There seems to be some relation between the width of the belt within which a stream meanders, and the width of the stream itself. Recently it has been estimated that the ratio between them is 18:1.[72]
During the development of the meanders it is to be noted that lateral planation on the one side of a stream is accompanied by deposition on the other. This is cut-and-fill. The sediment eroded from the curve which is concave toward the stream is shifted down-stream, while that deposited in the curve which is convex toward the stream is brought down from above. Thus even in the development of meanders, the material which is dislodged is shifted down-stream. Since the current directed against the down-stream side of a growing meander is on the average stronger than that directed against the opposite side, the meander itself has a tendency to migrate down-stream ([Fig. 182]).
In their evolution, the curves of a stream’s channel often reach and undermine the valley bluff ([Pl. VII]). Since the meanders are, on the average, shifted down-stream individually, and since meanders are frequently developed in new places, it follows that a meandering stream tends to widen its valley throughout. Widening is also effected in other ways, for a stream with a flood-plain sometimes abandons its channel altogether for miles at a stretch, and the new course chosen may be against one of the bluffs of the valley. Such changes are most likely to take place where deposition along channel and levees has brought the part of the flood-plain (though not necessarily the bottom of the channel) adjacent to the stream above the level of that farther from it ([Fig. 178]). The change is likely to be effected in time of flood.
Flood-plains often attain great size. That of the Mississippi below the Ohio ([Fig. 179]) has a width ranging from rather more than 20 miles at Helena (Ark.), to something like 80 miles in the latitude of Greenville (Miss.).[73] Below the Ohio its area is something like 30,000 square miles, and its entire area has been estimated at about 50,000 square miles.[74]
Theoretically, the rotation of the earth should affect the erosion of streams, increasing it on the one bank (the right in the northern hemisphere and the left in the southern) and decreasing it on the other.[75] The streams doubtless accommodate themselves to the rotation of the earth in the original development of their gradation-plains and flood-plains, and the later effects of rotation are usually inconspicuous.
Fig. 184.—Meanders of Trout Creek, Yellowstone Park. (Walcott, U. S. Geol. Surv.)
Scour-and-fill.—It has already been shown that aggrading streams cut laterally at the same time that they build up their plains. It is now to be added that they periodically deepen their channels to a notable extent, and that the deepening of the channel takes place at the very time when the flood-plain is being aggraded. In other words, the stream in flood aggrades its plain, and degrades its channel. This follows from the fact that the current is sluggish in the former position, where the water is shallow, and rapid in the latter, where it is deep. When the flood subsides, the channel, deepened while the current was torrential, is filled again by the feebler current which follows. This alternate deepening and filling is known as scour-and-fill. It is well illustrated by the Missouri River. At Nebraska City, scour is believed to occasionally reach depths of 70 to 90 feet.[76] At Blair, about 25 miles above Omaha, the same river is believed to cut to bed-rock (about 40 feet below the bottom of the channel in low water) twice a year, that is, during floods.[77] [Fig. 185] shows the changes recorded in the channel of the river at this point during the year 1883. It shows that the scour-and-fill during this year amounted to almost 40 feet. All streams similarly situated do a like work. The material thus eroded is shifted down-stream, some of it for short distances only, and some of it to the sea. Even an aggrading stream therefore is not without erosive activity; it is a stream whose fill exceeds its scour, not one which has ceased to erode.
Fig. 185.—Diagram illustrating scour and fill in the Missouri River. A record of soundings at Blair Bridge (near Omaha), 1883. Shows also the cross-sections of the river at various rates. (Todd, Bull. 158, U. S. Geol. Surv.)