Growth of Present-Day Concepts, up to 1977
" ... meanders are the result of erosion-deposition processes tending toward the most stable form in which
the variability of certain essential properties is minimized. This minimization involves the adjustment of
the planimetric geometry and the hydraulic factors of
depth, velocity, and local slope. The planimetric geometry of a meander is that of a random walk whose most
frequent form minimizes the sum of the squares of the
changes in direction in each sut;cessive unit length. The
direction angles are then sine functions of channel distance."
This theoretical conclusion has been used in
models of river meanders and in attempts to reconstruct the sinuosity of paleostreams fr om the record
of preserved bedforms.
From the geological viewpoint, quantitative geomorphology has been brought to a relatively advanced state by the work of Schumm, in a variety of
papers culminating in a review article (Sch1,1mm
1972b). Schumm provided a family of empirical
equations relating various hydraulic parameters
to fe atures that could be studied and measured in
ancient fluvial deposits. Leeder (1973) provided a
useful supplement to this, dealing with channel dimensions, and Ethridge and Schumm (1978) provided a review of the methodology. There remains
the problem, mentioned earlier, regarding the applicability of these relationships to riVers flowing under
different climatic regimes. Even in that classic river,
the Mississippi, the concept of the graded river and
all its quantitative ramifications were not fu lly appreciated for many years, as shown by the history of
the many man�made n�ck cutoffs made in the river
since 1931, the success of which appears to have
ranged fr om the dubious to the disastrous (Winkley
1977).
2.3.4 Sediment Transport and Textural Studies
The physics of particle movement is of importance to
fluvial sedimentologists for a variety of reasons: ( 1)
for an understanding of the gross variation in grainsize and other textural parameters in fluvial deposits; (2) as a basis to the understanding of bedform
generation and flow regime concepts; and (3) in
providing an explanation for density sorting of
clastic grain$, of importance in petrological studies,
particularly those dealing with economic placer deposits.
Early studies were concerned with empirical mea�
sures of the current velo<;:ities requjred to move material of diffe rent sizes and with the total volume of
17
sediment transported under various flow condi�
tions. Grabau (l913a) summarized earlier work on
this topic, which included the use of hazelnuts, waln1ltS, peas, pigeons' eggs, and hens' eggs as comparative grain-size standards. However, this pict\lresque
approach to quantification was quickly lost by later
workers. Grabau (1913a) also summarized early
work dealing with particle sorting and roundness, it
being understood that the latter depended on the
size, spedfic gravity, and hardness of the grains,
their distance of transport, and the agents by which
they had been transported. Sorby ( 1908), in a classic
paper on quantification in geological studies, reported on his investigations into particle settling
velociti�s, and angl� of repose. He was the first to
attempt to use experimental laboratory studies in
investigations of geological problems (see also Sect.
2.3.5), but he appears to have been been ignorant of
the many advances made by this time in fluid hydraulics.
An important, widely quoted paper by Gilbert
(1914) reported an extensive series of flume investigations into the transport of sediment by streams,
the stimulus for which arose fr om "an investigation
of problems occasioned by the overloading of certain California rivers with waste from hydraulic
mines". Gilbert was concerned mainly with investigating stream capacity. He examined modes of
transport and concluded:
"Some particles of the bed loild slide; r:pany roll; the
multitide make short sl<:ips or leaps, the process being
called saltation. Saltation grades into suspension.''
Gilbert varied the grade and quantity of debris,
width, and discharg�, and measured the «slope to
which the stream automatically adjusted its bed so as
to enable the current to transport the load". He also
investigated the velocity required to move particles
of different sizes and concluded that competence
varied between the 3.2 and 4.0 power of mean velocity, depending on which experimental conditions,
discharge, slope, and depth, were varied. Gilbert's
(1914) paper was an important bridge between the
disciplines in that he brought many of the techniques of fluid hydraulics to bear on a subject of
considerable geological significance.
Several theoretical developments fo llowed during
the 1920s, including the boundary layer theory, developed mainly by aeronautical engineers, recognition of the importance of bed roughness, and the
suggestion by Jeffreys ( 1929) that particle movement
depends not on velocity or drag force, but upon lift
induced by the velocity gradient or the rat�' of shear
" ... meanders are the result of erosion-deposition processes tending toward the most stable form in which
the variability of certain essential properties is minimized. This minimization involves the adjustment of
the planimetric geometry and the hydraulic factors of
depth, velocity, and local slope. The planimetric geometry of a meander is that of a random walk whose most
frequent form minimizes the sum of the squares of the
changes in direction in each sut;cessive unit length. The
direction angles are then sine functions of channel distance."
This theoretical conclusion has been used in
models of river meanders and in attempts to reconstruct the sinuosity of paleostreams fr om the record
of preserved bedforms.
From the geological viewpoint, quantitative geomorphology has been brought to a relatively advanced state by the work of Schumm, in a variety of
papers culminating in a review article (Sch1,1mm
1972b). Schumm provided a family of empirical
equations relating various hydraulic parameters
to fe atures that could be studied and measured in
ancient fluvial deposits. Leeder (1973) provided a
useful supplement to this, dealing with channel dimensions, and Ethridge and Schumm (1978) provided a review of the methodology. There remains
the problem, mentioned earlier, regarding the applicability of these relationships to riVers flowing under
different climatic regimes. Even in that classic river,
the Mississippi, the concept of the graded river and
all its quantitative ramifications were not fu lly appreciated for many years, as shown by the history of
the many man�made n�ck cutoffs made in the river
since 1931, the success of which appears to have
ranged fr om the dubious to the disastrous (Winkley
1977).
2.3.4 Sediment Transport and Textural Studies
The physics of particle movement is of importance to
fluvial sedimentologists for a variety of reasons: ( 1)
for an understanding of the gross variation in grainsize and other textural parameters in fluvial deposits; (2) as a basis to the understanding of bedform
generation and flow regime concepts; and (3) in
providing an explanation for density sorting of
clastic grain$, of importance in petrological studies,
particularly those dealing with economic placer deposits.
Early studies were concerned with empirical mea�
sures of the current velo<;:ities requjred to move material of diffe rent sizes and with the total volume of
17
sediment transported under various flow condi�
tions. Grabau (l913a) summarized earlier work on
this topic, which included the use of hazelnuts, waln1ltS, peas, pigeons' eggs, and hens' eggs as comparative grain-size standards. However, this pict\lresque
approach to quantification was quickly lost by later
workers. Grabau (1913a) also summarized early
work dealing with particle sorting and roundness, it
being understood that the latter depended on the
size, spedfic gravity, and hardness of the grains,
their distance of transport, and the agents by which
they had been transported. Sorby ( 1908), in a classic
paper on quantification in geological studies, reported on his investigations into particle settling
velociti�s, and angl� of repose. He was the first to
attempt to use experimental laboratory studies in
investigations of geological problems (see also Sect.
2.3.5), but he appears to have been been ignorant of
the many advances made by this time in fluid hydraulics.
An important, widely quoted paper by Gilbert
(1914) reported an extensive series of flume investigations into the transport of sediment by streams,
the stimulus for which arose fr om "an investigation
of problems occasioned by the overloading of certain California rivers with waste from hydraulic
mines". Gilbert was concerned mainly with investigating stream capacity. He examined modes of
transport and concluded:
"Some particles of the bed loild slide; r:pany roll; the
multitide make short sl<:ips or leaps, the process being
called saltation. Saltation grades into suspension.''
Gilbert varied the grade and quantity of debris,
width, and discharg�, and measured the «slope to
which the stream automatically adjusted its bed so as
to enable the current to transport the load". He also
investigated the velocity required to move particles
of different sizes and concluded that competence
varied between the 3.2 and 4.0 power of mean velocity, depending on which experimental conditions,
discharge, slope, and depth, were varied. Gilbert's
(1914) paper was an important bridge between the
disciplines in that he brought many of the techniques of fluid hydraulics to bear on a subject of
considerable geological significance.
Several theoretical developments fo llowed during
the 1920s, including the boundary layer theory, developed mainly by aeronautical engineers, recognition of the importance of bed roughness, and the
suggestion by Jeffreys ( 1929) that particle movement
depends not on velocity or drag force, but upon lift
induced by the velocity gradient or the rat�' of shear