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The transport from the upper mixed layer into the pycnocline of particles with negative buoyancy is considered. Assuming the hydrodynamic parameters to be timeindependent, an adjoint model is resorted to that provides a general expression of the residence time in the mixed layer of the constituent under study. It is seen that the residence time decreases as the settling velocity increases or the diffusivity decreases. Furthermore, it is demonstrated that the residence time must be larger than z/w and smaller than h/w, where z, h and w denote the distance to the pycnocline, the thickness of the mixed layer and the sinking velocity. In the vicinity of the pycnocline, the residence time is not necessarily zero; its behaviour critically depends on the eddy diffusivity profile in this region. Closed-form solutions are obtained for constant and quadratic diffusivity profiles, which allows for an analysis of the sensitivity of the residence time to the Peclet number. Finally, an approximate value is suggested of the depth-averaged value of the residence time.

International audiencePerfectly matched layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both time-dependent and time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyze how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one-dimensional and two-dimensional representative time-dependent cases. This study highlights the advantages of the so-called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions