RIVER PROCESSES

An introduction to fluvial dynamics

Andre Robert

• Publisher: Routledge
• Year: 2014
• ISBN:
  9781134639311
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geography
• Index: Geography

River Processes deals primarily with flow and sediment dynamics in alluvial channels. It emphasises water flows (basic principles and characterisation), fluvial sediment, processes of erosion and sediment transport, bedforms that result from flow-bed sediment interactions in sand and gravel, flow and sedimentary processes in curved, braided and confluent channels, as well as aquatic habits. River Processes provides a comprehensive synthesis of current knowledge about physical processes in alluvial channels, with an emphasis on the recent work on flow-bed-sediment transport interactions. It is intended primarily for undergraduate students interested in fluvial studies as part of physical geography, earth sciences, environmental sciences and ecology courses. The textbook is fully illustrated throughout with line drawings and photographs.

1

FLUVIAL PROCESSES: AN INTRODUCTION

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1.1 BASIC PRINCIPLES

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The word fluvial is a general term that refers to anything produced by the action of a river, and also to organisms that are found in rivers (i.e. fluvial forms, fluvial processes, fluvial sediments and freshwater organisms; Thomas and Goudie, 2000).Dynamics, in turn, is a branch of physical science (and a subdivision of mechanics) that is concerned with moving bodies and the physical factors that affect the motion: force, mass, momentum and energy.(Kinematics, in comparison, describes motion, without regard to its causes in terms of position, velocity, and acceleration.) The term fluvial dynamics, therefore, is generally used with reference to water flow, sediment movement, and to bedform features resulting from the interactions of flow and sediment transport in alluvial channels.

1.1.1 Physical quantities

A relatively small number of quantities are needed to explain fluvial geo-morphic processes. One of these quantities therefore is force, which can be loosely defined as anything that changes or tends to change the state of motion in a body (Ritter et al., 1995). Force is a vector quantity, which means that it has both magnitude and direction. A force balance relation is often used in fluvial geomorphology, where a driving force and a resistance force are investigated together. To paraphrase Ritter et al. (1995), fluvial geomor-phology can then be examined by using physical concepts that revolve around the application of force on surface materials. All movement is the result of forces, and in the natural environment, several forces are generally involved in a particular situation.

In more specific terms, a force is defined in terms of moving a mass with a particular acceleration:

F = ma (1.1)

where F is force, m is the mass of a body and a is acceleration. Gravitational attraction is a basic force in Earth science. Acceleration due to gravity varies very little over the Earth’s surface, and is considered constant at 9.81 m s⁻². The measure of force (F) is weight and the standard unit of force is the newton (or dyne). A newton is the force necessary to give a mass of 1 kg an acceleration of 1 m s⁻². When expressed as a force per unit area, this is referred to as stress, and expressed in newtons per square metre (N m⁻²) or pascal (Pa). It is common in fluvial studies to employ dynes cm⁻², where 1 dyne = 10⁻⁵ N (with 10 dyn cm⁻² being equal to 1 N m⁻²). The concept of shear stress, for instance, is absolutely crucial in fluvial studies, and this will be explained in detail later.

There are a number of additional quantities derived from force. Work (W) is determined from the product of force and distance. More specifically, the amount of work done is defined as the product of force and the displacement of the body in the direction of the force. For instance, in order for a stream to move a cobble from one point to another, an adequate force must be exerted over the required distance (and therefore work must be done). The unit of work is the joule (J), which is the work done when a force of 1 N acts over a distance of 1 metre.

Related to the concept of work is energy, which can be defined as the ability or capacity to do work. Work and energy possess the same units. Water flowing above a rough surface involves the expenditure of energy (see section 2.2 for a detailed account of energy principles). In simple terms, the potential energy of a body results from its position relative to some reference level, while the kinetic energy of a body results from its motion. The potential energy of water therefore decreases along the length of a stream as its elevation above sea-level decreases. On the other hand, average stream velocity increases along river segments of sufficient length and the kinetic energy of the flow increases as potential energy decreases and water flows down the channel. The flow of water downstream is obviously resisted by the alluvial channel sediment (which tends to significantly limit flow acceleration), and the energy expenditure is significantly affected by changes in bed material size and related depositional features in the downstream direction in rivers (see Chapters 3 and 4 in particular).

Finally, the concept of power is also directly related to force and work. Power is the rate of doing work, and is obtained by dividing the work done by the time period considered. In order to push a body from one point to another, a small force can be exerted over a long period of time or a large force over a short period of time. The net effect is the same but, in the second strategy, higher power must be developed. Stream power has been a dominant concept in fluvial geomorphology in relation to sediment transport processes (Bagnold, 1977, 1980).

1.1.2 Dimensional character

A number of rules can be formulated for the analysis and manipulation of physical quantities commonly encountered in fluvial studies (Dingman, 1984, pp. 7–11). Most of them are very simple but are sometimes neglected or overlooked.

■ The numerical magnitude of a physical quantity has no meaning without complete information on the unit(s) of measurement.

■ The dimensional character of a physical quantity is expressed as either some combination of length (L), mass (M), time (T) and temperature, or is dimensionless (although temperature is often neglected in fluvial studies, unless dealing with viscosity and Reynolds numbers, as explained later).

■ The dimensional character of each physical quantity can be expressed as:

M^a L^b T^c

where a, b, and c are integers or a ratio of integers. For dimensionless numbers, a = b = c = 0, and the dimensional character is expressed as [1].

■ An equation that completely and correctly describes a physical relation has the same dimensions on both sides of the equal sign.

■ When the dimensions are different, such an equation is referred to as inhomogeneous. In an inhomogeneous equation, the units of each variable in the equation must be specified. In this type of equation, all constants must be changed if the equation is to be used in another system of units (and the equation expresses, at best, a correlation).

The basic physical quantities and their dimensional character used in fluvial studies are the following:

■ Velocity, a vector quantity, is the rate at which the position of a given body changes with time (L T⁻¹⁾).

■ Acceleration is the rate of change of velocity with time and has the dimensions:

(L T⁻¹)/T = L T⁻¹ T⁻¹ = L T⁻²

Thus a body is said to have an acceleration when its velocity changes in magnitude as the motion proceeds.

■ Momentum is a vector defined by the product of the mass of a given body and its velocity (M L T⁻¹). Momentum flux (M L T⁻²) is also often used in fluvial studies. The momentum per unit time (or momentum flux; Chanson, 1999) of a water body passing a particular point in a stream can be determined from ρQU, where ρ is water density (usually assumed to be constant at 1000 kg m⁻³), Q is discharge (L³ T⁻¹), and U is average velocity.

■ Force is defined in terms of moving a mass with a particular acceleration, and hence has a dimension resulting from multiplying mass and acceleration, i.e. M L T^–2.

■ Stress is force divided by area, and the dimensional character becomes (M L T²)/L² =M L⁻¹ T². Pressure also has dimensions resulting from dividing a force by an area. The measure bar (as often used, for instance, in meteorology) is taken to be equivalent to a pressure of 10⁵ N m⁻².

■ Work is defined as force times distance, which becomes M L T². L = M L²T². The unit for work is the joule (J).

■ Energy is defined as the ability or capacity to do work, and is dimension-ally equivalent to work.

■ Power is the rate of doing work. Rate of doing work is work divided by time: (M L²T²)/T, which becomes M L² T³. The units for power are watts (W). This is achieved when one joule is being expended per second (1 watt =...