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).

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Among the current problems that hydrogeologists face, perhaps there is none as challenging as the characterization of fractured rock (Faybishenko and Benson 2000). This paper discusses issues associated with the quantification of flow and transport through fractured rocks on scales not exceeding those typically associated with single- and multi-well pressure (or flow) and tracer tests. As much of the corresponding literature has focused on fractured crystalline rocks and hard sedimentary rocks such as sandstones, limestones (karst is excluded) and chalk, so by default does this paper. Direct quantification of flow and transport in such rocks is commonly done on the basis of fracture geometric data coupled with pressure (or flow) and tracer tests, which therefore form the main focus. Geological, geophysical and geochemical (including isotope) data are critical for the qualitative conceptualization of flow and transport in fractured rocks, and are being gradually incorporated in quantitative flow and transport models, in ways that this paper unfortunately cannot describe but in passing. The hydrogeology of fractured aquifers and other earth science aspects of fractured rock hydrology merit separate treatments. All evidence suggests that rarely can one model flow and transport in a fractured rock consistently by treating it as a uniform or mildly nonuniform isotropic continuum. Instead, one must generally account for the highly erratic heterogeneity, directional dependence, dual or multicomponent nature and multiscale behavior of fractured rocks. One way is to depict the rock as a network of discrete fractures (with permeable or impermeable matrix blocks) and another as a nonuniform (single, dual or multiple) continuum. A third way is to combine these into a hybrid model of a nonuniform continuum containing a relatively small number of discrete dominant features. In either case the description can be deterministic or stochastic. The paper contains a brief assessment of these trends in light of recent experimental and theoretical findings, ending with a short list of prospects and challenges for the future.

Trends, prospects and challenges in quantifying flow and transport through fractured rocks

A Modern Introduction to the Mathematical Theory of Water Waves. By R. S. Johnson. Cambridge University Press, 1997. xiv+445 pp. Hardback ISBN 0 521 59172 4 £55.00; paperback 0 521 59832 X £19.95.

Hydrodynamic and hydromagnetic stability

Structural permeability effects on the interaction of a solitary wave and a submerged breakwater

Turbulence and energy dissipations of surf-zone spilling breakers

In the present study, the flow field of a momentum jet discharged vertically into a wave environment has been investigated. Three distinct processes which increase the dilution rate of the pollutant concentration have been identified by the flow visualization method. They are jet deflection, “wave tractive mechanism”, and wake vortex structure. A highly precise LIF-LDV system was developed to measure simultaneously the two-dimensional velocity field and tracer concentration. The measurements show dramatic variations not only in the longitudinal distribution of the mean jet axis but also in the cross-sectional profiles. A realistic model is also derived to estimate the initial dilution rate under the wave action.

On the interaction of a turbulent jet with waves

Examination of empirical formulas for wave shoaling and breaking on steep slopes

In order to understand the relationship between entrained air bubbles and energy transfer inside surf zone, a special technique of He-Ne laser and 2D LDV were employed to investigate the characteristics of air bubbles concentration and velocity fields, respectively. The experimental results shows that the concentration profiles of air bubbles decay hyperbolically in the vertical direction and exponentially in the horizontal direction. With appropriate parameter groups, the distributions of air bubbles show a characteristics of similarity. The potential energy, kinematic energy and total energy decrease with the horizontal distance except that the kinematic energy slightly increases between the impinging point and the maximum penetration. Within this region, the energy loss of potential energy and kinematic energy is almost transferred to the air bubbles to merge into the water body.

/pdf/energy-dissipation-and-air-bubbles-mixing-inside-surf-zone-1wijzgj3fj.pdf

Hwung-Hweng Hwung

Papers

Structural permeability effects on the interaction of a solitary wave and a submerged breakwater

Turbulence and energy dissipations of surf-zone spilling breakers

On the interaction of a turbulent jet with waves

Examination of empirical formulas for wave shoaling and breaking on steep slopes

Energy dissipation and air bubbles mixing inside surf zone