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.

/pdf/a-new-view-of-nonlinear-water-waves-the-hilbert-spectrum-42def0zzxb.pdf

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

A nonlinear theory is presented for the resonance of long gravity waves trapped on an uneven bottom when a long packet of short swells is incident. By allowing the trapped wave to be comparable in amplitude to the incident swells, the transient evolution of trapped waves is studied from initial growth through maturity to final decay, for swell packets of finite duration. For a totally submerged ridge, it is found that, while the trapped waves are resonated by second-order periodic modulations of the swell envelope, energy transfer to short swells and nonlinear emission of long waves act as damping mechanisms to limit the amplification. Bottom friction is not qualitatively crucial and affects the results only quantitatively. For a closed beach, breaking of short swells is dealt with empirically but resonant modulation is still the primary factor in exciting surf beats.

Nonlinear excitation of long-trapped waves by a group of short swells

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112084000331

Long waves induced by short-wave groups over an uneven bottom

Oscillating water column at a coastal corner for wave power extraction

The majority of existing single-unit devices for extracting power from sea waves relies on resonance at the peak frequency of the incident wave spectrum. Such designs usually call for structural dimensions not too small compared to a typical wavelength and yield high efficiency only within a limited frequency band. A recent innovation in Norway departs from this norm by gathering many small buoys in a compact array. Each buoy is too small to be resonated in typical sea conditions. In this article a theoretical study is performed to evaluate this new design. Within the framework of linearization, we consider a periodic array of small buoys with similarly small separation compared to the typical wavelength. The method of homogenization (multiple scales) is used to derive the equations governing the macroscale behaviour of the entire array. These equations are then applied to energy extraction by an infinite strip of buoys, and by a circular array. In the latter case, advantages are found when compared to a single buoy of equal volume.

/pdf/wave-power-extraction-by-a-compact-array-of-buoys-4ixqhhtd7i.pdf

Wave-power extraction by a compact array of buoys

Although waves are the primary cause of sediment resuspension in the nearshore zone, in existing theoretical models, long-scale currents induced by the mean wind are often taken to be the only agent for the diffusion and convection of resuspended sediments. We present here theoretical examples where waves play a direct role in all aspects of sediment transport. Details are given for the simple case where only waves are present; the wave-induced current and diffusivity are shown to be no less important than similar factors in the wind-driven current. Hence, in a comprehensive model, one should include not only the current forced directly by the mean wind, but also the current forced by waves which may or may not be forced by the local wind.

/pdf/resuspension-and-transport-of-fine-sediments-by-waves-11zsf4zk25.pdf

Chiang C. Mei

Papers

Nonlinear excitation of long-trapped waves by a group of short swells

Long waves induced by short-wave groups over an uneven bottom

Oscillating water column at a coastal corner for wave power extraction

Wave-power extraction by a compact array of buoys

Resuspension and transport of fine sediments by waves