A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: Effects of different solid matrix geometries, solid boundaries, and two porosity scales

In this study, we address the question of whether turbulent structures in a porous medium are restricted in size by the pore scale or whether the size of eddies may exceed the pore scale, leading to the formation of macroscopic coherent structures. Based on direct numerical simulations in porous media, we conclude that the size of turbulent eddies is restricted by the pore size, leading to the pore scale prevalence hypothesis (PSPH). We prove this hypothesis by considering four different porous matrices. In particular, we simulated turbulent flow in a two-dimensional matrix, a three-dimensional unbounded matrix, a three-dimensional matrix bounded by two parallel solid walls, and a three-dimensional matrix with two characteristic pore scales. The obtained results for the four simulated porous matrices support the PSPH. However, there is a partly open question of whether turbulent structures can reach the size of the largest pore scale if the solid matrix is characterized by more than one length scale.

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A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: Effects of different solid matrix geometries, solid boundaries, and two porosity scales