International audienceWe present a comprehensive parametric study of the transition scenario of freely falling discs. The motion of the discs is investigated by a direct numerical simulation of the solid-fluid interaction. The discs are assumed to be homogeneous and infinitely thin. The problem is shown to depend on two independent parameters, the Galileo number expressing the ratio between effects of gravity and viscosity and the non-dimensionalized mass characterizing the inertia of the disc. The obtained results are in agreement with known experimental and numerical data and provide both detailed and comprehensive picture of the transition scenario in the two-parameter plane defined by the Galileo number and the non-dimensionalized mass. C 2013 American Institute of Physics. [http://dx

International audienceAn exhaustive parametric study of the transition scenario in the wake of oblate spheroids and flat cylinders placed with their rotation axis parallel to the flow is presented. The flatness of the investigated objects is classified by the aspect ratio χ defined as χ = d/a for spheroids (with d the diameter and a the length of the polar axis) and as χ = d/ h for cylinders (with h the cylinder height). We find a significant qualitative similarity between both configurations. At large aspect ratios (χ > 2.3 for spheroids and χ > 4 for cylinders), the secondary bifurcation giving rise to a periodic state without planar symmetry is subcritical with a hysteresis interval of about two Reynolds number units. For spheroids, the sphere-like scenario is recovered only at aspect ratios very close to one (χ > 1 are considered), while for cylindrical bodies the same holds for χ 6 1.7. For intermediate aspect ratios, a domain of states with non-zero net helicity separates states typical for the sphere wake from those of an infinitely flat disk

The standard formulation of 4D-Var assumes random zero-mean errors for all sources of information used in the analysis. This assumption is usually not well verified in real-world applications. The performance of a weak-constraint 4D-Var formulation ("forcing" formulation) is studied in this paper in a simplified experimental setting using additive model errors of different length-scales and observing systems of different coverage and accuracy. A set of twin experiments is carried out and results show that weak-constraint 4D-Var can accurately estimate the actual model errors and the initial state only when background and model errors have different spatial scales and when the observations are unbiased and spatially homogeneous. We also present preliminary results from a different weak-constraint 4D-Var formulation ("state" formulation) which could in principle overcome some of these limitations, but at the cost of a substantial increase of computational and memory requirements. These findings help identify the potential but also the intrinsic limitations of the weak-constraint 4D-Var approach. They also help to clarify the experimental results seen in the operational ECMWF analysis system where the analysis and first-guess temperature bias is reduced by up to 50% in the stratosphere.