Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

Abstract

The interaction between boundary layer turbulence and a porous layer is the cornerstone of interface engineering. In this study, the spatial and spectral-resolved transfer entropy is used to assess the asymmetry of the causal interaction next to the permeable wall. The analysis is based on pore-resolved direct numerical simulation of turbulent channel flow over cylinder arrays. The spatial map of transfer entropy reveals the information flux between the porous medium and arbitrary nearby positions, and paths connecting locations with maximum information transfer are identified. The paths in the ‘top-down’ and ‘bottom-up’ directions, respectively, lean upstream and downstream, demonstrating that the coupling process is directionally dependent. The scale dependence of transfer entropy is inspected with a surrogate data strategy. As wall permeability increases, the active scale range in causal interaction shifts from near-wall vortices to Kelvin–Helmholtz type eddies. In addition, linear stochastic estimation is used to determine the statistical velocity field for a local informative event. In an average sense, the interaction between a convecting sweep or ejection event and the up/down-welling motions at the pore unit is the core mechanism that contributes to the causal coupling. The statistical findings derived from the transfer entropy are then validated using a neural network-based remote sensing model.

Turbulent flows over porous lattices: alteration of near-wall turbulence and pore-flow amplitude modulation

“…The K Br condition was obtained using linear stability analysis of permeable wall boundary conditions derived using the Darcy-Brinkman equation but remain applicable to the pore-scale resolved DNS data in this study, indicating that the microstructure details of the porous substrates do not have a leading-order impact on the instability. This agrees with the argument made by White & Nepf (2007), who assessed that only the overall resistance of the porous layer is important and not the details of its geometry in bringing about and sustaining the instability.…”

“…arrays of cylinders serving as models for vegetation canopies. White & Nepf (2007) demonstrated that the coherent motion at the top of the arrays exhibited a single dominant frequency which was the same as that in free shear layers subject to K-H instability. They therefore characterized the flows as being similar to mixing layers where the instability originates at the inflection point of the mean velocity profile inside the porous region.…”

“…They concluded that for low to moderate permeabilities, the coherent turbulent motion in the vicinity of the permeable surface is not due to the inflectional instability of the mean velocity profile. In a recent DNS study by Wang et al (2022) where transfer entropy was used to measure causal interactions between porous media and turbulent flows, the frequencies at which these interaction took place over the various porous media were in agreement with the results of Manes et al (2011). The dominant frequency reported by White & Nepf (2007) was f = 0.032 Ū/θ, where θ = ∞ −∞ (1/4 + (U − Ū/ U) 2 ) dy; U = U y=δ − U P ; Ū = (U y=δ + U P )/2 and U P is the velocity deep inside the porous medium.…”

“…Outside of this mixing layer regime, the notable flow activity below the surface mainly resides in the pore-coherent scales of the flow which undergo modulation by the turbulence at substrate's surface. Manes et al (2011) examined whether the resulting eddy structures over their porous foams shared the same characteristics as those reported over canopies and which are associated with an inflectional instability of the mean velocity (White & Nepf 2007). They observed this to not be the case for low to intermediate ranges of permeability.…”

“…In the experiments of turbulent flows over porous metal foams conducted by Manes et al (2011), they examined whether the resulting turbulent flow at the permeable surface of the media were similar to those reported by White & Nepf (2007) for sparse porous Appendix C. Comparison of surface flow features between HP2, HP3 and HP2 , HP3 Thus far, it has been shown that the flow structure close to the surface of the substrates are quite different between the LP and HP cases. The LP cases are essentially smooth-wall-like and permit very little turbulent activity from taking place in the proximity of the surface and hence do not motivate further examination.…”