The Main Problem in Satellite Theory Revisited

Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal form of the main problem (J ₂ perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given through order four. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fatal ingestion of floating net debris by two sperm whales (Physeter macrocephalus)

In 2008 two male sperm whales (Physeter macrocephalus) stranded along the northern California coast with large amounts of fishing net scraps, rope, and other plastic debris in their stomachs. One animal had a ruptured stomach, the other was emaciated, and gastric impaction was suspected as the cause of both deaths. There were 134 different types of nets in these two animals, all made of floating material, varying in size from 10 cm² to about 16 m². The variability in size and age of the pieces suggests the material was ingested from the surface as debris rather than bitten off from active gear. These strandings demonstrate that ingestion of marine debris can be fatal to large whales, in addition to the well documented entanglements known to impact these species.     

Hydrodynamic conditions associated with the formation,maintenance and dissipation of a phytoplankton thin layer in a coastal upwelling system

During May–June 2005, a 17-d cruise was carried out in Ría de Pontevedra (Galician Rías Baixas) to study the physical–biological interactions that may lead to subsurface aggregations of phytoplankton organisms in thin layers (TLs). Physical processes governed the initiation and development, maintenance, and decline of a diatom (toxin producing Pseudo-nitzschia spp. and Chaetoceros socialis) TL during an upwelling relaxation-upwelling–downwelling sequence. Differences in shear profiles appeared to lead to the formation of a TL during upwelling events. These results reveal that the coupling between maximum values of shear and buoyancy frequency can shape a subsurface chlorophyll maximum (SCM) into a TL. The effect of shear upon phytoplankton patches, which has been predicted on the basis of theoretical studies, has been corroborated in this study in which the vertical distribution of an observed TL was controlled by physical processes.     

Interpreting erosion rates from cosmogenic radionuclide concentrations measured in rapidly eroding terrain

A combination of numerical analysis and ¹⁰Be concentrations measured in sediment samples from the high‐relief Torrente catchment, southern Spain, allows us to investigate the sampling requirements for determining erosion rates using cosmogenic nuclides in high‐relief, landslide‐dominated terrain. We use simple modelling to quantify the effect of particle spalling and/or landsliding on erosion rates determined using a cosmogenic in‐situ produced isotope. Analytical results show that the cosmogenic nuclide concentration of a surface experiencing regular detachment of a grain or block may be considered to be in steady state, and ‘in‐situ’ erosion rates estimated, when an appropriate number of spatially independent samples are amalgamated. We present equations that enable calculation of the number of bedrock samples that must be amalgamated for the estimation of mean erosion rates on an outcrop experiencing regular detachment of a grain or chip of thickness L every T years. Our findings confirm that mean catchment erosion rates may be reliably estimated from ¹⁰Be concentrations in fluvial sediment in high‐relief rapidly eroding terrain. These catchment‐wide integrated erosion rates can be calculated where erosion is primarily accomplished through shallow (<3 m) spalling processes; where deep‐seated (>3 m) landslides are the dominant mode of erosion only minimum erosion rates can be determined. Lastly, we present erosion rate measurements from the Torrente catchment that reveal variation of two orders of magnitude (0·03–1·6 m ka^?1) quantifying the high degree of spatial variation in erosion rates expected within rapidly uplifting catchments. Copyright © 2006 John Wiley & Sons, Ltd.