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Effective conductivity of inertial flows through porous media
Gerardo Severino1, Francesco Giannino2, Francesco De Paola3
1Division of Water Resources Management, University of Naples-Federico II via Universitá 100-I80055, Portici (NA), Italy.
Abstract:
We study two-dimensional incompressible inertial flows through porous media. At core (small) scale, we prove that the constitutive, nonlinear model can be rewritten into a linear one by means of a new parameter K^{★} which encompasses all the inertial effects. In natural (large-scale) formations, K^{★} is erratically changing, and we analytically compute its counterpart, which is coined generalized effective conductivity, by the self-consistent approach (SCA). In spite of its approximate nature, the SCA leads to simple results that are in good agreement with Monte Carlo simulations.
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