This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 18315Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Two models of the flow over and through an immersed, vegetated layer are examined to study the onset of instability waves across the layer and to assess the effect of mild variations in the mean flow and in the drag force exerted by the canopy onto the frequency and growth rate of the monami instability. One of the two models, based on the use of Darcy's equation, with a tensorial permeability, within the canopy is more robust than the other (which uses a scalar drag coefficient), i.e., it is less sensitive to the inevitable imperfections or approximations in the input data. Published by AIP Publishing. [http://dx To cite this version:

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 20150 a b s t r a c tThe flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading -after applying an intrinsic averaging procedure -to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction which lies on the plane perpendicular to the fibers' axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers' axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete, albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time.

The coupling betwe e n the flow through a fi brous porous medium and that in a free-fluid region is studied. The flow dynamics inside the porous medium are described using the volume averaging method applied to the incompressible Navier-Stokes equations in the laminar regime. The two diff erent flow domains are coupled via a penalization method that consists of varying the porous medium properties (porosity and permeability) continuously across the interface. This approach permits the use of the same set of the equations throughout the whole domain. The averaging method is validated against simulations which Jully account for the presence of cylindrical fibers positioned at the bottom wall of a square driven cavity. Numerical experiments are carried out for two diff erent Reynolds numbers, large enough to ensure that inerti a l effects inside the porous domain are not negligible. Good agreement is found when comparing the two approaches.