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1. A Numerical Investigation of the Effects of Rotation on Turbulent Pipe Flows

   Brehm, C.; Davis, J.; Ganju, S; Bailey, S. (January 2019, 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11))

   In past experiments, simulations and theoretical analysis, rotation has been shown to dramatically effect the characteristics of turbulent flows, such as causing the mean velocity profile to appear laminar, leading to an overall drag reduction, as well as affecting the Reynolds stress tensor. The axially rotating pipe is an exemplary prototypical model problem that exhibits these complex turbulent flow physics. For this flow, the rotation of the pipe causes a region of turbulence suppression which is particularly sensitive to the rotation rate and Reynolds number. The physical mechanisms causing turbulence suppression are currently not well-understood, and a deeper understanding of these mechanisms is of great value for many practical examples involving swirling or rotating flows, such as swirl generators, wing-tip vortices, axial compressors, hurricanes, etc. In this work, Direct Numerical Simulations (DNS) of rotating turbulent pipe flows are conducted at moderate Reynolds numbers (Re=5300, 11,700, and 19,000) and rotation numbers of N=0 to 3. The main objectives of this work are to firstly quantify turbulence suppression for rotating turbulent pipe flows at different Reynolds numbers as well as study the effects of rotation on turbulence by analyzing the characteristics of the Reynolds stress tensor and the production and dissipation terms of the turbulence budgets. 

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2. The Onsager theory of wall-bounded turbulence and Taylor’s momentum anomaly

   https://doi.org/10.1098/rsta.2021.0079  

   Eyink, Gregory L.; Kumar, Samvit; Quan, Hao (March 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We discuss the Onsager theory of wall-bounded turbulence, analysing the momentum dissipation anomaly hypothesized by Taylor. Turbulent drag laws observed with both smooth and rough walls imply ultraviolet divergences of velocity gradients. These are eliminated by a coarse-graining operation, filtering out small-scale eddies and windowing out near-wall eddies, thus introducing two arbitrary regularization length-scales. The regularized equations for resolved eddies correspond to the weak formulation of the Navier–Stokes equation and contain, in addition to the usual turbulent stress, also an inertial drag force modelling momentum exchange with unresolved near-wall eddies. Using an Onsager-type argument based on the principle of renormalization group invariance, we derive an upper bound on wall friction by a function of Reynolds number determined by the modulus of continuity of the velocity at the wall. Our main result is a deterministic version of Prandtl’s relation between the Blasius − 1 / 4 drag law and the 1/7 power-law profile of the mean streamwise velocity. At higher Reynolds, the von Kármán–Prandtl drag law requires instead a slow logarithmic approach of velocity to zero at the wall. We discuss briefly also the large-eddy simulation of wall-bounded flows and use of iterative renormalization group methods to establish universal statistics in the inertial sublayer. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’. 

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3. Amplitude and wavelength scaling of sinusoidal roughness effects in turbulent channel flow at fixed

   https://doi.org/10.1017/jfm.2022.118  

   Ganju, Sparsh; Bailey, Sean C.C.; Brehm, Christoph (April 2022, Journal of Fluid Mechanics)

   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. 

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4. A scaling law for the shear-production range of second-order structure functions

   https://doi.org/10.1017/jfm.2016.427  

   Pan, Y.; Chamecki, M. (August 2016, Journal of Fluid Mechanics)

   null (Ed.)

   Dimensional analysis suggests that the dissipation length scale ( $$\ell _{{\it\epsilon}}=u_{\star }^{3}/{\it\epsilon}$$ ) is the appropriate scale for the shear-production range of the second-order streamwise structure function in neutrally stratified turbulent shear flows near solid boundaries, including smooth- and rough-wall boundary layers and shear layers above canopies (e.g. crops, forests and cities). These flows have two major characteristics in common: (i) a single velocity scale, i.e. the friction velocity ( $$u_{\star }$$ ) and (ii) the presence of large eddies that scale with an external length scale much larger than the local integral length scale. No assumptions are made about the local integral scale, which is shown to be proportional to $$\ell _{{\it\epsilon}}$$ for the scaling analysis to be consistent with Kolmogorov’s result for the inertial subrange. Here $${\it\epsilon}$$ is the rate of dissipation of turbulent kinetic energy (TKE) that represents the rate of energy cascade in the inertial subrange. The scaling yields a log-law dependence of the second-order streamwise structure function on ( $$r/\ell _{{\it\epsilon}}$$ ), where $$r$$ is the streamwise spatial separation. This scaling law is confirmed by large-eddy simulation (LES) results in the roughness sublayer above a model canopy, where the imbalance between local production and dissipation of TKE is much greater than in the inertial layer of wall turbulence and the local integral scale is affected by two external length scales. Parameters estimated for the log-law dependence on ( $$r/\ell _{{\it\epsilon}}$$ ) are in reasonable agreement with those reported for the inertial layer of wall turbulence. This leads to two important conclusions. Firstly, the validity of the $$\ell _{{\it\epsilon}}$$ -scaling is extended to shear flows with a much greater imbalance between production and dissipation, indicating possible universality of the shear-production range in flows near solid boundaries. Secondly, from a modelling perspective, $$\ell _{{\it\epsilon}}$$ is the appropriate scale to characterize turbulence in shear flows with multiple externally imposed length scales. 

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5. Drag enhancement by the addition of weak waves to a wave-current boundary layer over bumpy walls

   https://doi.org/10.1017/jfm.2022.628  

   Patil, Akshay; Fringer, Oliver (September 2022, Journal of Fluid Mechanics)

   We present direct numerical simulation results of a wave-current boundary layer in a current-dominated flow regime (wave driven to steady current ratio of 0.34) over bumpy walls for hydraulically smooth flow conditions (wave orbital excursion to roughness ratio of 10). The turbulent, wave-current channel flow has a friction Reynolds number of $350$ and a wave Reynolds number of $351$ . At the lower boundary, a bumpy wall is introduced with a direct forcing immersed boundary method, while the top wall has a free-slip boundary condition. Despite the hydraulically smooth nature of the wave-driven flow, the phase variations of the turbulent statistics for the bumpy wall case were found to vary substantially when compared with the flat wall case. Results show that the addition of weak waves to a steady current over flat walls has a negligible effect on the turbulence or bottom drag. However, the addition of weak waves to a steady current over bumpy walls has a significant effect through enhancement of the Reynolds stress (RS) accompanied by a drag coefficient increase of $$11\,\%$$ relative to the steady current case. This enhancement occurs just below the top of the roughness elements during the acceleration portion of the wave cycle: Turbulent kinetic energy (TKE) is subsequently transported above the roughness elements to a maximum height of roughly twice the turbulent Stokes length. We analyse the TKE and RS budgets to understand the mechanisms behind the alterations in the turbulence properties due to the bumpy wall. The results provide a mechanistic picture of the differences between bumpy and flat walls in wave-current turbulent boundary layers and illustrate the importance of bumpy features even in weakly energetic wave conditions. 

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