(a) Why do natural streams carry sediments? What mechanical process enables sediment entrainment and transport? What are typical values of bed-material sediment concentration in natural streams? (b) What is wash load?
(a) Natural streams carry sediment because of the no-slip condition, which is due to the finite value of friction at the boundaries. The effect of bottom friction is to produce a bottom shear stress, which is a function of the vertical velocity gradient (Newton's law of viscosity). Typical values of bed-material sediment concentration are 200 to 300 ppm (mg/L).
(b) Wash load is the fraction of sediment load (being transported by the flow), which is not significantly represented in the channel bed and, therefore, not subject to hydraulic calculation.
(a) Describe the criterion describing initiation of motion in natural streams. State the variables involved in the equations. (b) What is the typical value of Froude number that assures initiation of motion?
The Shields criterion describes the condition of initiation of motion in alluvial open-channel flow. This criterion is a dimensionless function expressing the relation between critical dimensionless shear stress τ_*c in the ordinates, and the boundary Reynolds number R_* in the abscissas. In turn, the latter is a function of the shear velocity U_*.
τ_*c = τ_o / [ ( γ_s - γ_s ) d_s ]
R_* = (U_* d_s ) / ν
U_* = (τ_o / ρ )^1/2
The typical value of Froude number that assures initiation of motion is F = 0.08.
What parameter describes the relation between bottom shear stress and mean velocity?
The dimensionless Chezy friction factor f. The relation is:
τ_o = ρ f V²
(a) What is autodredging? Where does it occur? How does it occur? What is the depth of autodredging in the Upper Paraguay river? (b) What is the ecological benefit of autodredging?
(a) Autodredging is the process by which a river increases its bottom roughness and flow depth during low flows, at constant discharge. It occurs where rivers are able to move their beds, i.e., in predominantly alluvial rivers. At low flows, lower regime prevails, and the flow increases form roughness by way of ripples and dunes, effectively leading to an increase in flow depth. The depth of autodredging in the Upper Paraguay river has been documented at 1.2 m.
(b) Autodredging assures a minimum flow depth during the dry season to assure the survival of stream fisheries and related biota.
(a) How may a river profile (bottom slope profile) be used as an indication of changes in sediment transport capacity? (b) In the absence of geologic controls, what is the typical shape of a stream/river profile? Why?
(a) The shape or form of the river profile is an indication that the stream/river is either:(a) alluvial, or (b) controlled by geologic uplift. If the profile is entirely alluvial, the profile will be concave when observed from above, with large slopes upstream (headwaters) and small slopes downstream, at or near the estuary. If the profile is not entirely alluvial, it will show a succession of hills and valleys, where the hills reveal the upward movement of the Earth's crust, and the intervening valleys fill in with sediment, mostly sand-size.
(b) In the absence of geologic controls, the typical shape of a river profile is concave when observed from above. This is because the presence of the ocean, which imposes a hard boundary condition, forcing the stream slopes to gradually reduce as they approach their mouth in the proximity of the ocean.
How does tectonism and the enduring presence of the oceans combine to assure the process of soil sedimentation and, consequently, of valley formation?
Due to tectonism, the upland slopes are typically steep, and the presence of the ocean as a strong downstream boundary condition assures that the channel slope will gradually reduce from steep in the uplands to small in the estuarial lowlands. This fact assures increasing sediment retention in the mid-central valleys, effectively contributing to valley formation.
(a) Explain the relation between the existence of forests, floods, and springs. (b) What was Humboldt's major contribution to science in the early 1900s?
(a) The more forests, the more subsurface flow and, consequently the more the number of springs. The less forests, the more surface flow and, consequently, the larger the floods. When forests are destroyed, the springs dry up entirely or become less abundant, and the river beds are converted into torrents whenever great rains fall.
(b) Humboldt's major contribution to science was his practice of interdiscipline, which disappeared for nearly two centuries after his time.

8. (a) Explain the factors that lead to the meandering of rivers. To what did Albert Einstein attribute the cause of meandering? (b) Is river straightening a solution to river meandering? What is the role of time engineering in river engineering?
(a) The factors responsible for river meandering include: (a) nonuniformity (spatial geometry and sediment size), (b) the Earth's rotation, and (c) the force balance in the transversal direction. Einstein attributed river meandering to the imbalance between forces acting in the transversal direction.
(b) River straightening is not a solution for river meandering, because meandering is a natural process which cannot be completely eliminated. Time engineering has a role explaining river engineering when accomplished specifically for the purpose of controlling meandering. Sooner or later the project will fail and Nature will once again reclaim its course.

9. (a) What distinctive geologic event led to the formation of the Colorado Desert, later renamed Imperial Valley? Describe the sequence of events. (b) What geologic feature assured the existence of the Salton Depression, which in the past century has been used as a repository for agricultural drainage (the Salton Sea)?
(a) Millions of year ago, the Gulf of California extended north to the current geographical location of Indio, north of the Salton Sea. The Colorado river did not exist, and its current hydrologic basin, in Utah and Arizona, was endorheic. About 4-5 million years ago, the Colorado river formed the canyon through Northwestern Arizona, and reached its mouth near Yuma. The large quantities of sediment eroded from the canyon made it to the mouth, and a great portion settled in its proximity, creating a mound with a crest about 13 m above mean sea level. This event effectively isolated the Salton Depression from the sea, and led to the formation of the Colorado Desert.
(b) Active tectonism in the immediate vicinity of the Colorado Desert, including a graben, a depressed block of the Earth's crust, bordered by parallel faults, produced the regional geomorphology that led to the Salton Depression, which in contemporary times (since the 1920's) has been used as a repository for agricultural drainage.

10. (a) Why is a clearwater stream/river hungry for sediment? Explain in detail. (b) Which parameter (or parameters) in the Modified Lane relation are the only ones to be determined empirically? In practice, how does the value of the sediment rating exponent affect the value of the coefficient? Why?
(a) Every natural stream has the built-in capacity to carry sediment, if available in the immediate vicinity, typically the streambed. The amount of sediment a stream/river can carry is referred to as the sediment transport capacity. In general, stream/rivers strive to transport the sediment transport capacity. If for some external reason, the stream loses the sediment it is transporting, it will develop a tendency to pick up bed sediment and other sediment in the vicinity to satisfy its mechanical predilection to transport a certain amount of sediment. This is the reason for the "hungry water."
(b) The coefficient k₁ and exponent m. The lower the value of m, the larger the value of k₁; conversely, the higher the value of m, the smaller the value of k₁. The reason for this behavior is the characteristic shape of the rating curve, featuring a larger slope for low flows and a smaller slope for the high flows.

11. (a) In sand-and-gravel mining of streambeds. Will the negative bed perturbation move upstream or downstream? Explain. (b) What equation is used in sediment routing? What is the limitation of sediment routing as it is practiced?
(a) The negative bed perturbation will move downstream in a one-dimensional analysis. However, the upstream edge may be subject to erosion in three dimensions, in which case the so-called knickpoint will move upstream.
(b) The Exner equation, or sediment continuity equation, is used in sediment routing to model the unsteady transport of sediment. The limitation is that the steady sediment rating curve (steady sediment transport equation) is generally used, for lack of an unsteady rating. The unsteady rating, however, may deviate substantially from the steady rating.