Instabilities and Bifurcations in Turbulent Porous Media Flow

Abstract

Microscale turbulent flow in porous media is conducive to the development of flow instabilities due to strong vortical and shearing flow occurring within the pore space. When the flow instabilities around individual solid obstacles interact with numerous others within the porous medium, unique symmetry-breaking phenomena emerge as a result. This paper focuses on investigations of the vortex dynamics and flow instabilities behind solid obstacles in porous media, emphasizing how solid obstacle geometry and porosity influence both microscale and macroscale flow behavior. Two distinct symmetry-breaking mechanisms were identified in different porosity ranges. In low porosity media (< 0.8), a “deviatory flow” phenomenon occurs, where the macroscale flow deviates from the direction of applied pressure gradient at Reynolds numbers above 500. Deviatory flow is a source of macroscale Reynolds stress anisotropy, which is counterbalanced by a diminished vortex core size. In the intermediate porosity regime (0.8–0.95), a “jetting flow” mechanism creates asymmetric microscale velocity channels in the pore space through temporally biased vortex shedding, occurring during the transition to turbulence. Both symmetry-breaking phenomena are critically influenced by solid obstacle shape, porosity, and Reynolds number. Circularity of solid obstacle geometry and an adequately high-Reynolds number provide critical conditions for symmetry-breaking, whereas porosity can be used to parametrize the degree of symmetry-breaking. This paper provides fundamental insights into the intricate flow dynamics in porous media, offering a comprehensive understanding of how microscale vortex interactions generate macroscale flow asymmetries across different geometric configurations.