Sketch of the coronal heating process. Above: the general problem of photospheric injection, transmission, turbulent dissipation, and leakage back to the photosphere. Red thick arrows at the left foot point represent the surface shear forcing. Below: the three numerical models considered in this paper: a) closed model (no leakage) with imposed velocity at the coronal base, b) semi-transparent corona with imposed wave input at the coronal base, c) semi-transparent corona including chromospheric turbulence with imposed wave input at the chromospheric base. Thin arrows indicate the wave reflection and transmission, white thick arrows represent the leakage out of the numerical domain.