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).

Mathematical Handbook for Scientists and Engineers

Classifications, applications, and design challenges of drones: A review

According to small subunit ribosomal RNA (ss rRNA) sequence comparisons all known Archaea belong to the phyla Crenarchaeota, Euryarchaeota, and--indicated only by environmental DNA sequences--to the 'Korarchaeota'. Here we report the cultivation of a new nanosized hyperthermophilic archaeon from a submarine hot vent. This archaeon cannot be attached to one of these groups and therefore must represent an unknown phylum which we name 'Nanoarchaeota' and species, which we name 'Nanoarchaeum equitans'. Cells of 'N. equitans' are spherical, and only about 400 nm in diameter. They grow attached to the surface of a specific archaeal host, a new member of the genus Ignicoccus. The distribution of the 'Nanoarchaeota' is so far unknown. Owing to their unusual ss rRNA sequence, members remained undetectable by commonly used ecological studies based on the polymerase chain reaction. 'N. equitans' harbours the smallest archaeal genome; it is only 0.5 megabases in size. This organism will provide insight into the evolution of thermophily, of tiny genomes and of interspecies communication.

A new phylum of Archaea represented by a nanosized hyperthermophilic symbiont

Transport impacts on atmosphere and climate: Shipping

Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.

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Long Nonlinear Internal Waves

Digital particle image velocimetry (DPIV) measurements of the velocity eld under breaking waves in the laboratory are presented. The region of turbulent fluid directly generated by breaking is too large to be imaged in one video frame and so an ensemble-averaged representation of the flow is built up from a mosaic of image frames. It is found that breaking generates at least one coherent vortex that slowly propagates downstream at a speed consistent with the velocity induced by its image in the free surface. Both the kinetic energy of the flow and the vorticity decay approximately as t 1 . The Reynolds stress of the turbulence also decays as t 1 and is, within the accuracy of the measurements, everywhere negative, consistent with downward transport of streamwise momentum. Estimates of the mometum flux from waves to currents based on the measurements of the Reynolds stress are consistent with earlier estimates. The implications of the measurements for breaking in the eld are discussed. Based on geometrical optics and wave action conservation, we suggest that the presence of the breaking-induced vortex provides an explanation for the suppression of short waves by breaking. Finally, in Appendices, estimates of the majority of the terms in the turbulent kinetic energy budget are presented at an early stage in the evolution of the turbulence, and comparisons with independent acoustical measurements of breaking are presented.

The velocity field under breaking waves: coherent structures and turbulence

Surface waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean. The development of the wave field depends on wind, wave-wave and wave-current interactions and wave dissipation owing to breaking, which is accompanied by momentum fluxes from waves to currents. Wave breaking supports air-sea fluxes of heat and gas, which have a profound effect on weather and climate. But wave breaking is poorly quantified and understood. Here we present measurements of wave breaking, using aerial imaging and analysis, and provide a statistical description of related sea-surface processes. We find that the distribution of the length of breaking fronts per unit area of sea surface is proportional to the cube of the wind speed and that, within the measured range of the speed of the wave fronts, the length of breaking fronts per unit area is an exponential function of the speed of the front. We also find that the fraction of the ocean surface mixed by breaking waves, which is important for air-sea exchange, is dominated by wave breaking at low velocities and short wavelengths.

Distribution of breaking waves at the ocean surface

The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211200700897X

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

Recent field measurements by Agrawal et al. have provided evidence of a shallow surface mixed layer in which the rate of dissipation due to turbulence is one to two orders of magnitude greater than that in a comparable turbulent boundary layer over a rigid wall. It is shown that predictions by Phillips of the energy lost by breaking surface waves in an equilibrium regime and laboratory measurements by Rapp and Melville of the mixing and turbulence due to breaking together lead to estimates of the enhanced dissipation rate and the thickness of the surface layer consistent with the field measurements. Wave-age-dependent scaling of the dissipation layer is proposed. Laboratory measurements of dissipation rates in both unsteady and quasi-steady breaking waves are examined. It is shown that an appropriately defined dimensionless rate of dissipation in unsteady breaking waves is not constant, but increases with a measure of the wave slope. Differences between dissipation rates in quasi-steady and unste...

W. Kendall Melville

Papers

Long Nonlinear Internal Waves

The velocity field under breaking waves: coherent structures and turbulence

Distribution of breaking waves at the ocean surface

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

Energy Dissipation by Breaking Waves