Mainstream length in river networks from various parts of the world varies statistically in proportion to basin area raised to a power that decreases from about 0.6 for small to medium basins (1–10 3 km 2 ) to near 0.5 for the largest in the world (nearly 10 7 km 2 ). This relationship is predicted by the statistical theory of channel networks, which is founded on the basic postulates that (1) natural channel networks in the absence of strong geologic controls are very nearly topologically random and (2) interior and exterior link lengths and associated areas in basins with homogeneous climate and geology have separate statistical distributions that are approximately independent of location. The calculation was carried out by a Monte Carlo method, which produced a random sample of networks from the postulated population, and was checked by analytical results for networks up to magnitude 500. The necessary empirical data on link lengths and associated areas were obtained by measurement on maps of an 80‐km 2 basin in relatively flatlying coal‐bearing sandstones in eastern Kentucky. Agreement with observation is excellent for the small to medium basins, but the ratio of predicted to observed mainstream length progressively decreases to about 0.7 for the largest basins. This discrepancy can be accounted for by moderate downstream increase in channel sinuosity and decrease in drainage density. The particular data on link lengths and associated areas used in the calculation have only slight influence because mean link length varies statistically directly as the square root of mean associated area, so that taking data from different areas merely displaces the predicted points nearly parallel to their trend.
Theoretical modeling of the subduction channel (shear zone) at convergent plate margins quantifies the processes of sediment subduction, offscraping, underplating and formation of subduction melange by upwelling. Although bedding anisotropy and variations in lithology and pore-fluid pressure control the details of the deformation near the inlet to the subduction channel, the theory shows there are only five basic kinematic patterns which can result in the development of a distinctive type of margin (Types A-E). All incoming sediment is subducted and subduction erosion can occur at Type A margins. All sediment is subducted but a thick, narrow accretionary prism grows by underplating of subducted sediment at Type B margins. Offscraping leads to the development of a broad, tapering prism at Type C, D, and E margins. Incoming sediment is offscraped and subducted sediment is underplated at Type C margins. Melange upwells from depth and is offscraped and underplated at Type D and E margins. Incoming sediment is also offscraped at Type D margins. The structural and metamorphic histories of the fundamental tectonostratigraphic units within the accretionary prism are distinct during steady-state subduction. The bedded slope cover is not metamorphosed and not intensely tectonized upslope from the inlet. During final dewatering andmore » accretion, offscraped materials undergo a subhorizontally-directed compression whereas underplated materials undergo a simple-shear-style of deformation. The metamorphic changes in subducted sediment or upwelled melange depend upon the depth of maximum burial and the thermal structure of the margin. Various episodic factors, such as seamount or ridge subduction, can modify the structural and metamorphic contrasts.« less
In natural flows, bed sediment particles are entrained and moved by the fluctuating forces, such as lift and drag, exerted by the overlying flow on the particles. To develop a better understanding of these forces and the relation of the forces to the local flow, the downstream and vertical components of force on near‐bed fixed particles and of fluid velocity above or in front of them were measured synchronously at turbulence‐resolving frequencies (200 or 500 Hz) in a laboratory flume. Measurements were made for a spherical test particle fixed at various heights above a smooth bed, above a smooth bed downstream of a downstream‐facing step, and in a gravel bed of similarly sized particles as well as for a cubical test particle and 7 natural particles above a smooth bed. Horizontal force was well correlated with downstream velocity and not correlated with vertical velocity or vertical momentum flux. The standard drag formula worked well to predict the horizontal force, but the required value of the drag coefficient was significantly higher than generally used to model bed load motion. For the spheres, cubes, and natural particles, average drag coefficients were found to be 0.76, 1.36, and 0.91, respectively. For comparison, the drag coefficient for a sphere settling in still water at similar particle Reynolds numbers is only about 0.4. The variability of the horizontal force relative to its mean was strongly increased by the presence of the step and the gravel bed. Peak deviations were about 30% of the mean force for the sphere over the smooth bed, about twice the mean with the step, and 4 times it for the sphere protruding roughly half its diameter above the gravel bed. Vertical force correlated poorly with downstream velocity, vertical velocity, and vertical momentum flux whether measured over or ahead of the test particle. Typical formulas for shear‐induced lift based on Bernoulli's principle poorly predict the vertical forces on near‐bed particles. The measurements suggest that particle‐scale pressure variations associated with turbulence are significant in the particle momentum balance.
Abstract In August 1961 an aluminum pipe (3.5 cm. internal diameter, 4.2 cm. external diameter) having 92 specially modified socket couplings (5.0 cm. external diameter) sealed with a quick-polymerizing synthetic rubber was sunk 226 m. in a vertical water-filled bore hole in Blue Glacier, Washington. U.S.A. The geometry of threads and mating surfaces of pipe and coupling was designed to cause increasing external water pressure to tighten the seal. One joint at a depth of 66 m. immediately developed an extremely slow leak (probably because of faulty cleaning), but the other 91 joints apparently were sound, as the pipe was free of water to a depth of at least 157 m. when resurveyed after one year.
Individual channel networks ordinarily are portions of far larger, essentially infinite, networks. The overall network is by definition at infinite topologically random network if the populations of subnetworks within it are topologically random. From such a network, the probability of randomly drawing a link, a subnetwork, or a basin with Strahler order $$\omega is 1/2^{\omega}$$; and that of randomly drawing a stream of order $$\omega is 3/4^{\omega}$$. The probability of drawing a link of magnitude $$\mu$$, that is, one having $$\mu$$ sources ultimately tributary to it, is equal to the probability of a first passage through the origin at step $$2\mu - 1$$ in a symmetric random walk, a fact which suggests a useful mathematical analogy between random walks and infinite topologically random networks. Assuming uniform link length equal to the constant of channel maintenance, which in turn is the reciprocal of drainage density, the probability distributions for links and streams of various orders may be interpreted as crude geomorphological "laws" analogous to Horton's laws of drainage composition. These distributions predict geometric-series "laws" in which, using Strahler orders, the bifurcation ratio is 1/4, the link-number ratio is 1/2, the length ratio is 2, the cumulative-length ratio is 4, and the basin-area ratio is 4, all in good agreement with the observed ratios. They also predict values of 4/3 and 2/3, respectively, for the dimensionless ratios of total number of Strahler streams to network magnitude and of Strahler stream frequency to the square of the drainage density, in agreement with the values of 1.34 and 0.694 found empirically.
Abstract A network of passages situated along three-grain intersections enables water to percolate through temperate glacier ice. The deformability of the ice allows the passages to expand and contract in response to changes in pressure, and melting of the passage walls by heat generated by viscous dissipation and carried by above-freezing water causes the larger passages gradually to increase in size at the expense of the smaller ones. Thus, the behavior of the passages is primarily the result of three basic characteristics: (1) the capacity of the system continually adjusts, though not instantly, to fluctuations in the supply of melt water; (2) the direction of movement of the water is determined mainly by the ambient pressure in the ice, which in turn is governed primarily by the slope of the ice surface and secondarily by the local topography of the glacier bed; and, most important, (3) the network of passages tends in time to become arborescent, with a superglacial part much like an ordinary river system in a karst region, an englacial part comprised of tree-like systems of passages penetrating the ice from bed to surface, and a subglacial part consisting of tunnels in the ice carrying water and sediment along the glacier bed. These characteristics indicate that a sheet-like basal water layer under a glacier would normally be unstable, the stable form being tunnels; and they explain, among other things, why ice-marginal melt-water streams and lakes are so common, why eskers, which are generally considered to have formed in subglacial passages, trend in the general direction of ice flow with a tendency to follow valley floors and to cross divides at their lowest points, why they are typically discontinuous where they cross ridge crests, why they sometimes contain fragments from bedrock outcrops near the esker but not actually crossed by it, and why they seem to be formed mostly during the later stages of glaciation.
Blackhawk Mountain, a resistant mass of marble thrust northward over uncemented sandstone and weathered gneiss, rises above southeastern Lucerne Valley at the eastern end of the rugged 4000-foot escarpment that separates the San Bernardino Mountains on the south from the Mojave Desert on the north. Spread out on the alluvial apron at the foot of the mountain is the Blackhawk rockslide, a lobe of nearly monolithologic marble breccia 30 to 100 feet thick, 2 miles wide, and nearly 5 miles long. At least two earlier similar but smaller rockslides have occurred in the area.
The rocks of the area comprise late Tertiary and Quaternary fanglomerates and breccias derived mainly from the gneiss, quartzite, Carboniferous marble, and Cretaceous quartz-monzonite of the San Bernardino Mountains. Uplift of Blackhawk Mountain occurred in two stages after deposition of the older fanglomerates and breccias: the first by over-thrusting from the south, and the second by monoclinal folding along a northwest-trending axis.
Geological evidence in the area shows that the Blackhawk rockslide traversed the gently inclined alluvial slope as a nearly nondeforming sheet of breccia moving more than 50 miles per hour. The hypothesis that compressed air, rather than water or mud, constituted the lubricating layer on which the breccia sheet slid qualitatively explains all of the principal physical features of the slide lobe. Theoretical analysis of the flow in the lubricating air layer indicates the quantitative feasibility of the air-lubrication hypothesis for the Blackhawk slide.
The proceedings of the 4th Symposium on River, Coastal and Estuarine Morphodynamics offers the latest research results concerning quantitative modelling of the interaction of water and sediment and the shapes this interaction makes in rivers, watersheds, estuaries, the coast, the continental shelf and the deep sea. Morphodynamics is the study of the evolution of landscape and seascape features, from small scale to large.
