It is widely believed that at high Reynolds number (Re) all turbulent flows approach a state of "fully developed turbulence" defined by a unique, Re-independent statistics of the velocity fluctuations. Yet direct measurements of the velocity fluctuations have failed to yield clear-cut empirical evidence of the existence of fully developed turbulence. Here we relate the friction coefficient ($f$) of rough-conduit flows to the statistics of the velocity fluctuations. In light of experimental measurements of $f$, our results yield unequivocal evidence of the existence of fully developed turbulence.
This paper presents an experimental study on the transition from smooth to rough walls, and back to the smooth one, in turbulent closed-conduit flows. These transitions cause a shift on flow velocity profiles that changes their parameters when compared to the flow over a smooth wall. Different water flow rates were imposed in a closed conduit of rectangular cross section, where rough elements consisting of cavities of d- and k-type were positioned covering a part of the bottom wall of the test section. Reynolds numbers based on the channel half-height were moderate, varying between 7800 and 96…
Turbulence intensity profiles are compared for smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. The profile development in the transition from hydraulically smooth to fully rough flow displays a propagating sequence from the pipe wall towards the pipe axis. The scaling of turbulence intensity with Reynolds number shows that the smooth- and rough wall level deviates with increasing Reynolds number. We quantify the correspondence between turbulence intensity and the friction factor.
Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the …
We study streamwise turbulence intensity definitions using smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. Scaling of turbulence intensity with the bulk (and friction) Reynolds number is provided for the definitions. The turbulence intensity scales with the friction factor for both smooth- and rough-wall pipe flow. Turbulence intensity definitions providing the best description of the measurements are identified. A procedure to calculate the turbulence intensity based on the bulk Reynolds number (and the sand-grain roughness for rough-wall pipe flow) is outlined.
Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how…
In the present study, we use a fifth-order ordinary differential equation, a generalization of the Blasius equation derived from the Leray-alpha model, to examine the transition to turbulence in rough-wall boundary-layer flows. This equation, combined with a weaker formulation of the von Karman log law modified to include the effects of surface roughness, provides a family of turbulent velocity profiles with two free parameters: the momentum thickness based Reynolds number and the roughness function. As a result, a skin-friction correlation is obtained and predictions of the transitional Reyno…
Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor--Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, 3-D roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (\textit{Phys. Fluids}, vol. 18, 0…
A turbulent mean profile for pipe flow is prescribed which closely matches experimental observations. The nature of perturbations superimposed upon this profile is then considered. Optimal growth calculations predict two distinct classes of structures, clearly associated with near-wall and large-scale structures. Quantitative correspondence of the spanwise wavelength of wall-structures with experimental observations is very good. The response to harmonic forcing is also considered, and the linear growth tested with direct numerical simulation of forced turbulence. Despite the very simple eddy …
Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. E…
We experimentally investigate the influence of alternating rough and smooth walls on bubbly drag reduction (DR). We apply rough sandpaper bands of width $s$ between $48.4\,mm$ and $148.5\,mm$, and roughness height $k = 695\,μm$, around the smooth inner cylinder (IC) of the Twente Turbulent Taylor-Couette facility. Between sandpaper bands, the IC is left uncovered over similar width $s$, resulting in alternating rough and smooth bands, a constant pattern in axial direction. We measure the DR in water that originates from introducing air bubbles to the fluid at (shear) Reynolds numbers $\textit{…
Direct numerical simulations (DNSs) are performed to analyze the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number $Ta=10^{10}$. The dimensionless torque $Nu_ω$ shows an effective scaling of $Nu_ω\propto Ta^{0.42\pm0.01}$, which is steeper than the ultimate regime effective scaling $Nu_ω\propto Ta^{0.38}$ seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough sur…
Short term unpredictability is discovered numerically for high Reynolds number fluid flows under periodic boundary conditions. Furthermore, the abundance of the short term unpredictability is also discovered. These discoveries support our theory that fully developed turbulence is constantly driven by such short term unpredictability.
Direct numerical simulations were performed to characterize fully developed supersonic turbulent channel flows over isothermal rough walls. The effect of roughness was incorporated using a level-set/volume-of-fluid immersed boundary method. Turbulence statistics of five channel flows are compared, including one reference case with both walls smooth and four cases with smooth top walls and bottom walls with two-dimensional (2D) and three-dimensional (3D) sinusoidal roughnesses. Results reveal a strong dependence of the turbulence on the roughness topography and the associated shock patterns. Sp…
We experimentally study the influence of wall roughness on bubble drag reduction in turbulent Taylor-Couette flow, i.e.\ the flow between two concentric, independently rotating cylinders. We measure the drag in the system for the cases with and without air, and add roughness by installing transverse ribs on either one or both of the cylinders. For the smooth wall case (no ribs) and the case of ribs on the inner cylinder only, we observe strong drag reduction up to $DR=33\%$ and $DR=23\%$, respectively, for a void fraction of $α=6\%$. However, with ribs mounted on both cylinders or on the outer…
The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and independent, the Fourier coefficients tend to Gaussian and independent of each other. Velocity fluctuations accordingly tend to Gaussian. However, if energy-containing motions are intermittent or contaminated with bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to non-Gaussian and dependent of each other. Velocity fluctuations accord…
Recently, by analyzing the measurement data of Nikuradze, it has been proposed (N. Goldenfeld, Phys. Rev. Lett. {\bf{96}}, 044503, 2006) that the friction factor, $f$, of rough pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form, thereby relating $f$ to the intermittency exponent, $η$. By statistically analyzing the measurement data of $f$, we infer a satisfactory estimate for $η$ ($\approx 0.02$), the inclusion of which is shown to improve the data-collapse c…
I propose a new theory on the nature of turbulence: when the Reynolds number is large, violent fully developed turbulence is due to "rough dependence on initial data" rather than chaos which is caused by "sensitive dependence on initial data"; when the Reynolds number is moderate, (often transient) turbulence is due to chaos. The key in the validation of the theory is estimating the temporal growth of the initial perturbations with the Reynolds number as a parameter. Analytically, this amounts to estimating the temporal growth of the norm of the derivative of the solution map of the Navier-Sto…
We study energy scale-transfer in Rayleigh-Taylor (RT) flows by coarse-graining in physical space without Fourier transforms, allowing scale analysis along vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $Λ$, due to large-scale pressure gradients acting on small-scales of density and velocity, and deformation work $Π$, due to multi-scale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to RT mixing layer. We find that $Λ$ is a conduit for potential energy, tra…
We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin type model.
Following the findings in \cite{wangsawijaya2020}, we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths $0.32 \leq S/\overlineδ \leq 3.63$, where $S$ is the width of the roughness strips and $\overlineδ$ is the spanwise-averaged boundary-layer thickness. The heterogeneous cases induce counter-rotating secondary flows, and these are compared to the large-scale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high- and low-momentum streaks in the instantaneous…
In this study we experimentally investigate bubbly drag reduction in a highly turbulent flow of water with dispersed air at $5.0 \times 10^{5} \leq \text{Re} \leq 1.7 \times 10^{6}$ over a non-wetting surface containing micro-scale roughness. To do so, the Taylor-Couette geometry is used, allowing for both accurate global drag and local flow measurements. The inner cylinder - coated with a rough, hydrophobic material - is rotating, whereas the smooth outer cylinder is kept stationary. The crucial control parameter is the air volume fraction $α$ present in the working fluid. For small volume fr…
The large-scale structures in the ocean and the atmosphere are in geostrophic balance, and a conduit must be found to channel the energy to the small scales where it can be dissipated. In turbulence this takes the form of an energy cascade, whereas one possible mechanism in a balanced flow at large scales is through the formation of fronts, a common occurrence in geophysical dynamics. We show in this paper that an iconic configuration in laboratory and numerical experiments for the study of turbulence, that of the Taylor-Green or von Kármán swirling flow, can be suitably adapted to the case of…
Knowledge of turbulent flows over non-flat surfaces is of major practical interest in diverse applications. Significant work continues to be reported in the roughness regime at high Reynolds numbers where the cumulative effect of surface undulations on the averaged and integrated turbulence quantities is well documented. Even for such cases, the surface topology plays an important role for transitional roughness Reynolds numbers that is hard to characterize. In this work, we attempt to develop a bottom up understanding of the mechanisms underlying turbulence generation and transport, particula…
In this combined experimental and numerical study on thermally driven turbulence in a rectangular cell, the global heat transport and the coherent flow structures are controlled with an asymmetric ratchet-like roughness on the top and bottom plates. We show that, by means of symmetry breaking due to the presence of the ratchet structures on the conducting plates, the orientation of the Large Scale Circulation Roll (LSCR) can be locked to a preferred direction even when the cell is perfectly leveled out. By introducing a small tilt to the system, we show that the LSCR orientation can be tuned a…
A class of spectral subgrid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of subgrid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale extension where anomalous exponents are measured by roughly one order of magnitude, when compared to direct numerical simulations or to other popular subgrid closures at the same resolution. We found a first indication that intermittency for high order moments is not captured by many of the popular phenomenological models developed so far.
The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of continuity and Navier-Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulat…
We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and enhance kinetic and potential energy dissipation, providing a possible explanation for the observed variability of the local energy dissipation in the bulk of oceanic flows, and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in geophysical scenarios, roughly 10…
We perform direct numerical simulations of turbulent flow at friction Reynolds number $Re_τ\approx 500-2000$ grazing over perforates plates with moderate viscous-scaled orifice diameter $d^+\approx40$--$160$ and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coeffi…
Large-eddy simulations are conducted to contrast momentum and passive scalar transport over large, three-dimensional roughness elements in a turbulent channel flow. Special attention is given to the dispersive fluxes, which are shown to be a significant fraction of the total fluxes within the roughness sublayers. Based on point-wise quadrant analysis, the turbulent components of the transport of momentum and scalars are found to be similar in general, albeit with increasing dissimilarity for roughnesses with low frontal blockage. However, strong dissimilarity is noted between the dispersive mo…
The fluid dynamics video considers an array of two NREL 5-MW turbines separated by seven rotor diameters in a neutral atmospheric boundary layer (ABL). The neutral atmospheric boundary-layer flow data were obtained from a precursor ABL simulation using a Large-Eddy Simulation (LES) framework within OpenFOAM. The mean wind speed at hub height is 8m/s, and the surface roughness is 0.2m. The actuator line method (ALM) is used to model the wind turbine blades by means of body forces added to the momentum equation. The fluid dynamics video shows the root and tip vortices emanating from the blades f…
Nearly homogeneous and isotropic, highly turbulent flow, generated by an original multi-scale injector is experimentally studied. This multi-scale injector is made of three perforated plates shifted in space such that the diameter of their holes and their blockage ratio increase with the downstream distance. The Multi-Scale Turbulence Injector (hereafter, MuSTI) is compared with a Mono-Scale Turbulence Injector (MoSTI), the latter being constituted by only the last plate of MuSTI. This comparison is done for both cold and reactive flows. For the cold flow, it is shown that, in comparison with …
Direct estimation of Lagrangian turbulence statistics is essential for the proper modeling of dispersion and transport in highly obstructed canopy flows. However, Lagrangian flow measurements demand very high rates of data acquisition, resulting in bottlenecks that prevented the estimation of Lagrangian statistics in canopy flows hitherto. We report on a new extension to the 3D Particle Tracking Velocimetry (3D-PTV) method, featuring real-time particle segmentation that outputs centroids and sizes of tracer particles and performed on dedicated hardware during high-speed digital video acquisiti…
We investigate rough-wall turbulent flows through direct numerical simulations of flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at $k^+=10$, where $k$ is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity, $Λ$ (frontal area divided by plan area) ranging from 0.05 to 0.54. The high cost of resolving both the flow around the dense roughness elements and the bulk flow is circumvented by the use of the minimal-span channel technique, recently demonstrated by Chung et al. (J. Flui…
We study the global, i.e. radially averaged, high Reynolds number (asymptotic) scaling of streamwise turbulence intensity squared defined as ${I^2=\overline{u^2}/U^2}$, where $u$ and $U$ are the fluctuating and mean velocities, respectively (overbar is time averaging). The investigation is based on the mathematical abstraction that the logarithmic region in wall turbulence extends across the entire inner and outer layers. Results are matched to spatially integrated Princeton Superpipe measurements [Hultmark M, Vallikivi M, Bailey SCC and Smits AJ. Logarithmic scaling of turbulence in smooth- a…
In recent works we developed a model of balanced gas flow where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the thir…
The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. The…
We investigate the turbulence statistics in a {multiphase plume made of heavy particles (particle Reynolds number at terminal velocity is 450)}. Using refractive-index-matched stereoscopic particle image velocimetry, we measure the locations of particles {whose buoyancy drives the formation of a multiphase plume,} {together with the local velocity of the induced flow in the ambient salt-water}. {Measurements in the plume centerplane exhibit self-similarity in mean flow characteristics consistent with classic integral plume theories.} The turbulence characteristics resemble those measured in a …
The classical experiments on turbulent friction in rough pipes were performed by J. Nikuradse in the 1930's. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmogórov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler, and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existe…
High-fidelity large-eddy simulations of the flow around two rectangular obstacles are carried out at a Reynolds number of 10,000 based on the free-stream velocity and the obstacle height. The incoming flow is a developed turbulent boundary layer. Mean-velocity components, turbulence fluctuations, and the terms of the turbulent-kinetic-energy budget are analyzed for three flow regimes: skimming flow, wake interference, and isolated roughness. Three regions are identified where the flow undergoes the most significant changes: the first obstacle's wake, the region in front of the second obstacle,…
We investigate the large-scale intermittency of vertical velocity and temperature, and the mixing properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations, in a parameter space relevant for the atmosphere and the oceans. Over a range of Froude numbers of geophysical interest ($\approx 0.05-0.3$) we observe very large fluctuations of the vertical components of the velocity and the potential temperature, localized in space and time, with a sharp transition leading to non-Gaussian wings of the probability distribution functions. T…
We present a model for the scaling of mixing in weakly rotating stratified flows characterized by their Rossby, Froude and Reynolds numbers Ro, Fr, Re. It is based on quasi-equipartition between kinetic and potential modes, sub-dominant vertical velocity and lessening of the energy transfer to small scales as measured by the ratio rE of kinetic energy dissipation to its dimensional expression. We determine their domains of validity for a numerical study of the unforced Boussinesq equations mostly on grids of 10243 points, with Ro/Fr> 2.5 and with 1600< Re<1.9x104; the Prandtl number is one, in…
Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterise surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement …
