clay can be present in suspension near the bottom, (2) the size of the particles in suspension depends upon the velocity of the current near the bottom and the roughness of the bottom, (3) the greater the velocity and the greater the roughness the larger are the suspended particles, and (4) the coarseness of the suspended material decreases rapidly with increasing distance from the bottom, provided that material of different particle sizes is present on the bottom.

In shallow water, currents of all types can bring particles into suspension. The periodic currents such as tidal currents and currents associated with seiches (p. 538) or tsunamis (p. 544) are probably the strongest; but besides these, permanent currents reaching to the bottom may exist which will carry the suspended material away. The smaller particles can then accumulate only where the deposition is greater than the transportation. This may be the case in shallow areas to which the supply of fine material is great, for example, the Mississippi Delta, or in depressions out of which no fine material is transported, for example those off the coast of southern California (fig. 264, p. 1025), or in landlocked fjords.

In deep water, tidal currents are weak, but currents associated with internal waves (p. 590) may have appreciable velocities near the bottom. The permanent currents are very weak but no matter how weak they are they will transport material, which can accumulate, therefore, only where the permanent currents practically vanish, that is, in the deeper parts of ocean basins. A mechanism thus exists which will tend to sweep all finer material away from submarine ridges and peaks and will lead to accumulation of this material in the ocean basins regardless of

---

whether they are small or large depressions. This mechanism also leads to a sorting of the material. In some regions fine sand may be deposited because the velocities of the currents which carry the particles may decrease, whereas silt may remain in suspension and may be deposited elsewhere. The mechanism of transportation which has been described is so far hypothetical, but studies of the distribution of sediments strongly indicate that a mechanism of this character operates.

Effects of Transportation. The effects of transportation by the various agencies outlined above can be considered from two points of view. One can examine what happens to the shape, size, and composition of individual particles during transportation in the sea, or one can examine the net effect of transporting agencies upon the distribution of sediments. As in other aspects of sedimentation, it is impossible to do more than indicate the general character of the effects because they have not yet been studied sufficiently to afford any quantitative data. Furthermore, the physical or chemical characteristics which may be used as indices of the magnitude of transformation have not been generally applied to the study of marine sediments although the methods have been developed (Krumbein and Pettijohn, 1938).

The effects of transportation upon individual particles may modify their size, shape, and composition. In some cases the size may be increased by, say, the precipitation of calcium carbonate, but in general, transportation will tend to reduce the dimensions of solid material. Such breakdown may be the result of mechanical or chemical processes and generally both will be active. Impact or abrasion may lead to mechanical disintegration and solution, or interaction of the dissolved substances with the solid particles may tend to a reduction in size. These processes may influence not only the size of the particles but also their shape. Fracturing will reduce the size and give rise to angular fragments, whereas abrasion will generally tend to round off the sharp edges and corners. A distinction is drawn between the sphericity of particles, that is, their approach to true spherical form, and the roundness which is a measure of the smoothing away of edges and corners.

The size and shape of individual particles are not only indicative of the character of the transporting agencies and source of material but will also determine many of the properties of the sediment, for example the water content and cohesive properties of the material when wet and when dry and, for larger particles, the character of the orientation and hence the bedding of the individual grains.

The composition of the particles may be affected by the wearing away of the softer or less cohesive material by mechanical agencies or by the solution of the more soluble or more readily attacked portions by chemical processes. Such changes may be determined by examination under the petrographic microscope or by certain chemical or physical tests.

---

If we consider the relative effectiveness of various transporting agencies in affecting the size, shape, and composition of sedimentary material it is obvious that mechanical breakdown is most likely to occur in material moved over the sea bottom by rolling and saltation. Mechanical wear will be most rapid where particles are thrown together violently and repeatedly. In the sea such conditions are found in shallow water, where currents are strong and where the wave action extends to the bottom. The extent to which chemical weathering may act in the sea is not known, but because of the high surface: volume ratio it is undoubtedly effective on small particles and will be a function of the time of exposure rather than the character of the transporting agency. The progressive change in the character of material transported by a given agency depends upon the character of the source material, the changes in competency of the transporting agency, and the material itself and that forming the sea bottom. This general statement applies only to transportation in the water by saltation or rolling over the sea floor, as in all other agencies one or more of the variables are eliminated.

The characteristics of wind-borne material will be largely determined before it reaches the sea and are therefore outside the problem under consideration. The same is generally true of river-borne debris. Discussions of the processes of transformation associated with transportation are given by Twenhofel (1932, 1939) and Russell (1939), and the methods of determining the properties of individual grains are given by Krumbein and Pettijohn (1938).