The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied numerically. The transpiration is assumed to be proportional to the local pressure fluctuations. It is first shown that the friction coefficient increases by up to 40% over passively porous walls, even for relatively small porosities. This is associated with the presence of large spanwise rollers, originating from a linear instability which is related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral inviscid shear waves of the mean turbulent profile. It is shown that the rollers can be forced by patterned active transpiration through the wall, also leading to a large increase in friction when the phase velocity of the forcing resonates with the linear eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used to further clarify the flow mechanism. This study is motivated by the control of separation in boundary layers.