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Direct numerical simulations are performed for incompressible, turbulent channel flow over a smooth wall and different sinusoidal wall roughness configurations at a constant $Re_\tau = 720$ . Sinusoidal walls are used to study the effects of well-defined geometric features of roughness-amplitude, $a$ , and wavelength, $\lambda$ , on the flow. The flow in the near-wall region is strongly influenced by both $a$ and $\lambda$ . Establishing appropriate scaling laws will aid in understanding the effects of roughness and identifying the relevant physical mechanisms. Using inner variables and the roughness function to scale the flow quantities provides support for Townsend's hypothesis, but inner scaling is unable to capture the flow physics in the near-wall region. We provide modified scaling relations considering the dynamics of the shear layer and its interaction with the roughness. Although not a particularly surprising observation, this study provides clear evidence of the dependence of flow features on both $a$ and $\lambda$ . With these relations, we are able to collapse and/or align peaks for some flow quantities and, thus, capture the effects of surface roughness on turbulent flows even in the near-wall region. The shear-layer scaling supports the hypothesis that the physical mechanisms responsible for turbulent kinetic energy production in turbulent flows over rough walls are greatly influenced by the shear layer and its interaction with the roughness elements. Finally, a semiempirical model is developed to predict the contribution of pressure and skin friction drag on the roughness element based purely on its geometric parameters and the corresponding shear-layer velocity scale. 

Rotating and swirling turbulence comprises an important class of flows, not only due to the complex physics that occur, but also due to their relevance to many engineering applications, such as combustion, cyclone separation, mixing, etc. In these types of flows, rotation strongly affects the characteristics and structure of turbulence. However, the underlying turbulent flow phenomena are complex and currently not well understood. The axially rotating pipe is an exemplary prototypical model problem that exhibits these complex turbulent flow physics. By examining the complex interaction of turbulent structures within rotating turbulent pipe flow, insight can be gained into the behavior of rotating flows relevant to engineering applications. Direct numerical simulations are conducted at a bulk Reynolds number up to Re_D = 19,000 with rotation numbers ranging from N = 0 to 3. Coherence analysis, including Proper Orthogonal Decomposition and Dynamic Mode Decomposition, are used to identify the relevant (highest energy) modes of the flow. Studying the influence of these modes on turbulent statistics (i.e. mean statistics, Reynolds stresses, turbulent kinetic energy, and turbulent kinetic energy budgets) allow for a deeper understanding of the effects of coherent turbulent flow structures in rotating flows. 

Highly-resolved, direct numerical simulations of turbulent channel flows with sub- Kolmogorov grid resolution are performed to investigate the characteristics of wall-bounded turbulent flows in the presence of sinusoidal wall waviness. The wall waviness serves as a simplified model to study the effects of well-defined geometric parameters of roughness on the characteristics of wall-bounded turbulent flows. In this study, a two-dimensional wave profile with steepness ranging from 0.06 to 0.25 and wave amplitudes ranging from 9 to 36 wall units were considered. For the smooth and wavy-wall simulations, the Reynolds number based on the friction velocity was kept constant. To study the effects of wave amplitude and wavelength on turbulence, two-dimensional time and spanwise averaged distributions of the mean flow, turbulent kinetic energy, and Reynolds stresses as well as turbulent kinetic energy production and dissipation are examined. Furthermore, in order to provide a more direct comparison with the smooth-wall turbulent channel flow one-dimensional pro- files of these quantities are computed by averaging them over one wavelength of the wave profile. A strong effect of the wall-waviness and, in particular, the wave amplitude and wavelength on the characteristics of the turbulence was obtained. Wall waviness mainly affected the inner flow region while all recorded turbulent statistics collapsed in the outer flow region. Significant reductions in turbulent kinetic energy, production and dissipation were obtained with increasing wave amplitudes when reported in inner scale. While production is lower for all wavy wall cases considered here in comparison to the smooth wall, reducing the wavelength caused an increase in production and a decrease in dissipation.