Turbulent flow above a porous surface

Abstract

We have investigated a fully turbulent, low-Reynolds number plane channel with one impermeable and one porous wall. The latter is assumed to obey Darcy's law and to be mass-neutral in the mean. Our DNS data show an enhancement of wall friction up to 40%, along with an increase in overall turbulence intensity. Most strikingly, a strong spanwise organization of the flow is observed due to the presence of large-scale, roller-like structures. Their effect is to alternatively energize and almost laminarize the buffer zone and the sublayer streaks. Linear analysis of the turbulent mean profile over a porous surface shows it to be unstable, with spanwise two-dimensional eigenfunctions whose shape and phase velocity are similar to those of the observed rollers. Finally, we show that the above effects of passive porosity can be duplicated by means of active two-dimensional wall transpiration, with the right shape and advection velocity. Interestingly, active injection with the wrong advection velocity has no effect on the average skin friction.