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

Erratum for “Mass Transport by Waves and Offshore Sand Bedforms”

Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake tsunamis in the open ocean in that (i) the affected areas are usually within the near-field of the source, (ii) the highest runup occurs within the time period of the geophysical event, and (iii) the enclosed geometry of a lake does not let the tsunami energy escape. To address the problem of transient landslide tsunami runup and to predict the resulting inundation, we utilize a nonlinear model equation in the Lagrangian frame of reference. The motivation for using such a scheme lies in the fact that the runup on an inclined boundary is directly and readily computed in the Lagrangian framework without the need to resort to approximations. In this work, we investigate the inundation patterns due to landslide tsunamis in a lake. We show by numerical computations that Airy's approximation of an irrotational theory using Lagrangian coordinates can legitimately predict runup of large amplitude. We also demonstrate that in a lake of finite size the highest runup may be magnified by constructive interference between edge-waves that are trapped along the shore and multiple reflections of outgoing waves from opposite shores, and may occur somewhat later after the first inundation.

Landslide Tsunamis in Lakes

Sandbar Formation Under Surface Waves

The tidal waves scattered by a small island and a small cape of elliptical shape are derived by the method of matched asymptotics. The results complement the irrotational flow approximation of the near field by Proudman (Proc. Lond. Math. Soc., vol. 14, 1915, pp. 89–102). The potential for harnessing tidal power is assessed for the limiting case of a coast-connected thin dam.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5BDDA5A63C9BF8C4FBF372950F95219D/S0022112020003778a.pdf/div-class-title-tidal-diffraction-by-a-small-island-or-cape-and-tidal-power-from-a-coastal-barrier-div.pdf

Tidal diffraction by a small island or cape, and tidal power from a coastal barrier

: When a fluid is in periodic wave motion, the particles are carried by a varying velocity field The location of a particle varies as does the immediate velocity field Fluid particles may have a net mean drift even if the local velocity field has zero mean; this is the case in irrotational gravity waves In viscous fluid, wave-induced Reynolds stress imparts steady momentum to the fluid; a steady shear is the set up to balance it, hence a further mean velocity field results The sum of these two steady currents provides the total drift by which a fluid particle migrates, ie mass transport velocity This report is a description of theoretical and experimental aspects of mass transport by waves Part I reviews basic assumptions of existing theories Part II checks and evaluates theoretical deductions in Part I (Author)

Chiang C. Mei

Papers

Erratum for “Mass Transport by Waves and Offshore Sand Bedforms”

Landslide Tsunamis in Lakes

Sandbar Formation Under Surface Waves

Tidal diffraction by a small island or cape, and tidal power from a coastal barrier

Mass Transport in Water Waves. Part I. Theory. Part II. Experiments.