The minimal channel: A fast and direct method for characterising roughness

Roughness only alters the near-wall region of turbulent flow and leaves the outer-layer unaffected, making it a prime candidate for the minimal-span channel framework which only captures the near-wall flow. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418-431) showed that the minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following on from this, we aim to further optimise the minimal-span channel framework by primarily noting that the outer layer it produces is inherently incorrect, and as such modifications to this region can be made to improve performance. Firstly, a half-height channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. The streamwise length of the channel is also investigated independent of the previous improvements, and suggests the minimum length should be at least 3 times the spanwise width and also 1000 viscous-units long, whichever is longer. Finally, an investigation is conducted to see if varying the roughness Reynolds number with time is a feasible method for obtaining the full hydraulic behaviour of a rough surface, instead of running multiple simulations at fixed roughness Reynolds numbers.