Solitary waves propagating over variable topography

Solitary water waves are long nonlinear waves that can propagate steadily over long distances. They were first observed by Russell in 1837 in a now famous report [26] on his observations of a solitary wave propagating along a Scottish canal, and on his subsequent experiments. Some forty years later theoretical work by Boussinesq [8] and Rayleigh [25] established an analytical model. Then in 1895 Korteweg and de Vries [21] derived the well-known equation which now bears their names. Significant further developments had to wait until the second half of the twentieth century, when there were two parallel developments. On the one hand it became realised that the Korteweg-de Vries equation was a valid model for solitary waves in a wide variety of physical contexts. On the other hand came the discovery of the soliton by Kruskal and Zabusky [27], with the subsequent rapid development of the modern theory of solitons and integrable systems

Rogue Waves: Analytical Predictions

Rogue waves observed in the ocean and elsewhere are often modelled by certain solutions of the nonlinear Schrodinger equation, describing the modulational instability of a plane wave and the subsequent development of multi-phase nonlinear wavetrains. In this paper, we describe how integrability and application of the inverse scattering transform can be used to construct a class of explicit asymptotic solutions that describe this process. We discuss the universal mechanism of the onset of multiphase nonlinear waves (rogue waves) through the sequence of successive multi-breather wavetrains. Some applications to ocean waves and laboratory experiments are presented. © 2013 The Author(s) Published by the Royal Society. All rights reserved

Instability and filamentation of finite-amplitude waves on vortex lavers of finite thickness

We study the instability of finite-amplitude waves on uniform vortex layers of finite thickness bounded by a plane rigid surface. A weakly nonlinear analysis of vorticity interface perturbations, and spectral stability calculations using the full equations of motion, together show that steady progressive waves are unstable to general subharmonic perturbations in the range 0.094 < d/λ< 1.7, where d is the mean layer thickness and λ is the primary wavelength. The relevance of this instability to ultimate interface filamentation is tested by performing several numerical contour-dynamical simulations of the nonlinear interface evolution for initial disturbances consisting of the finite amplitude wave plus eigenfunctions obtained from the spectral calculations. The results indicate that within the band of unstable wavelengths, small perturbations to the steady non-uniform flow given by the finite amplitude wave motion (vortex equilibrium) are able to grow in magnitude, until at a time t, the wave extremum encounters a hyperbolic critical point of the velocity field after which filamentation occurs. Arguments are put forward based on the unsteady simulations with the purpose of identifying the preferred frame of reference for viewing the kinematical events controlling the filamentation process. An estimate for tis then made, and the mechanism of filamentation found is discussed in relation to the recently proposed nonlinear-cascade mechanism of Dritschel (1988a)

Chernobyl fallout in a Swedish spruce forest ecosystem

An assessment of the distribution of Chernobyl fallout in a Swedish forest was carried out and showed more than 95% of the in the system to be of Chernobyl origin. The data show that approximately 87% of total fallout is found in soils, 6% in the bryophyte layer and 7% in standing biomass of trees. The mean deposition of in the system (including soils, bryophytes, understorey vegetation, fungi, trees, moose and roe deer) was 54 kBq m−2. Fungi, understorey vegetation and ruminant populations collectively contained approximately 1% of total radiocaesium in the system. However, actual concentrations in these sample types were higher than in any other category, mostly exceeding the limit of 1500 Bq kg−1 for consumption of wild produce in Sweden. These categories represent the principal foodstuffs responsible for radiation transfer to man from the system and though negligible in total biomass there is potential for significant dose transfer to individuals who are regular consumers of wild forest produce