to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Recent advances in theory and experimen- tation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid-fluid mixtures provide a foundation for a com- prehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoret- ical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining stat- ic; both can deform in a slow, tranquil mode character- ized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompress- ible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (mea- sured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibra- tional energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of ;10 m 3 of poorly sorted, water-saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse-grained surge fronts have little or no pore fluid pressure. In contrast, finer-grained, thoroughly saturated debris be- hind surge fronts is nearly liquefied by high pore pres- sure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic mod- els of debris flows therefore require equations that sim- ulate inertial motion of surges in which high-resistance fronts dominated by solid forces impede the motion of low-resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristi- cally originate as nearly rigid sediment masses, trans- form at least partly to liquefied flows, and then trans- form again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth-averaged equations of motion patterned after those of the Savage-Hutter theory for gravity-driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behav- iors intermediate between those of wet rock avalanches and sediment-laden water floods. With appropriate pore pressure distributions the equations yield numerical so- lutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

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The physics of debris flows

The flow of homogeneous fluids through porous media: analogies with other physical problems

The finite difference method at arbitrary irregular grids and its application in applied mechanics

Nearly 40 years of theoretical development and practical experience has been incorporated in this book, which has won numerous awards as a scientific and technical publication in China. Now updated and fully translated into English, this volume is the first attempt in the field to unify the movement of sediment and boundary conditions. Going far beyond any book of its kind, it presents a synthetic analysis and thorough coverage of many schools of thought and provides practical survey of this discipline of the science. The authors introduce a synthesis of information gleaned from more than 800 papers spanning the fields of hydraulic engineering, mathematics, physics, geology, rheology, and chemistry, giving the reader a profound understanding of the present status and direction of the industry's research efforts. The volume includes chapters dedicated to rate phenomena and topics such as hyperconcentrated flows, effect of sediment existence on water flow, large-scale hydraulic construction on sediment-laden streams, and specialized research not available outside of China.

Mechanics of Sediment Transport

A solution is obtained for stream flow depletion created by pumping from a well beside a stream. This solution assumes that streambed penetration of the aquifer and dimensions of the streambed cross section are all relatively small. It also assumes that the streambed is clogged and that a linear relationship exists between the outflow seepage through the streambed and the change in piezometric head across the semipervious clogging layer. The solution is general enough to include the earlier solutions of Theis, Glover and Balmer, and Hantush. A solution is also obtained for the drawdown at any point within the aquifer, and it is suggested that this solution might be matched with experimental field data to obtain estimates for aquifer and streambed leakage parameters.

Unsteady Stream Depletion from Ground Water Pumping

Calculations are carried out first for steady fully developed laminar flow on a slope. Application of this result to field data published in a previous paper by another author suggests that many debris flows are laminar. Then singular perturbation techniques are used to obtain first‐order solutions for unsteady non‐uniform flow from a point source on a steep slope. Solutions are obtained for both laminar and turbulent flows, and it is found that the laminar flow model gives the best description of laboratory data obtained by a previous investigator. A number of differences are observed in the behavior of the outer (kinematic wave) solutions for laminar and turbulent flow, and it is suggested that it is probably not possible to describe all debris flows and avalanches with laminar flow models. It is also suggested that more comparisons need to be made between theoretical results and field data measurements.

Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches

Solutions and verification of a scale-dependent dispersion model.

Solutions are given for instantaneous, continuous, and steady-state sources of pollution in uniform ground water flow. Then these solutions are used to determine how long a continuous source must be in place before steady-state conditions are approached, to determine the effect of a finite aquifer depth upon solutions for an infinite aquifer depth, to calculate maximum concentrations for instantaneous sources, and to determine the time required for solutions for a point source and a source of finite size to approach each other.

Dispersive Sources in Uniform Ground-Water Flow

A solution is obtained for flow depleted from a stream when water is pumped from an adjacent well in a semiconfined aquifer. The streambed partially penetrates the aquitard, which forms the top boundary of the pumped aquifer, and the distance between the well and stream is assumed large enough to allow the stream to be modeled with a zero width. The governing partial differential equations for this problem are shown to be equivalent to the equation postulated and solved by Boulton for flow to a well in a delayed-yield aquifer. Consequently, drawdown curves and plots of stream depletion versus time are all found to have two inflection points. However, unlike the solution behavior for Boulton’s problem, aquifer recharge furnished by the stream causes all drawdown and stream depletion curves to approach horizontal asymptotes as time becomes infinite. The solution calculated herein is general enough to reduce to a solution calculated earlier by Hunt when the aquitard becomes impermeable.

Bruce Hunt

Papers

Unsteady Stream Depletion from Ground Water Pumping

Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches

Solutions and verification of a scale-dependent dispersion model.

Dispersive Sources in Uniform Ground-Water Flow

Unsteady Stream Depletion when Pumping from Semiconfined Aquifer