Hydrated porous substrates modulate the spatiotemporal dynamics of bacterial turbulence

Boundary conditions strongly influence bacterial turbulence, motivating the question of how hydrated porous substrates affect near-interface collective motion. We characterize the spatiotemporal dynamics of dilute and dense Escherichia coli suspensions above agar substrates of varying concentrations, with glass serving as a nonporous reference. In dense suspensions shortly after loading, collective in-plane kinetic energy varies nonmonotonically with agar concentration, while individual swimming energy and characteristic spatial scales show comparatively little variation. Over five minutes above agar, the collective flow attenuates strongly, accompanied by shorter spatial correlations, longer temporal correlations, and a greater relative spectral weight at higher wavenumbers. To explore how the porous boundary may contribute to these changes, we extend mean-field kinetic theory (MFKT) to incorporate normal seepage and tangential slip at the interface. Linear stability analysis distinguishes near-interface collective modes from those in the bulk and identifies how fluid-layer thickness and permeability-dependent slip length modify the instability cutoff. The predicted reduction in the associated length scale provides a qualitative interpretation of the smaller flow structures observed over time and at higher agar concentrations. These findings reveal distinct substrate-dependent changes in the intensity, persistence, and spatial organization of near-interface bacterial turbulence.