Fully resolved DNSs of turbulence over anisotropic permeable substrates

While roughness generally increases drag, small anisotropic permeable substrates have been proposed to reduce skin-drag. Their drag optimum is set by the competing contributions of a known drag-reducing slip effect and by adverse mechanisms which we do not fully understand, both of which increase with texture size. Prevalent disrupting features can be Kelvin-Helmholtz rollers and the texture-coherent flow, whose effect is drag-degrading. If the scale of the texture-induced flow is much smaller than the near-wall cycle, their signature appears distinct on the wavelength energy spectra. This separation of scales gradually diminishes with increasing texture size and eventually leads to their spectral overlap, making Fourier filters ill-suited to decompose the flow. Motivated by this, we have conducted fully resolved direct numerical simulations (DNS) for circular fibres with pitch ranging from L⁺ = 1 to L⁺ = 5 , which include the optimal size and well beyond. We decompose the flow into three components: the texture-coherent flow, the Kelvin-Helmholtz rollers and the background turbulence. When there is overlap between components, we use their different advection velocities to separate them and quantify their respective contribution to the total Reynolds stress.