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).

Sea wave energy is being increasingly regarded in many countries as a major and promising resource. The paper deals with the development of wave energy utilization since the 1970s. Several topics are addressed: the characterization of the wave energy resource; theoretical background, with especial relevance to hydrodynamics of wave energy absorption and control; how a large range of devices kept being proposed and studied, and how such devices can be organized into classes; the conception, design, model-testing, construction and deployment into real sea of prototypes; and the development of specific equipment (air and water turbines, high-pressure hydraulics, linear electrical generators) and mooring systems.

Wave energy utilization: A review of the technologies

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

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A new view of nonlinear water waves: the Hilbert spectrum

Dynamics of structures

Equations of motion are derived for long waves in water of varying depth. The equations are for small amplitude waves, but do include non-linear terms. They correspond to the Boussinesq equations for water of constant depth. Solutions have been calculated numerically for a solitary wave on a beach of uniform slope. These solutions include a reflected wave, which is also derived analytically by using the linearized long-wave equations.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112067002605

Long waves on a beach

Fluid mud found at the bottom of some estuaries and coastlines contains a high concentration of clay particles. The rheological properties of this cohesive material is very complex and there have been vastly different models for predicting the mutual effects of mud and waves. In this paper we focus on the Bingham-plastic behavior known to exist in estuary and river mud with high concentration. By including interfacial friction, motion in a thin mud layer Induced by a solitary wave propagating in a much thicker layer of overlaying water is analyzed. Effects of the mud motion on wave damping is then calculated for both horizontal and sloping sea beds.

Effects of Wave-Induced Friction on a Muddy Seabed Modelled as a Bingham-Plastic Fluid

Transmission of random wind waves through perforated or porous breakwaters

: Problems of scattering and radiation of water waves by rectangular or circular bodies are formulated within the framework of linearized potential theory The objective is to find the far field wave amplitude due to radiation by a body oscillating in a prescribed manner or the disturbance caused by a body fixed in the path of an obliquely incident train of waves The radiation results can be used in conjunction with Haskind's theorem to establish the forces (moment) an incident wave induces on a fixed body Further, the radiation results are useful in establishing the damping coefficients associated with forced body oscillation Specific results which are obtained are the complex reflection and transmission coefficients for two dimensional obstacles including the limiting cases of thin vertical barriers, thin surface strip, and submerged gap Also the total and differential scattering cross-sections for vertical circular cylinders are presented Radiated wave amplitudes are given for bodies oscillating in heave, sway, or roll, as well as the forces induced on fixed bodies by incident waves Comparison with experimental and theoretical results by others is included (Author)

Scattering and radiation of water waves.

The time required to pull a large object from a sandy seabed is estimated by assuming that the seabed is porous but rigid. The phenomenon of breakout (i.e., sudden release) is shown to occur without the assumption of elasticity of the soil skeleton (Foda 1982). A new case of wedge-shaped gap is also studied, and compared to a uniform gap, Laboratory experiments are shown to support the theory.

Chiang C. Mei

Papers

Effects of Wave-Induced Friction on a Muddy Seabed Modelled as a Bingham-Plastic Fluid

Transmission of random wind waves through perforated or porous breakwaters

Scattering and radiation of water waves.

Lifting of a large object from a porous seabed

Note on sediment sorting in a sandy bed under standing water waves