Surface roughness is a defining feature of many of the high Reynolds-numbers flows found in engineering. In fact, the higher the Reynolds number (Re), the more likely the effects of roughness are significant, since the size of the roughness elements becomes increasingly large compared to the near-surface viscous length appropriate for smooth-wall flows. As a result, turbulent boundary layers over the hulls of ships and submarines, within turbo-machinery, and over the surface of the earth are all cases to which the smooth-wall idealization rarely applies. Unfortunately the impact of surface roughness is not entirely understood, and a number of important fundamental questions have not yet received a satisfactory answer.
The goal of our research problem is to answer the following questions
1. what are the length scales associated with the inhomogenous layer or the roughness-sublayer ?
2. Does roughness affect the outer layer statistics ?
3. Are the turbulent structures and the dynamical mechanisms significantly affected by roughness ?
4. How to parameterize the roughness problem ?
5. How to parameterize the form drag associated with roughness ?
6. To resolve the controversy regarding the critical Reynolds number for the transition from hydrodynamically smooth to rough surface ?
Direct numerical simulation (DNS) have been performed for $\RE_\tau$=400 (Reynolds number based on wall-shear velocity $\u_\tau$ and channel half-height H) in a periodic channel of streamwise and spanwise size ${L_x}/{H}=2 \pi$ and ${L_z}/{H}=\pi$, where $2 H$ is the distance between the plane walls (one of which now lies outside the active flow domain, below the virtual rough surface). The spatial discretization used 256 streamwise Fourier modes, 257 wall-normal compact finite-difference grid points of fourth-order accuracy and 256 spanwise Fourier modes. In the figure above, the channel is shown from the lower-wall (y = -1) to the center of the channel. The virtual no-slip roughness surface is at $\sigma=-0.96$.
The figures show the comparison between streaks in the $x$-$z$ plane for the rough-wall and the smooth-wall at two different $y^+$ locations of $y^+$= 5 and 80. At $y^+$=5 the streaks are long and elongated at the smooth side of the channel, whereas at the same $y^+$ location the structures of the streaks look significantly different at the rough-wall side. At $y^+$=80, on the smooth-wall side of the channel the organized structures are not very apparent, whereas at the same $y^+$ location on the rough-wall side of the channel they appear more organized. This suggests that roughness results in organized structures for a larger $y^+$ location compared to case with absence of roughness.
This figure is a contour plot of the $u$,$v$ and $w$ velocity components in an $x$-$y$ plane. The structure of $u$ at the rough lower-wall side of the channel is distinctly different from the smooth upper-wall of the channel. There is increased activity present near the rough-wallside. The structure of $v$ is such that the roughness results in making the structures more elongated along the wall-normal direction. This is consistent with the conclusions drawn from the statistical results, that roughness modifies the transport process in the wall-normal direction. The structure of $w$ component of velocity shows an increased activity in the rough-wall side of the channel, and the angle of inclination of the structures also differs.