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

Effects of a narrow gap between a bottom-seated structure and the seafloor (Technical Note)

Longshore bars are often found on many gently sloping beaches of large lakes, bays and sea coasts. A beautiful example can be seen in Fig. 20.1 which gives the aerial view of the Escambia Bay in Florida. Several other typical observations are summarized in Table 20.1. In contrast to bars found in rivers where the flows are essentially unidirectional and characterized by very long time scales (see Chap. 15), coastal bars are usually the products of waves. Of scientific interests are the detailed physics of their generation by waves, as well as their influence on the propagation of waves.

Longshore Bars and Bragg Resonance

Scattering of SH waves in a half-space with simple overground structures is studied analytically. For two-dimensional structures, such as shells, shear walls and a slab-bridge over a river, the method of matched asymptotics is used for sinusoidal waves long compared to the thickness of the structures. Resonance features are deduced analytically and calculated numerically for various incidences and other parameters.

An analytical theory of resonant scattering of SH waves by thin overground structures

For protection against storm tides, four mobile barriers, each of which consists of 20 gates hinged at the bottom axis, have been proposed to span the three inlets of the Venice lagoon. In stormy weather these gates are raised from their housing to an inclination of 50° from the horizon, so as to act as a dam and to keep the water-level difference up to 2 m across the barrier. The gates were originally expected to swing in unison in response to the normally incident waves, but subsequent laboratory experiments revealed that the neighboring gates can oscillate out of phase in a variety of ways and affect the intended efficiency. In this paper we extend the linear theory of Mei, Sammarco, Chan, and Procaccini for trapped waves around vertical rectangular gates and examine the inclined gates by using the hybrid finite-element method to account for the prototype geometry of the gates, the local bathymetry, and the intended sea-level differences. Finite elements are employed only in the immediate neighborhood ...

Numerical solution for trapped modes around inclined Venice gates

For a gradually varying bottom, an approximate theory is developed for the calculation of scattering properties of two-dimensional water waves. An integral representation is first formed with the help of a Green's function. An iterative solution is then obtained by using Rayleigh's wave shoaling equation as the first approximation. The reflection coefficient is found to depend on the smoothness of the obstacle; more abrupt depth changes at the ends cause stronger wave interference. For obstacles with a flat top it is found that under certain conditions only the sloping ends are responsible for wave scattering.

Chiang C. Mei

Papers

Effects of a narrow gap between a bottom-seated structure and the seafloor (Technical Note)

Longshore Bars and Bragg Resonance

An analytical theory of resonant scattering of SH waves by thin overground structures

Numerical solution for trapped modes around inclined Venice gates

Weak Reflection of Water Waves by Bottom Obstacles