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

Persistent pumping of groundwater is known to cause subsidence of the ground surface. When the soil is composed of alternating layers of sand and clay, subsidence is, in general, a consequence of pressure change in and deformation of all layers. Even with various simplifications, the mathematical task for the mechanics of a layered soil is complex and, in the past, many idealizations have been introduced in the literature. Among the existing approximations, a well-known approximation by Hantush1 for well-hydraulics in leaky aquifers is intuitively attractive. He used the fact known to be strictly true for simple flows in a soil system with horizontal layers, that the flow must be mainly horizontal in a relatively porous aquifer and mainly vertical in a highly impervious aquitard, and invoked the same approximation for transient flows induced by well-pumping. In this paper we shall apply a perturbation analysis to give a mathematical confirmation of the hydrological approximation and to show its degree of accuracy. In particular, we treat a three-layered system, where the middle layer is a relatively soft aquitard, and the well withdraws water from the artesian aquifer at the bottom. The upper aquifer has a phreatic surface. Physically, we examine the often ignored effects of self-weight which is important for thick aquitards. The perturbation theory is worked out for sufficiently weak pumping rates and small soil deformation. Subsidence in the vertical direction due mainly to the deformation of the soft aquitard is studied. Results show that the common assumption of constant total stress with respect to depth is valid only when the storage coefficient is very small.

Subsidence due to pumping from layered soil—a perturbation theory

https://repository.library.noaa.gov/view/noaa/9606/noaa_9606_DS1.pdf

Hybrid element method for calculating three-dimensional water wave scattering

Theoretical formulation describing the wave generation by a slender solid landslide is presented. The slide motion is coupled with the surface wave dynamics and both the fluid viscous (lubricative) resistance and the solid friction are considered. Numerical results are obtained for a cosine function shape slide. Numerical results show clearly the importance of the dynamic nonlinear coupling. The effects of lubricative resistance, solid friction, initial landslide speed and the slide height are discussed.

Solid landslide generated waves

We present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt-Vaisala frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Buhler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271-293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

Scattering of internal tides by irregular bathymetry of large extent

In laboratory experiments, it is known that the mobile storm barriers designed for Venice inlets can be excited subharmonically by incident waves to oscillate in modes that can reduce the efficienc...

Chiang C. Mei

Papers

Subsidence due to pumping from layered soil—a perturbation theory

Hybrid element method for calculating three-dimensional water wave scattering

Solid landslide generated waves

Scattering of internal tides by irregular bathymetry of large extent

Linear response of Venice storm gates to incident waves