Similarity of the streamwise velocity component in very-rough-wall channel flow

Abstract

The streamwise velocity component is studied in fully developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly nonGaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (± the standard deviation) are, respectively, about 76(±42) and 145(±150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of velocity. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04 6 y/ h 6 0.06, but the profile over the mesh surface does not, even though the mean velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single-and twopoint velocity correlations reveal the presence of large-scale streamwise structures with circulation in the plane orthogonal to the mean velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.

Parametric forcing approach to rough-wall turbulent channel flow

“…This is in line with general observations that the structure of turbulence is changed strongly only in the region close to the roughness elements, not in the outer layer (Birch & Morrison 2011;Singh et al 2007;Ashrafian & Andersson 2006).…”

“…However, the roughness element might affect the flow not only in its immediate surroundings but also change the flow further away from the wall, and secondly random roughness elements can give a wide range of height values (see e.g. Birch & Morrison 2011;Langelandsvik et al 2008) better described by a distribution of roughness heights. In order to make the effects of different shape functions and different roughness height parameters comparable, a clear definition for the roughness height of a profile and a rule for the normalisation of the shape function are needed.…”

“…The streamwise velocity shows in these respects for small to moderate roughness heights similar behaviour to the fully resolved direct numerical simulations discussed above. However, one significant difference can be observed: the negative minimum of the spanwise correlation the streamwise velocity increases with increasing strength of the roughness term whereas it decreases or remains approximately constant for rough wall flows (DeMarchis et al 2010;Birch & Morrison 2011) indicating that the alternating positive-negative pattern in the streamwise velocity field is weakened (Leonardi et al 2004). This difference is probably due to the damping nature of the roughness term which does not reproduce the detailed interaction of the flow with the roughness elements, leading rather to a coarsening of the structure of the velocity field than an increased level of small scale structures as one would expect for a fully resolved rough surface (see for example figure 15 in Bhaganagar et al (2004)).…”

Development of turbulent boundary layers past a step change in wall roughness

“…Two rough surfaces were considered, an abrasive grit and an extruded wire mesh, which are similar to those found in Birch & Morrison (2011). The grit-type roughness consists of sheets of 16-gauge industrial open-type silicone carbide abrasive.…”

“…The grit-type roughness consists of sheets of 16-gauge industrial open-type silicone carbide abrasive. The topology of this surface is sparse and considered isotropic and highly non-Gaussian, as is shown by Birch & Morrison (2011). The mesh-type roughness is formed from an expanded aluminium sheet consisting of twisted rectangular elements, of cross section 2.35 × 1.5 mm, forming a diamond-shaped pattern.…”