International audienceThis paper focuses on the energy conservation properties of a hydrostatic, Boussinesq, coastal ocean model using a classic finite difference method. It is shown that the leapfrog time-stepping scheme, combined with the sigma-coordinate formalism and the motions of the free surface, prevents the momentum advection from exactly conserving energy. Because of the leapfrog scheme, the discrete form of the kinetic energy depends on the product of velocities at odd and even time steps and thus appears to be possibly negative when high-frequency modes develop. Besides, the study of the energy balance clarifies the numerical choices made for the computation of mixing processes. The time-splitting technique used to reduce the computation costs associated to the resolution of surface waves leads to the well-known external and internal mode equations. We show that these equations do not conserve energy if the coupling of these two modes is forward in time. Even if non-linear terms are negligible, this shortcoming can be significant regarding the pressure gradient term ‘frozen' over a baroclinic time step. An alternative energy-conserving time-splitting technique is proposed in this paper. Discussion and conclusions are conducted in the light of a set of numerical experiments dedicated to surface and internal gravity waves
International audienceInternal (gravity) wave attractors may form in closed containers with boundaries non-parallel and non-normal to the gravity vector. Such attractors have been studied from a theoretical point of view, in laboratory experiments and using linear numerical computations. In the present paper two-dimensional numerical simulations of an internal wave attractor are reported, based upon the nonlinear and non-hydrostatic MIT-gcm numerical code. We first reproduce the laboratory experiment of a wave attractor performed by Hazewinkel et al. (J. Fluid Mech. Vol. 598, 2008 p. 373) and obtain very good agreement with the experimental data. We next propose simple ideas to model the thickness of the attractor. The model predicts that the thickness should scale as the 1/3 power of the non-dimensional parameter measuring the ratio of viscous to buoyancy effects. When the attractor is strongly focusing, the thickness should also scale as the 1/3 power of the spatial coordinate along the attractor. Analysis of the numerical data for two different attractors yields values of the exponent close to 1/3, within 30%. Finally, we study nonlinear effects induced by the attractor
International audienceAn innovative experiment was carried out in the vicinity of the Rhône River mouth in February 2014. An instrumentalpackage, composed of a CTD, a LISST-100 type B (1.25–250 μm), and a LISST-HOLO (20–2000 μm), wasused to characterize the hydrological parameters and suspended particles properties (concentration, size, composition,shape, and effective density) in the region of freshwater influence (ROFI) of the Rhône River. Besides,a coastal SLOCUMglider, equipped with a CTD and optical backscattering sensors at severalwavelengths,was deployedto detail the spatial description of the hydrological parameters and some particle properties. Large riverdischarge (annual flood ~5000 m3 s−1) and strong wind conditions favored the dispersal of the river plume onthe shelf. Surface suspended particulate matter concentrations decreased rapidly seaward from 20 mg L−1next to the river mouth to 1.5 mgL−1 at the shelf break. A persistent bottomnepheloid layerwas observed acrossthe shelf with concentrations decreasing from8 mg L−1 at the coast to 1 mg L−1 at the shelf break. Observationsshowed that most of suspended particles were mainly flocculated in micro and macro-flocs (30–400 μm) ininner-shelf waters. The particle assemblage in the Rhône River plume and in the bottomnepheloid layer becameprogressively finer seaward and the associated effective density increased from 370 to 1600 kgm−3. Outside theplume, planktonic organisms increasingly contributed to the total volume concentration. Finally,we demonstratedthe ability of gliders, equipped with optical backscattering sensors at severalwavelengths, to describe the finescale distributions of suspended particles, and provide an index of their size distribution
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