Tortuosity is one of the fundamental effective parameters describing
hydrodynamic properties of porous media. However, the fact it can be
defined in several different ways, e.g. via the length of the
streamlines or as a statistic of the pore-scale velocity field, may
cause inconsistency between the results. For example, the equivalence
between the weighted streamline-based tortuosity and the easier to
calculate volume-integrated tortuosity was analytically proven by Duda
and others for Stokes flows, with the latter being larger then the
former when inertial effects show up. In the present work we study the
sources of this inequality. In particular, we investigate the
contributions to the tortuosity from the recirculation zones and the
percolating part of the flow separately. We do so in terms of the
volume of the recirculation zones and the kinetic energy/momentum
contained therein, as well as the viscous momentum transfer from the
percolating to the recirculation zones. We relate the changes of those
quantities to the known regimes of inertial flows. Our results explain
the observations on the deviation from each other of the values of
variously defined tortuosities, presented in previous works. They
deepen the understanding of the pore-scale mechanisms of the onset of
inertial effects in porous media and can serve as the theoretical
baseline for the formulation of reduced models of inertial transport
therein.