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

Laboratory experiments by earlier authors have shown that the near-surface velocity of an otherwise uniform current is reduced by following waves, but is increased by opposing waves. By a boundary-layer analysis with depth-dependent eddy viscosities, we show analytically that this is the consequence of second-order effects of wave-current interaction. Physical effects of waves on the current profile due to the moving free surface, wave attenuation and convective inertia are discussed. Comparisons with available experiments for smooth and rough seabeds are discussed. New predictions of the longitudinal variations along the current are made.

Effects of surface waves on a turbulent current over a smooth or rough seabed

Mathematical Analysis in Engineering

Future designs of systems for power extraction from ocean waves will likely involve a periodic array of absorbing units. We report an asymptotic theory of scattering and radiation by a linear array of heaving buoys in a channel and attached to power-takeoff devices. The spacing between buoys is assumed to be comparable to the incident wavelength and sea depth but much greater than the buoy size. The effects of extraction rate on the buoy motion, transmission and reflection coefficients for a range of frequencies in and outside the band gap are studied. It is found that strong reflection for frequencies inside the band gap of Bragg resonance reduces the extraction efficiency significantly. For comparison an alternate theory for the efficiency away from the band gap is derived by using Froude-Krylov approximation. The predictions confirms and complements the asymptotic theory.

/pdf/bragg-scattering-and-wave-power-extraction-by-an-array-of-2hzo724szd.pdf

Bragg scattering and wave-power extraction by an array of small buoys

For a long breakwater on a slowly varying bottom as asymptotic theory is given which accounts for the combined effects of refraction and Fresnel diffraction of water waves. Numerical examples are given for two cases: an offshore breakwater and an isolated jetty.

Water motion on a beach in the presence of a breakwater: 1. Waves

Oscillating flows over periodic ripples are of practical as well as scientific interest because of their relevance to beach processes. When either the ripples are sufficiently steep or the amplitude of ambient oscillations large, streamlines of a viscous flow are no longer parallel to the ripple surface. Circulation cells are formed which can help redistribute suspended sediments. Here we study theoretically these cells for a low-viscosity fluid such as pure water over rigid ripples. In particular we have calculated cells whose dimensions are as large as the ripple wavelength and therefore represent viscous effects far above the usual Stokes boundary layer. An idea of Stuart which was originated for stationary mean circulations around a cylinder is extended here. For large ambient amplitude, large oscillating vortices drifting with the ambient flow are found by seeking the stationary cells in a moving coordinate system.

Chiang C. Mei

Papers

Effects of surface waves on a turbulent current over a smooth or rough seabed

Mathematical Analysis in Engineering

Bragg scattering and wave-power extraction by an array of small buoys

Water motion on a beach in the presence of a breakwater: 1. Waves

Oscillating flows over periodic ripples