Luna Bergere Leopold

The hydraulic geometry of stream channels and some physiographic implications

Some hydraulic characteristics of stream channels — depth, width, velocity, and suspended load — are measured quantitatively and vary with discharge as simple power functions at a given river cross section. Similar variations in relation to discharge exist among the cross sections along the length of a river under the condition that discharge at all points is equal in frequency of occurrence. The functions derived for a given cross section and among various cross sections along the river differ only in numerical values of coefficients and exponents. These functions are:

The concept of entropy in landscape evolution

_________________________________________ _ General statement _________________________________ _ Aspects of entropy ______ . __________________________ _ Open systems _____________________________________ _ Principle of least work and entropy __________________ _ Longitudinal profile of rivers ________________________ _ Demonstration by use of a random-walk modeL _______ _ Effect of constraint on stream length _________________ _ Pae:e

Bedload transport of fine gravel observed by motion-picture photography

Motion pictures taken at Duck Creek, a clear stream 6.5 m wide and 35 cm deep near Pinedale, Wyoming, provide detailed, quantitative information on both the modes of motion of individual bedload particles and the collective motions of large numbers of them. Bed shear stress was approximately 6 Pa (60 dynes cm −2 ), which was about twice the threshold for movement of the 4 mm median diameter fine gravel bed material; and transport was almost entirely as bedload. The displacements of individual particles occurred mainly by rolling of the majority of the particles and saltation of the smallest ones, and rarely by brief sliding of large, angular ones. Entrainment was principally by rollover of the larger particles and liftoff of the smaller ones, and infrequently by ejection caused by impacts, whereas distrainment was primarily by diminution of fluid forces in the case of rolling particles and by collisions with larger bed particles in the case of saltating ones. The displacement times averaged about 0.2−0.4 s and generally were much shorter than the intervening repose times. The collective motions of the particles were characterized by frequent, brief, localized, random sweep-transport events of very high rates of entrainment and transport, which in the aggregate transported approximately 70% of the total load moved. These events occurred 9% of the time at any particular point of the bed, lasted 1–2 s, affected areas typically 20–50 cm long by 10–20 cm wide, and involved bedload concentrations approximately 10 times greater than background. The distances travelled during displacements averaged about 15 times the particle diameter. Despite the differences in their dominant modes of movement, the 8–16 mm particles typically travelled only about 30% slower during displacement than the 2–4 mm ones, whose speeds averaged 21 cm s −1 . Particles starting from the same point not only moved intermittently downstream but also dispersed both longitudinally and transversely, with diffusivities of 4.6 and 0.26 cm 2 s −1 , respectively. The bedload transport rates measured from the films were consistent with those determined conventionally with a bedload sampler. The 2–4 mm particles were entrained 6 times faster on finer areas of the bed, where 8–16 mm particles covered 6% of the surface area, than on coarser ones, where they covered 12%, even though 2–4 and 4–8 mm particles covered practically the same percentage areas in both cases. The 4–8 and 8–16 mm particles, in contrast, were entrained at the same rates in both cases. To within the statistical uncertainty, the rates of distrainment balanced the rates of entrainment for all three sizes, and were approximately proportional to the corresponding concentrations of bedload.

Bedload sheets in heterogeneous sediment

Field observations in streams with beds of coarse sand and fine gravel have revealed that bedload moves primarily as thin, migrating accumulations of sediment, and coarse grains cluster at their leading edge. These accumulations are one or two coarse grains high and are much longer (0.2-0.6 m long in sand; 0.5-2.0 m in fine gravel) than their height. The authors propose the term bedload sheet for these features, and the authors argue that they result from an instability inherent to bedload movement of moderately and poorly sorted sediment. In essence, coarse particles in the bedload slow or stop each other, trap finer particles in their interstices, and thus cause the coarse particles to become mobile again. Bedload sheets develop on the stoss side of dunes, causing the dune to advance incrementally with the arrival of each sheet. Successive deposition of coarse sediment from the leading edge followed by fine sediment may generate the grain-size sorting that distinguishes cross-bedding. Available flume experiments and field observations indicate that bedload sheets are a common, but generally unrecognized, feature of heterogeneous sediment transport.

River Channel Change with Time: An Example

Monumented channel cross sections were resurveyed over a period of 20 yrs (1953 to 1972) to determine the amount and kind of change of channel area and position on a 3.7-sq-mi basin, Watts Branch near Rockville, Maryland. For the first 12 yrs, the channel progressively but slowly became smaller as urbanization of the basin gradually proceeded. After 1966, a threshold of change apparently was passed and, probably as a result of an increased rate of land alteration upstream, large amounts of sediment were deposited within the channel and overbank. The number of floods exceeding channel capacity increased dramatically from an average of two to more than ten per year. Simultaneously, the channel area began to increase. Despite the trend toward increasing cross-sectional area, the net result after 20 yrs was a channel smaller by 20 percent than it had been originally. Urbanization did not alter the rate of channel migration.

The Greater Yellowstone ecosystem: redefining America's wilderness heritage.

In this important book, experts in science, economics, and law discuss key resource managment issues in the Greater Yellowstone Ecosystem---among them the managment of fire, elk, wolves, and bison---using them as starting points to debate the matter in which humans should interact with the environment of this region. Generously illustrated with special archival photographs of the Yellowstone area, the book will be the major source of information on this area and a valuable resource for worldwide wildland preservation for years to come. This edition contains a postscript written specifically to bring readers up to date on developments affecting the Yellowstone ecosystem between 1990 and 1993.

Trees and streams: The efficiency of branching patterns

Abstract Extending the analysis of branching patterns of the drainage net of rivers, originated by Horton, the relation of average numbers and lengths of tree branches to size of branch was investigated. Size of branch was defined by branch order, or its position in the hierarchy of tributaries. It was found that, as in river drainage nets, there is a definite logarithmic relation between branch order and lengths and numbers. This definite relation is quantitatively comparable, within limits, among river networks, tree branching systems, and several random-walk models in both two and three dimensions. Such a relation appears to be the most probable under the applicable constraints. Moreover the most probable arrangement appears to minimize the total length of all stems in the branching system within other constraints and so, to that extent, achieves a certain efficiency.

River Channel Patterns

From the consistency with which rivers of all sizes increase in size downstream, it can be inferred that the physical laws governing the formation of the channel of a great river are the same as those operating in a small one. One step towards understanding the mechanisms of operation is to describe many rivers of various kinds. The present study is concerned principally with channel pattern. The term refers to limited reaches of channel that can be defined as straight, sinuous, meandering or braided. Channel patterns do not, however, fall easily into well-defined categories, for, as will be discussed, there is a gradual merging of one pattern into another. The difference between a sinuous course and a meandering one is a matter of degree. Similarly, there is a gradation between the occurrence of scattered islands and a truly braided pattern.

Hydrology of some tidal channels in estuarine marshland near San Francisco

Abstract Measurements of velocity, depth, discharge, and slope were simultaneously made at ten gages along a natural estuarine channel 19,000 feet in length in Petaluma Marsh, California. Along the study reach the channel decreases from a width of 47 feet at its mouth to nearly zero at its headward extent, with accompanying decrease in depth. Though gage height varies with time in a smooth sinusoidal manner at all stations, this is not true for velocity, discharge, or slope. Velocity is rather constant for long periods in the ebb cycle and differs but little along the length of the channel. It is somewhat higher on ebb than on flood tide. At most gage sites, velocity continues one-half to one hour after the gage height has reached its maximum or minimum value and reversed. In this channel water surface slope is considerably greater in the midreach of channel than in either the mouthward or headward reaches. Slopes vary from less than .0001 to about .0005 through much of a tidal cycle. At some stages of both ebb and flood, the upper end of the channel has a positive slope while the lower end a negative or adverse slope. At those times the longitudinal profile of water surface is bow shaped or V shaped.

Reversal of Erosion Cycle and Climatic Change

Abstract Successive surveys of the cross section of ephemeral channels in New Mexico over a period of 15 years 1960–1975, show that arroyos that were actively eroding early in the century have reversed the trend and are alluviating. This appears to be associated with the worldwide cooling trend that began about 1940. If the inference proves to be correct, it is significant hydrologically, for it provides some specific knowledge of the climatic conditions associated with the alternate periods of valley erosion and valley alluviation that created the widespread terraces of the semiarid West.