Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

Report on some species of Palaemonidae (Crustacea, Decapoda) from French Polynesia

Based on material collected from French Polynesia and deposited in the Museum national d'Histoire naturelle, Paris, the present paper reports 31 palaemonid shrimp species, which belong to the Palaemoninae (two genera, three species) and to the Pontoniinae (12 genera, 28 species), including six new species. The new species are: Izucaris crosnieri n. sp., Periclimenes alexanderi n. sp., P. josephi n. sp., P platydactylus n. sp., P polynesiensis n. sp. and P vicinus n. sp. Detailed descriptions and illustrations of the new species are provided. Besides the six new species, ten other species are recorded for the first time from French Polynesia: Exoclimenella maldivensis Duris & Bruce, 1995, Kemponia rapanui (Fransen, 1987) n. comb., Palaemonella crosnieri Bruce, 1978, P spinulata Yokoya, 1936, Periclimenaeus hecate (Nobili, 1904), P orbitocarinatus Fransen, 2006, Periclimenes aleator Bruce, 199 1, P paralcocki Li & Bruce, 2006, P uniunguiculatus Bruce, 1990, Pontonides loloata Bruce, 2005.