Free Shear Flows

Recently, Fan & Lou considered the excitation and time evolution of hydromagnetic density waves in a differentially rotating thin gaseous disc embedded in an azimuthal magnetic field. The authors found that both fast and slow hydromagnetic density waves are amplified while they `swing' from leading to trailing configurations, and gave a detailed description of the phenomenon. Fan & Lou noticed that the results of their numerical study indicate the existence of a `coupling' between slow and fast waves. In this Letter we prove, in a simple and exact analytic way, that the coupling between slow and fast waves, presumed by Fan & Lou on the basis of their numerical study, indeed exists. We show that the coupling is induced exclusively by the presence of the velocity shear in the gaseous disc, and that it leads to the mutual transformations of the different density wave modes. We argue that the shear-induced wave transformations may play a significant role in the overall dynamics of galactic MHD density waves.

The phenomenon of Shear Induced wave Transformations (SITs) , is a common feature of flows, sustaining n > 1 mode of wave motion. Until now this "nonmodal" phenomenon was described only in terms of the time evolution of individual Fourier harmonics of perturbations in the space of wave numbers (k-space). In this paper we present the results of the first, direct numerical simulations of SITs, giving compelling evidence in favor of the robust and recognizable character of SITs. The importance of these results for an understanding of physical processes in astrophysical shear flows is pointed out. Namely, concrete astrophysical situations (solar plasma flows, galactic gaseous disks, accretion disks and accretion-ejection flows), where this approach may help to shed some light on observational appearances of related objects, are indicated and discussed.

Recently, Fan & Lou considered the excitation and time evolution of hydromagnetic density waves in a differentially rotating thin gaseous disc embedded in an azimuthal magnetic field. The authors found that both fast and slow hydromagnetic density waves are amplified while they `swing' from leading to trailing configurations, and gave a detailed description of the phenomenon. Fan & Lou noticed that the results of their numerical study indicate the existence of a `coupling' between slow and fast waves. In this Letter we prove, in a simple and exact analytic way, that the coupling between slow and fast waves, presumed by Fan & Lou on the basis of their numerical study, indeed exists. We show that the coupling is induced exclusively by the presence of the velocity shear in the gaseous disc, and that it leads to the mutual transformations of the different density wave modes. We argue that the shear-induced wave transformations may play a significant role in the overall dynamics of galactic MHD density waves.

Atmospheric emissions related to harbor-related activities can significantly contribute to air pollution of coastal urban areas and so, could have implications to the citizens’ health that live in those areas. Of great concern is the local impact of the emissions that are generated while ships are at berth, since not all types of ships switch off the main engines. This paper intends to investigate the influence of the stack configuration for generic cargo ships on the exhaust smoke dispersion, using the Port of Leixões as a case study and a series of wind tunnel experiments with support of Particle Image Velocimetry (PIV) technique. For that, different configurations of the stack of a cargo ship (in terms of height, geometry and diameter) were simulated under the typical wind conditions of the study area. The PIV results indicate negligible differences between the medium and long stack height, with the short stack height presenting a strong impact on the flow field around the stack....

In this work discrete element modeling ͑DEM͒ was applied to the flow of granular jets against a target. The resulting sheetlike or conelike formations under different conditions are described and explained by means of kinetic analysis. A qualitative and quantitative comparison with experimental results ͓Cheng et al., Phys. Rev. Lett. 93, 188001 ͑2007͔͒ provides interesting insights in the theoretical treatment of the head-on collision of granular jets. Results presented in this paper provide a theoretical description of this type of physical system. However, there still exist obstacles in obtaining quantitative results.

In this work discrete element modeling ͑DEM͒ was applied to the flow of granular jets against a target. The resulting sheetlike or conelike formations under different conditions are described and explained by means of kinetic analysis. A qualitative and quantitative comparison with experimental results ͓Cheng et al., Phys. Rev. Lett. 93, 188001 ͑2007͔͒ provides interesting insights in the theoretical treatment of the head-on collision of granular jets. Results presented in this paper provide a theoretical description of this type of physical system. However, there still exist obstacles in obtaining quantitative results.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to Re τ = 395 GREGOIRE WINCKELMANS, UCL, Louvain School of Engineering, LAURENT BRICTEUX -Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at Re τ = u τ h/ν = 2000, 950, 550, and 395. We consider the turbulent region: y + = Re τ η (with η = y/h) larger than 70). A new model for the effective turbulent viscosity, ν t = -u v / du dy , is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a "modified law of the wall," 1 κ log(y + + y + 0 ) -η + C, with the added classical "law of the wake," D g(η). The new -η term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms "work together," as both are multiplied by the same 1 κ value (recall that D is not related to κ). Only at the highest Reynolds numbers does this correction become negligible. As to the y + 0 shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the ν t near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all Re τ cases. In particular, the von Kàrmàn constant is obtained as κ = 0.37: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to 0.38 as Spalart et al.

The dissimilarity between the Reynolds stresses and the heat fluxes in perturbed turbulent channel and plane Couette flows was studied using direct numerical simulation. The results demonstrate that the majority of the dissimilarity was due to the difference between the wall-normal fluxes, while the difference between the streamwise fluxes was lower. The main causes for the dissimilarity were the production terms, followed by the velocity-pressure interaction terms. Further insights into the importance of the velocity-pressure interaction in the origin of the dissimilarity are provided using two-point correlation. Furthermore, an octant conditional averaged dataset reveals that not only the wall-normal heat flux but also the streamwise heat flux is strongly related to the wall-normal gradient of the mean temperature. A simple Reynolds-averaged Navier–Stokes (RANS) heat flux model is proposed as a function of the Reynolds stresses. A comparison of the direct numerical simulation data...

Yield stress fluid flows in Couette cells have been widely studied in the last decades for their intriguingly exhibiting phenomena. In this paper, we use a PIV technique to investigate the axisymmetric flow and rheological properties of a Carbopol gel in a relatively wide cylindrical Couette device. Carbopol gel is known to exhibit viscoplastic behavior and is often described using a Herschel-Bulkley law, which is characterized by a plastic yield stress s y and a shear-dependent nonlinear viscosity. In some cases, the elasticity of the material has to be accounted for to understand the whole dynamics of the system, in particular for unsteady flows as observed in the present study. Two set of experiments are conducted here in order to highlight these different rheological behaviors and the resulting dynamics: (i) a steady shear configuration and (ii) an unsteady shear configuration, in which the angular velocity of the inner cylinder is either constant or time dependent (sin profile), respectively. In the steady configuration, a simple optimization model, based on the Herschel-Bulkley law, is developed to extract the rheological parameters of the viscoplastic contribution of the gel from the steady velocity fields. Results are shown to be in good agreements with rheological parameters obtained from a standard rheometer. On the other hand, the elastic contribution of the material is highlighted in the unsteady shear configuration, for which a spatio-temporal transition between solid-elastic and fluid behaviors is observed. Different models are proposed to describe the dynamics of the unsteady flow. First, quasi-steady state models allow to predict both the fluid shear zone close to the inner cylinder and the elastic deformation of the material as long as their contributions can be decoupled in space and in time. For more complex dynamics, i.e. when the flow becomes strongly unsteady, an elasto-viscoplastic model is developed to describe the flow dynamics. It is shown to quantitatively reproduce the experimental measurements. Finally, an elastic wave model is derived to describe an elastic front propagating from the inner cylinder to the outer one, and observed at every half forcing period. The front velocity is thus shown to scale on the phase velocity of an elastic wave in a deformable solid.

In this paper Spalding's formulation for the law of the wall with constants modified by Persen is used to describe the inner region (viscous sub-layer and certain portion of logarithmic layer) and a wake law due to Persen is used to describe the wake region (outer region). These two laws are examined in the light of measured data by Marušić and Perry for non-equilibrium adverse pressure gradient layers. It is observed that structure of turbulence for this flow is well-described by these two laws. From the known structure of turbulence eddy viscosity for the flow under consideration is calculated. Self similarity in eddy viscosity is observed in the wall region. Keywords. Non-equilibrium turbulent boundary layer; adverse pressure gradient; law of the wall; law of the wake.

Waves with constant, nonzero linearized frequency form an interesting class of nondispersive waves whose properties differ from those of nondispersive hyperbolic waves. We propose an inviscid Burgers-Hilbert equation as a model equation for such waves, and give a dimensional argument to show that it models Hamiltonian surface waves with constant frequency. Using the method of multiple scales, we derive a cubically nonlinear, quasilinear, nonlocal asymptotic equation for weakly nonlinear solutions. We show that exactly the same asymptotic equation describes surface waves on a planar discontinuity in vorticity in two-dimensional inviscid, incompressible fluid flows. Thus, the Burgers-Hilbert equation provides an effective equation for these waves. We describe the Hamiltonian structure of the Burgers-Hilbert and asymptotic equations, and show that the asymptotic equation may be also be derived by means of a near-identity transformation. We derive a semi-classical approximation of the asymptotic equation, and show that spatially periodic, harmonic traveling waves are linearly and modulationaly stable. Numerical solutions of the Burgers-Hilbert and asymptotic equations are in excellent agreement in the appropriate regime. In particular, the lifespan of small-amplitude smooth solutions of the Burgers-Hilbert equation is given by the cubically nonlinear timescale predicted by the asymptotic equation.

In some linearly unstable flows, secondary instability is found to have a much larger wavelength than that of the primary unstable modes, so that it cannot be recovered with a classical Floquet analysis. In this work, we apply a new formulation for capturing secondary instabilities coupling multiple length scales of the primary mode. This formulation, based on two-dimensional stability analysis coupled with a Bloch waves formalism originally described in Schmid et al. (2017), allows to consider high-dimensional systems resulting from several repetitions of a periodic unit, by solving an eigenproblem of much smaller size. Collective instabilities coupling multiple periodic units can be thus retrieved. The method is applied on the secondary stability of a swept boundary-layer flow subject to stationary cross-flow vortices, and compared with Floquet analysis. Two multi-modal instabilities are recovered: for streamwise wavenumber α v close to zero, approximately twelve sub-units are involved in large-wavelength oscillations; whereas a staggered pattern, characteristic of subharmonic instabilities, is observed for α v = 0.087.

In this paper we review the problem of the wake-flow stability for a thin airfoil by using both a locally plane-wave analysis, based on a WKBJ approximation, and a global numerical stability analysis. The core of the instability is further localized by performing a structural sensitivity analysis of the linearized Navier-Stokes operator as outlined in [7]. In particular the sensitivity of the eigenvalue to a spatially-localized feedback from velocity to force is evaluated by using the product of the direct and adjoint global mode. It is shown, using a plane wave analysis, that the flow at the trailing edge is absolutely unstable for any Reynolds number for values of the parameter m corresponding to separation of the base flow. The analysis further shows that the base flow at the trailing edge is not absolutely unstable as the value of m tends to zero. The global eigenvalue analysis shows that the frequency and growth rate are very similar to what is found with the local plane wave analysis at the trailing edge. Finally, the structural sensitivity analysis indicates that the wavemaker is situated just downstream of the trailing edge. .

The streamwise evolution of a turbulent boundary layer (TBL) developing under constant pressure on a smooth wall is considered. The closure problem is described for the zero pressure gradient (ZPG) flow where the only assumptions made are the use of classical similarity laws, such as Prandtl's law of the wall and Coles'[1, 2] law of the wake, together with the mean continuity and mean momentum differential and integral equations. The important parameters are identified and the problem is reduced to one semi-empirical input with the assumption that the Reynolds shear stress can be described by a two-parameter family. Good agreement is shown with the experimental data.

The purpose of this paper, dedicated to the memory of our friend Hieu Ha Minh, is to wander through the turbulence universe using deterministic computational tools based on large-eddy simulations (LES) in physical and spectral space. We first briefly recall the subgrid models used, then apply them to mixing layers, jets, separated flows (the backstep in particular, on which Hieu

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The transition from a regularly ordered state of fluid motion to chaotic and turbulent regime has been long observed and progressively understood through the discovery and application of theoretical tools and frameworks. One such lens through which the problem can be attacked confines the dynamics of a turbulent system to a set of ordinary differential equations describing the time evolution of velocity modes, allowing for the application of techniques from dynamical systems theory. In this body of work,this framework shall be applied to develop a series of low dimensional models of the transition to turbulence in plane Couette flow (fluid sheared between two parallel plates of anti-parallel velocity). These models will then be investigated to understand certain features of the transition. Initially, the transition to Newtonian turbulence is investigated, with the results used as a starting point for a study of viscoelastic turbulence. The first Chapter of this thesis will introduce...

Existing differences between experimental, computational and theoretical representations of a particular flow do not allow one-to-one comparisons, prevent us from identifying the absolute contributions of the various sources of uncertainty in each approach, and highlight the importance of developing suitable corrections for experimental techniques. In this study we utilize the latest Pitot tube correction schemes to develop a technique which improves on the outcome of hot-wire measurements of mean velocity profiles in ZPG turbulent boundary layers over the range 11 500 < Re θ < 21 500. Measurements by Bailey et al. (2013), carried out with probes of diameters ranging from 0.2 to 1.89 mm, supplemented by other data with larger diameters up to 12.82 mm, are used first to develop a somewhat improved Pitot tube correction which is based on viscous, shear and near-wall schemes (which contribute with around 85% of the effect), together with a turbulence scheme which accounts for 15% of the whole correction. The correction proposed here leads to similar agreement with available high-quality datasets in the same Reynolds number range as the one proposed by Bailey et al. (2013), but this is the first time that the contribution of the turbulence scheme is quantified. In addition, four available algorithms to correct wall position in hot-wire measurements are tested, using as benchmark the corrected Pitot tube profiles with artificially simulated probe shifts and blockage effects. We find that the κB-Musker correction developed in this study produces the lowest deviations with respect to the introduced shifts. Unlike other schemes, which are based on a prescribed near-wall region profile description, the κB-Musker is focused on minimizing the deviation with respect to theκB relation, characteristic of wall-bounded turbulent flows. This general approach is able to locate the wall position in probe measurements of the wall-layer profiles with around one half the error of the other available methods. The difficulties encountered during the development of adequate corrections for high-Re boundary layer measurements highlight the existing gap between the conditions that can be reproduced and measured in the laboratory and the so-called canonical flows.

This article reports on one component of a larger study on measurement of the zeropressure-gradient turbulent flat plate boundary layer, in which a detailed investigation was conducted of the suite of corrections required for mean velocity measurements performed using Pitot tubes. In particular, the corrections for velocity shear across the tube and for blockage effects which occur when the tube is in close proximity to the wall were investigated using measurements from Pitot tubes of five different diameters, in two different facilities, and at five different Reynolds numbers ranging from Re θ = 11 100 to 67 000. Only small differences were found amongst commonly used corrections for velocity shear, but improvements were found for existing nearwall proximity corrections. Corrections for the nonlinear averaging of the velocity fluctuations were also investigated, and the results compared to hot-wire data taken as part of the same measurement campaign. The streamwise turbulence-intensity correction was found to be of comparable magnitude to that of the shear correction, and found to bring the hot-wire and Pitot results into closer agreement when applied to the data, along with the other corrections discussed and refined here.

A more poetic long title could be ‘A voyage from the shifting grounds of existing data on zero-pressure-gradient (abbreviated ZPG) turbulent boundary layers (abbreviated TBLs) to infinite Reynolds number’. Aided by the requirement of consistency with the Reynolds-averaged momentum equation, the ‘shifting grounds’ are sufficiently consolidated to allow some firm conclusions on the asymptotic expansion of the streamwise normal stress $\langle uu\rangle ^{+}$, where the $^{+}$ indicates normalization with the friction velocity $u_{{\it\tau}}$ squared. A detailed analysis of direct numerical simulation data very close to the wall reveals that its inner near-wall asymptotic expansion must be of the form $f_{0}(y^{+})-f_{1}(y^{+})/U_{\infty }^{+}+\mathit{O}(U_{\infty }^{+})^{-2}$, where $U_{\infty }^{+}=U_{\infty }/u_{{\it\tau}}$, $y^{+}=yu_{{\it\tau}}/{\it\nu}$ and $f_{0}$, $f_{1}$ are $\mathit{O}(1)$ functions fitted to data in this paper. This means, in particular, that the inner peak ...

Effects of moderately large Reynolds numbers R are studied by considering higher order terms in the expansions for turbulent pipe and channel flows for R → ∞. Matched asymptotic expansions using two length scales are employed to emphasize the two-layer structure of turbulent shear flows near solid walls. The effects appear as additional terms in extended forms of the law of the wall, the logarithmic velocity law, the velocity defect law and the logarithmic skinfriction law. These generalizations are critically compared with experimental results for pipe flows of Patel & Head and extremely good agreement is obtained. Also, possible applications are discussed for extending the range of skin-friction and heat-transfer devices which are based on wall similarity.

The measured mean velocity profiles at the various stations along a conical diffuser (8 ° total divergence angle) were found to consist of log regions, half-power law regions and linear regions. The describing coefficients for the inner half-power law region (which followed a rather narrow log region) differed from the standard values due to the axi-symmetric geometry and lack of moving equilibrium of the flow as it attempted to adjust to a varying adverse pressure gradient. However, these coefficients (like those for the linear region) correlated with the local wall shear stress and the kinematic pressure gradient.

Coherent structures in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient have been studied using particle image velocimetry (PIV). The experimental setup is designed to achieve flow conditions corresponding to trailing-edge stall of an airfoil. Large sets of instantaneous velocity fields are acquired by PIV in streamwise-wall-normal planes at three different streamwise locations. Signatures of hairpin vortices are found in all the fields and hairpin packets occur in the majority of them. The essential features of the hairpins and hairpin packets are similar to those found in zero-pressuregradient turbulent boundary layers. The hairpin vortices are however slightly more inclined with respect to the wall in the present flow, and the upward growth of the hairpin packets in the streamwise direction is more important. The characteristics of the spanwise vortices are also documented.

The effects of efflux velocity, operational conditions, stack geometry, and buoyancy on the exhaust dispersion for a generic frigate are investigated numerically. The conservation of energy, momentum, mass, species, and turbulence equations have been solved using the finite volume method. It is found that the exhaust smoke dispersion is affected by the efflux velocity, operational conditions, buoyancy, and turbulence, as well as the geometry of the stack. The momentum of the exhaust gases and the plume height increase as the velocity ratio increases. The results for the slow ahead operation condition show that the buoyancy effect is the strongest, and the plume height is minimum for this case. The exhaust temperatures and velocity values for the full ahead operation are found to be the highest. However, the plume height for this case is not maximum. This may be attributed to the high turbulence levels for this case. It is found that the effect of stack geometry on the exhaust smoke ...

The main features of the urban boundary layer in the metropolitan region of São Paulo are estimated based on rawinsondes carried out (a) every 3 hr in two 10‐day field campaigns of the MCITY BRAZIL Project during the summer and winter of 2013 and (b) regularly once per day and continuously for 4 years from 2009 to 2013. On average, the boundary layer height showed a daytime maximum of 1476 ± 149 m in summer and 1122 ± 168 m in winter campaigns. The differences are related to seasonal variations in the (a) buoyancy flux at the surface, which was 30% larger in summer (4.7 ± 0.6 MJ m−2 day−1), and the (b) static stability of the free atmosphere, which was 15% smaller in summer (3.3 ± 0.1 K km−1). The average nighttime boundary layer height, estimated from equilibrium empirical expression, indicated maximum of 126 ± 13 m in summer and 122 ± 10 m in winter campaigns. The presence of a low‐level jet was identified in 80% of the field campaign nights, with intensity varying from 2.7 to 14 ...

increasing FST is known to increase skin friction and to enhance heat transfer (Hancock and Bradshaw 1989; Blair 1983). However, a large number of previous studies focused on the correlation between the increase of skin friction and heat transfer with FST. Hancock and Bradshaw (1989) showed that the effect of FST in the turbulent boundary layer does not only depend on the turbulence intensity level but on a characteristic scale in the FST, which they defined as the dissipation length scale. However, skin-friction coefficients were deduced from logarithmic plots on the assumption that the universal logarithmic law also applies in the presence of FST. Thole and Bogard (1996) performed extensive research on FST levels up to 20% and presented boundary layer statistics that confirmed the validity of the logarithmic law in the mean profiles of the boundary layer for high turbulence levels by comparing direct measurements of total shear stress with values obtained using a Clauser fit to the log region. Similarly, Stefes and Fernholz (2004) compared skin-friction data obtained from oil-film interferometry (OFI), wall hot wire, and Preston tube at relatively high Reynolds numbers and FST levels up to 13%, showing that all skin-friction data points lied within an error band of approximately 6% on C f. Traditional indirect pressure-based methods, such as the Preston tube, rely on the law of the wall and suffer from limitations arising from its intrusive nature. Velocity profile-based methods such as Clauser chart are also of limited applicability, since they also assume the existence of the law of the wall and require the knowledge of its extent and constants beforehand. Contrarily, Rodríguez-López et al. (2015) proposed to leave these constants free to adopt the value that best fits the data. In addition, this method does not require to prescribe the extent of the logarithmic layer (which can vary under FST conditions, see Dogan et al. 2016) and allows a certain uncertainty in the wall-probe initial position.

The statistical scaling properties of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) are presented. The intended flow is generated using the direct numerical simulation (DNS) TBL code of Simens et al. (2009) and Borrell et al. (2013), with a modified farfield boundary condition (BC). The conditions for self-similarity and appropriate scaling are derived, with mean and Reynolds stress profiles presented using this scaling. The APG and ZPG DNS are also compared under the classical viscous scaling.

The observation of large-scale coherent structures in turbulent boundary layers has sparked great experimental and numerical interest. While most studies have focussed on channel flows and zero pressure gradient (ZPG) boundary layer flows, our understanding of wall turbulence under the influence of a streamwise pressure gradient is still quite limited due to the lack of sufficiently high Reynolds number data and large facilities to reach an equilibrium state where theoretical scaling laws can be relevant [1]. The length of these structures (7-14 \delta [2]) requires a large field of view and a high spatial resolution to measure all relevant spatial scales. [1] L. Castillo and W. K. George. Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA journal, 39.1:41-47, 2001. [2] N. Hutchins and I. Marusic. Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech, 579:1-28, 2007.

Uniform momentum zones (UMZs) for an adverse pressure gradient turbulent boundary layer (APG-TBL) are characterised in this paper. The database described by Cuvier et al. [2017], which was obtained using 2-component 2-dimensional (2C-2D) particle image velocimetry (PIV) at two free-stream velocities of 5 m/s and 9 m/s, is used for this study. The methodology described by Adrian et al. [2000] is used to identify and hence, statistically characterise the UMZs and UMZ interfaces in the APG-TBL. This study shows that the number of detected UMZs increases in the streamwise direction for both free-stream velocities. This increase is primarily thought to be due to the adverse pressure gradient (APG) since a comparison of the results between the two free-stream velocity APG-TBLs did not show any statistically significant difference with Re θ for the range of Reynolds number examined in this study. The thickness of the UMZs, δ w and the jump in streamwise velocity across the UMZ interface were found to increase in the wall-normal direction, whereas the width of the UMZ interface, ∆ u , was found to decrease. The number of UMZs, N umz , identified appeared to influence the modal velocities/uniform velocities, geometrical properties of the UMZs and statistics of the flow. With increasing N umz , the modal velocities of the UMZs moved to higher values to accommodate new UMZs that developed closer to the wall and the thickness of each UMZ and ∆ u across the UMZ interface decreased, whereas δ w increased. A slight difference in the magnitude of streamwise Reynolds stress and Reynolds shear stress was observed in the inner and outer regions, and a slight difference in the magnitude of turbulence production was also observed in the inner region between the velocity fields having a low or high number of UMZs indicating that the flow statistics are influenced by the number of UMZs present in the APG-TBL.

The Prandtl Plus scaling parameters are reexamined theoretically. The flow governing equations approach is used to examine similarity issues of the inner region of wall-bounded turbulent flows as well as laminar flow cases. It is found that the Prandtl Plus parameters are in fact similarity scaling parameters for laminar sink flow but NOT the more general laminar Falkner-Skan boundary layer flows. For turbulent boundary layer flows along a wall, it is found that only turbulent sink flows show similarity with the Prandtl Plus scaling parameters. This is diametrically opposed to the accepted notion that the Prandtl Plus parameters work for every wall-bounded turbulent flow. To correct the problem with the Prandtl Plus parameters, we introduce a new set of scaling parameters that work for the Falkner-Skan boundary layer flows and satisfy the relevant part of the flow governing equations approach to similarity.

The purpose of this paper, dedicated to the memory of our friend Hieu Ha Minh, is to wander through the turbulence universe using deterministic computational tools based on large-eddy simulations (LES) in physical and spectral space. We first briefly recall the subgrid models used, then apply them to mixing layers, jets, separated flows (the backstep in particular, on which Hieu

By using the RANS boundary layer equations, it will be shown that the outer part of an adverse pressure gradient turbulent boundary layer tends to remain in equilibrium similarity, even near and past separation. Such boundary layers are characterized by a single and constant pressure gradient parameter, Λ, and its value appears to be the same for all adverse pressure gradient flows, including those with eventual separation. Also it appears from the experimental data that the pressure gradient parameter, Λθ, is also approximately constant and given by Λθ=0.21±0.01. Using this and the integral momentum boundary layer equation, it is possible to show that the shape factor at separation also has to within the experimental uncertainty a single value: Hsep≅2.76±0.23. Furthermore, the conditions for equilibrium similarity and the value of Hsep are shown to be in reasonable agreement with a variety of experimental estimates, as well as the predictions from some other investigators.

A Direct Numerical Simulation of turbulent flow subjected to an adverse pressure gradient (APG) was performed. As already noticed by many authors in such configurations, a second outer peak of turbulent kinetic energy is observed in the region of APG. In the present configuration, this peak is due to the production of intense vortices which are shown to be related to the instability of low speed streaks.

We focus on the wake function F (Y), where Y = y/δ: the excess velocity above the logarithmic profile in wall-bounded turbulence. It is first measured using direct numerical simulation data of turbulent channel flow at Re τ 5200, which has a distinguishable overlap layer. The function Q(Y) = Y F (Y) is seen to be significant only beyond Y c 0.16, and also linear (with a slope α 1.15) up to Y 0.5. Our simplest Q(Y) model is then a linear ramp function that starts at the measured intercept. Our Q(Y) model is furthermore extended up to the channel center, by subtracting a quadratic term which satisfies the boundary condition at Y = 1. The analytical integration of Q(Y) provides the model for the wake function with offset Y c , and which covers the full range; it is seen to fit very well the DNS data. Our Q(Y) model is also compared to the "extended law of the wall" model without offset. Furthermore, and to comply with some recent literature, a version of our model is also developed with some small slope α 0 α contribution to Q(Y) within the overlap layer. The DNS of a zero pressure gradient boundary layer at Re τ 2300 is considered next: the amplitude of the wake function is much larger than in channel flow (α 7.3) and the intercept is smaller (Y c 0.11). The obtained F (Y) model also compares very well with the DNS data over the full range. Lastly, we also revisit the Coles wake function model and we show that adding the offset improves it significantly.

The temporal evolution of global modes is studied, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. As basic Bow we consider weakly nonparallel three-dimensional shear Aows. A necessary condition for the existence of a global mode is the presence of at least two branches of the local dispersion relation and a location where they coalesce. It leads to a mode coupling in a neighborhood of that point. To analyze the mode coupling the uniform asymptotic description of Kravtsov and Ludwig is employed which also yields a general formula for the global eigenfrequency.

Direct numerical simulation (DNS) of a fully developed turbulent channel flow for various Reynolds numbers has been carried out to investigate the Reynolds number dependence. The Reynolds number is set to be Reτ=180, 395, and 640, where Reτ is the Reynolds number based on the friction velocity and the channel half width. The computation has been executed with the use of the finite difference method. Various turbulence statistics such as turbulence intensities, vorticity fluctuations, Reynolds stresses, their budget terms, two-point correlation coefficients, and energy spectra are obtained and discussed. The present results are compared with the ones of the DNSs for the turbulent boundary layer and the plane turbulent Poiseuille flow and the experiments for the channel flow. The closure models are also tested using the present results for the dissipation rate of the Reynolds normal stresses. In addition, the instantaneous flow field is visualized in order to examine the Reynolds numb...

A smoke visualization experiment has been performed in the first 3 m of the neutrally stable atmospheric boundary layer at very large Reynolds number (Re θ >10 6). Under neutral atmospheric conditions mean wind profiles are shown to agree well with those in the canonical flat plate zero-pressure-gradient boundary layer. The experiment was designed to minimize the temperature difference between the passive marker (smoke) and the air to insure that any observed structures were due to vortical, rather than buoyant motions. Data was acquired in the streamwise/wall-normal plane using a planar laser lightsheet and CCD cameras. Images obtained are strikingly similar to those observed in classical laboratory experiments at low to moderate Reynolds numbers and reveal large-scale ramp-like structures with downstream inclination of 3°-35° (see Figure 1). This inclination is interpreted as the hairpin packet growth angle following the hairpin vortex packet paradigm of Adrian et al. (2000). The distribution of this characteristic angle is shown to agree with the results of experiments at far lower Reynolds numbers, suggesting a similarity in structures at low, moderate, and high Reynolds number boundary layers. These results begin to suggest that the hairpin packet model is valid at high Reynolds numbers of technological interest. Figure 1. Two representative smoke visualization images in the first 3 m of the atmospheric boundary layer obtained using planar laser light sheet illumination. Flow is from left-to-right at Re θ = 9.2×10 6. The approximate extent of the large scale structures has been indicated with white lines inclined at the hairpin packet growth angle γ.

Wind tunnel flow visualization tests were conducted to analyse the efflux velocity impacts and the yaw angle on the smoke dispersion of the exhaust for a generic frigate. An analytical study was also implemented to obtain the exhaust plume trajectories. The 1/100 scale generic frigate, having a platform for helicopters on the aft of the ship, was built and employed during the experimental study. The forward and astern cruises of the frigate were considered. It is found that the plume height and the exhaust gases momentum increase with the velocity ratio. The problem of smoke nuisance was observed for the ratios with low velocity such as K=0.2. The plume was also directed towards the helicopter platform when the yaw angles are higher than 10°. The experimental results are compared with the analytical solutions for three different velocity ratios. The compliance between the experimental and analytical results is found to be consistent.

The principal purpose of this study is to understand the entropy generation rate in bypass, transitional, boundary-layer flow better. The experimental work utilized particle image velocimetry (PIV) and particle tracking velocimetry (PTV) to measure flow along a flat plate. The flow past the flat plate was under the influence of a negligible “zero” pressure gradient, followed by the installation of an adverse pressure gradient. Further, the boundary layer flow was artificially tripped to turbulence (called “bypass” transition) by means of elevated freestream turbulence. The entropy generation rate was seen to behave similar to that of published computational fluid dynamics (CFD) and direct numerical simulation (DNS) results. The observations from this work show the relative decrease of viscous contributions to entropy generation rate through the transition process, while the turbulent contributions of entropy generation rate greatly increase through the same transitional flow. A basi...

Fundamental understanding of the entropy generation process in characteristic wall shear flows is developed. For entropy generated by fluid friction, the rates are predictable for developed turbulent flows and pure laminar flows. The main concern lies in prediction for flows undergoing so-called ''bypass'' transition from laminar to turbulent state. In this study, the entropy generation process in the bypass transition scenario is investigated for a flat plate boundary layer under effects of adverse and favorable pressure gradients. For the case studied, transition occurs prematurely due to the presence of strong levels of freestream turbulence. Reynolds-Averaged Navier-Stokes (RANS) models and direct numerical simulations (DNS) are implemented to study the local entropy generation in pre-transitional and transitional regions. Three of these RANS models are transitional models such as, traditional SST k-x (2eq), SST k-x (4eq) and k-kl-x. They are used for prediction of the onset of transition and the results are compared with DNS. All the RANS models predicted transition onset prematurely and, consequently, over predict the integral entropy generation rate and the skin friction coefficient in the transition region. Four simulations have been performed for (1) zero, (2) favorable, (3) adverse and (4) strong-adverse pressure gradient cases. The numerical results show that the pressure gradient has a significant effect on the onset of transition and entropy generation. Transition is early and abrupt for the strong adverse pressure gradient but occurs further downstream and is longer with the increasingly favorable flows. Entropy generation rate at the wall increases as the pressure gradient grows.

This paper examines and contrasts the response of planar turbulent wakes with initially symmetric and asymmetric mean velocity profiles to identical imposed streamwise pressure gradients. The focus on near wake behavior, profile asymmetry, and pressure gradient is motivated by their relevance to high-lift systems for commercial transport aircraft. In the experiments, the symmetric wake is generated by a flat plate with a tapered trailing edge. Active and passive flow control are applied on an identical second plate in order to generate the asymmetric wake. Both favorable and adverse constant pressure gradients are imposed on the wakes by means of a downstream diffuser section with fully adjustable top and bottom wall contour. For both symmetric and asymmetric wakes, the effect of pressure gradient on wake spreading, mean velocity defect decay, and the streamwise evolution of the turbulent stresses are documented in detail. In this manner, the role of asymmetry in strained wake development is isolated. We also gauge the ability of commonly used one-and two-equation turbulence models to predict the streamwise wake evolution observed in the experiments.

An exercise is described aiming at the comparison of the results of seven mesoscale models used for the simulation of an ideal circulation case. The exercise foresees the simulation of the flow over an ideal sea-land interface including ideal topography in order to verify model deviations on a controlled case. All models involved use the same initial and boundary conditions, circulation and temperature forcings as well as grid resolution in the horizontal and simulate the circulation over a 24-h period of time. The model differences at start are reduced to the minimum by the case specification and consist mainly of the parameterisation and numerical formulation of the fundamental equations of the atmospheric flow. The exercise reveals that despite the reduction of the differences in the case configuration, the differences in model results are still remarkable. An ad hoc investigation using one model of the original seven identifies the treatment of the boundary conditions, the parameterisation of the horizontal diffusion and of the surface heat flux as the main cause for the model deviations. The analysis of ideal cases represents a revealing and interesting exercise to be performed after the validation of models against analytical solution but prior to the application to real cases.