Role of interfacial roughness in turbulence over porous substrates

A porous substrate affects the overlying turbulence via both its permeability, which allows penetration of flow into the substrate, and its interfacial rough topography, which introduces extra disturbances into turbulence. This work aims to understand the role of interfacial roughness in affecting the properties of overlying turbulence for relatively small grain sizes in wall units, L⁺ ~< 70. We use two methodologies to approach this issue: a systematic exploration of the space of substrate parameters, including grain size L, bulk permeability K, and depth h, using direct numerical simulations; and a linearized framework to access a substrate’s admittance of velocity in response to overlying stress excitations. Our results suggest that flow properties including interfacial slip, drag increase, and structures of near-wall turbulence are essentially governed by a substrate’s emergent macroscopic attributes and largely independent of its microscopic attributes at the pore grain scale. A typical rough surface can be essentially regarded as a shallow porous substrate whose admittance of wall-normal velocity in response to pressure fluctuations is partially suppressed by the proximity of an impermeable floor.