Volume 20, Issue 10, October 2008

Recent theoretical, numerical, and experimental investigations performed at the Department of Mechanics, KTH Stockholm, and the Department of Mechanical Engineering, Eindhoven University of Technology, are reviewed, and new material is presented to clarify the role of the boundarylayer streaks and their instability with respect to turbulentbreakdown in bypass transition in a boundary layer subject to freestream turbulence. The importance of the streak secondaryinstability process for the generation of turbulent spots is clearly shown. The secondary instability manifests itself as a growing wave packet located on the lowspeed streak, increasing in amplitude as it is dispersing in the streamwise direction. In particular, qualitative and quantitative data pertaining to temporal sinuous secondary instability of a steady streak, impulse responses both on a parallel and a spatially developing streak, a model problem of bypass transition, and full simulations and experiments of bypass transition itself are collected and compared. In all the flow cases considered, similar characteristics in terms of not only growth rates, group velocity, and wavelengths but also threedimensional visualizations of the streak breakdown have been found. The wavelength of the instability is about an order of magnitude larger than the local boundarylayer displacement thickness , the group velocity about 0.8 of the freestream velocity , and the growth rate on the order of a few percent of . The characteristic structures at the breakdown are quasistreamwise vortices, located on the flanks of the lowspeed region arranged in a staggered pattern.
 SPECIAL TOPIC: TURBULENCE PHYSICS AND CONTROL—PAPERS FROM A WORKSHOP IN HONOR OF JOHN KIM'S 60th BIRTHDAY, STANFORD, CALIFORNIA, SEPTEMBER 2007



Representing anisotropy of twopoint secondorder turbulence velocity correlations using structure tensors
View Description Hide DescriptionA locally homogeneous representation for the twopoint, secondorder turbulent velocity fluctuation is formulated in terms of three linearly independent structure tensors [Kassinos et al., J. Fluid Mech.428, 213 (2001)]: Reynolds stress, dimensionality , and stropholysis . These structure tensors are singlepoint moments of the derivatives of vector stream functions that contain information about the directional and componential anisotropies of the correlation. The representation is a sum of several rotationally invariant component tensors. Each component tensor scales like a power law in , while its variation in depends linearly on the structure tensors. Continuity and selfconsistency constraints reduce the number of degrees of freedom in the model to 17. A finite Re correction is introduced to the representation for separations of the order of Kolmogorov’s length scale. To evaluate our representation, we construct a model correlation by fitting the representation to correlations calculated from direct numerical simulation (DNS) of homogeneous turbulence and channel flow. Comparison of the model correlation to the DNS data shows that the representation can capture the character of the anisotropy of twopoint secondorder velocity correlation tensors.

The sound from mixing layers simulated with different ranges of turbulence scales
View Description Hide DescriptionThe role of turbulence scales in generating farfield sound in free shear flows is studied via direct numerical simulations of temporally developing, Mach 0.9 mixing layers. Four flows were simulated, starting from the same initial conditions but with Reynolds numbers that varied by a factor of 12. Above momentum thickness Reynolds number, all the mixing layers radiate over 85% of the acoustic energy of the apparently asymptotically highReynoldsnumber value that we are able to compute. Turbulence energy and pressure wavenumber spectra show the expected Reynolds number dependence; the two highest Reynolds number simulations show evidence of an inertial range and Kolmogorov scaling at the highest wavenumbers. Farfield pressure spectra all decay much more rapidly with wavenumber than the corresponding nearfield spectra and show significantly less sensitivity to Reynolds number. Low wavenumbers account for nearly all of the radiated acoustic energy. Farfield streamwise wavenumber pressure spectra scale well with the layer momentum thickness, consistent with the insensitivity to Reynolds number of the largest turbulence structures. At higher wavenumbers the streamwise spectra scale best with the Taylor microscale. Interestingly, none of the spanwise farfield pressure spectra scale well with momentum thickness despite doing so in the nearfield turbulence. Instead they scale well at all wavenumbers with the turbulence microscale. Implications of these results for largeeddy simulation of jet noise are discussed.

Modeling the pressure Hessian and viscous Laplacian in turbulence: Comparisons with direct numerical simulation and implications on velocity gradient dynamics
View Description Hide DescriptionModeling the velocity gradient tensor along Lagrangian trajectories in turbulent flow requires closures for the pressure Hessian and viscous Laplacian of . Based on an Eulerian–Lagrangian change in variables and the socalled recent fluid deformation closure, such models were proposed recently [Chevillard and Meneveau, Phys. Rev. Lett.97, 174501 (2006)]. The resulting stochastic model was shown to reproduce many geometric and anomalous scaling properties of turbulence. In this work, direct comparisons between model predictions and direct numerical simulation (DNS) data are presented. First, statistical properties of are described using conditional averages of strain skewness, enstrophy production, energy transfer, and vorticity alignments, conditioned upon invariants of the velocity gradient. These conditionally averaged quantities are found to be described accurately by the stochastic model. More detailed comparisons that focus directly on the terms being modeled in the closures are also presented. Specifically, conditional statistics associated with the pressure Hessian and the viscous Laplacian are measured from the model and are compared with DNS. Good agreement is found in straindominated regions. However, some features of the pressure Hessian linked to rotationdominated regions are not reproduced accurately by the model. Geometric properties such as vorticity alignment with respect to principal axes of the pressure Hessian are mostly predicted well. In particular, the model predicts that an eigenvector of the rate of strain will be also an eigenvector of the pressure Hessian, in accord with basic properties of the Euler equations. The analysis identifies under what conditions the Eulerian–Lagrangian change in variables with the recent fluid deformation closure works well, and in which flow regimes it requires further improvements.

On streak breakdown in bypass transition
View Description Hide DescriptionRecent theoretical, numerical, and experimental investigations performed at the Department of Mechanics, KTH Stockholm, and the Department of Mechanical Engineering, Eindhoven University of Technology, are reviewed, and new material is presented to clarify the role of the boundarylayer streaks and their instability with respect to turbulentbreakdown in bypass transition in a boundary layer subject to freestream turbulence. The importance of the streak secondaryinstability process for the generation of turbulent spots is clearly shown. The secondary instability manifests itself as a growing wave packet located on the lowspeed streak, increasing in amplitude as it is dispersing in the streamwise direction. In particular, qualitative and quantitative data pertaining to temporal sinuous secondary instability of a steady streak, impulse responses both on a parallel and a spatially developing streak, a model problem of bypass transition, and full simulations and experiments of bypass transition itself are collected and compared. In all the flow cases considered, similar characteristics in terms of not only growth rates, group velocity, and wavelengths but also threedimensional visualizations of the streak breakdown have been found. The wavelength of the instability is about an order of magnitude larger than the local boundarylayer displacement thickness , the group velocity about 0.8 of the freestream velocity , and the growth rate on the order of a few percent of . The characteristic structures at the breakdown are quasistreamwise vortices, located on the flanks of the lowspeed region arranged in a staggered pattern.

Local isotropy of the velocity and vorticity fields in a boundary layer at high Reynolds numbers
View Description Hide DescriptionMeasurements of the velocity and vorticity field with a 12sensor hotwire probe were carried out in the boundary layer of the test section ceiling of the NASA Ames wind tunnel at a turbulenceReynolds number of . Tests of local isotropy were applied to the data obtained at . In the inertial subrange, which extended over a decade of wave numbers for this experiment, both the velocity and vorticity component onedimensional spectra agree well with the isotropic spectra of Kim and Antonia [J. Fluid Mech.251, 219 (1993)]. This agreement extends into the dissipation range up to wave numbers at which the accuracy of the measurements is limited because of spatial resolution and other sources of error. Additional tests of local isotropy, from the characteristics of the Reynolds shear stress correlation coefficient cospectrum and from the isotropic relationships between the spectra of the streamwise velocity and vorticity components with the spectra of the respective crossstream components, also show evidence of local isotropy at these higher wave numbers.

Direct numerical simulation of the Ekman layer: A step in Reynolds number, and cautious support for a log law with a shifted origin
View Description Hide DescriptionResults at Ekman Reynolds numbers Re ranging from 1000 to 2828 expand the direct numerical simulation (DNS) contribution to the theory of wallbounded turbulence. An established spectral method is used, with rules for domain size and grid resolution at each Reynolds number derived from the theory. The Re increase is made possible by better computers and by optimizing the grid in relation to the wall shearstress direction. The boundarylayer thickness in wall units varies here by a factor of about 5.3, and reaches values near 5000, or 22 times the minimum at which turbulence has been sustained. An equivalent channel Reynolds number, based on the pressure gradient in wall units, would reach about . The principal goal of the analysis, the impartial identification of a log law, is summarized in the local “Karman measure” . The outcome differs from that for Hoyas and Jiménez [Phys. Fluids18, 011702 (2006)] and for Hu et al. [AIAA J.44, 1541 (2006)] in channelflow DNS at similar Reynolds numbers, for reasons unknown: Here, the law of the wall is gradually established up to a around 400, with little statistical scatter. To leading order, it is consistent with the experiments of Österlund et al. [Phys. Fluids12, 1 (2000)] in boundary layers. With the traditional expression, a logarithmic law is not present, in that the Karman measure drifts from about 0.41 at to the 0.37–0.38 range for , with . However, if a virtual origin is introduced with a shift of wall units, the data support a long logarithmic layer with a good fit to . A determination of the Karman constant from the variation of the skinfriction coefficients with Reynolds numbers also yields values near 0.38. The uncertainty is about . These values are close to the boundarylayer experiments, but well below the accepted range of [0.40,0.41] and the experimental pipeflow results near 0.42. The virtualorigin concept is also controversial, although nonessential at transportation or atmospheric Reynolds numbers. Yet, this series may reflect some success in verifying the law of the wall and investigating the logarithmic law by DNS, redundantly and with tools more impartial than the visual fit of a straight line to a velocity profile.

Direct numerical simulation of unsteady flow in channel with rough walls
View Description Hide DescriptionA fundamental study has been performed to understand the effect of unsteady forcing on turbulence statistics in channel flow with rough walls using direct numerical simulation. Unsteady flows have been generated by applying an unsteady nonzero mean forcing in the form of time varying pressure gradient such that the amplitude of oscillations is between 19% and 26% of mean centerline velocity and covering a range of forcing frequencies. The analysis has revealed unsteady forcing, depending on the forcing frequency, results in enhanced roughness compared to steady channel flow. The roughwall flow dynamics have been categorized into high, intermediate, and lowfrequency regimes. In the regime of highfrequency forcing, unsteadiness alters the mean velocity and turbulence intensities only in the inner layer of the turbulent boundary layer. Further, the turbulence intensities are out of phase with each other and also with the external forcing. In the regime of intermediatefrequency forcing, mean velocity and turbulence intensities are altered beyond the inner layer. In the inner layer, the turbulence intensities are out of phase with each other. The Reynolds stress is in phase with the external forcing in the inner layer, but it is out of phase in the outer layer. In the regime of lowfrequency forcing, the mean velocity and turbulence intensities are significantly altered throughout the turbulent boundary layer.

Control and system identification of a separated flow
View Description Hide DescriptionA procedure to construct linear optimal control for separated flows is presented. Unlike previous works in which a systemmodel is derived from the linearized Navier–Stokes equations, we use an approximate linear model for the flowsystem generated by a system identification method based on inputoutput data sequences from numerical solutions of the Navier–Stokes equations. The approximate model is used in linear quadratic Gaussian synthesis to compute feedback control laws. Various properties of the identified model are tested and discussed. The closedloop control is applied to a twodimensional separated boundary layer, aiming at reducing its separation bubble size.

Does the sailfish skin reduce the skin friction like the shark skin?
View Description Hide DescriptionThe sailfish is the fastest sea animal, reaching its maximum speed of 110 km/h. On its skin, a number of Vshaped protrusions pointing downstream exist. Thus, in the present study, the possibility of reducing the skinfriction using its shape is investigated in a turbulent boundary layer. We perform a parametric study by varying the height and width of the protrusion, the spanwise and streamwise spacings between adjacent ones, and their overall distribution pattern, respectively. Each protrusion induces a pair of streamwise vortices, producing low and high shear stresses at its center and side locations, respectively. These vortices also interact with those induced from adjacent protrusions. As a result, the drag is either increased or unchanged for most of the cases considered. Some of these cases show that the skinfriction itself is reduced but the total drag including the form drag on the protrusion is larger than that of a smooth surface. In a few cases, the drag is decreased only slightly but this amount is within the experimental uncertainty. Since the shape of present protrusions is similar to that used by Sirovich and Karlsson [Nature (London)388, 753 (1997)] where Vshaped protrusions pointing upstream were considered, we perform another set of experiments following their study. However, we do not obtain any drag reduction even with random distribution of those Vshaped protrusions.

Reynolds number effects on the Reynoldsstress budgets in turbulent channels
View Description Hide DescriptionBudgets for the nonzero components of the Reynoldsstress tensor are presented for numerical channels with Reynolds numbers in the range . The scaling of the different terms is discussed, both above and within the buffer and viscous layers. Above , most budget components scale reasonably well with , but the scaling with is generally poor below that level. That is especially true for the dissipations and for the pressurerelated terms. The former is traced to the effect of the wallparallel largescale motions, and the latter to the scaling of the pressure itself. It is also found that the pressure terms scale better near the wall when they are not separated into their diffusion and deviatoric components, but mostly only because the two terms tend to cancel each other in the viscous sublayer. The budgets, together with their statistical uncertainties, are available electronically from http://torroja.dmt.upm.es/channels.

Molecular effects on boundary condition in micro/nanoliquid flows
View Description Hide DescriptionWe experimentally investigated molecular effects of the slip/noslip boundary condition of Newtonian liquids in micro and nanochannels as small as 350 nm. The slip was measurable for channels smaller than approximately . The amount of slip is found to be independent of the channel size, but is a function of the shear rate, the type of liquid (polar or nonpolar molecular structure), and the morphology of the solid surface (molecularlevel smoothness).

Stability of a channel flow subject to wall blowing and suction in the form of a traveling wave
View Description Hide DescriptionInspired by the recent finding by Min et al. [J. Fluid Mech.558, 309 (2006)], the stability of a channel flow subject to wall blowing and suction in the form of a traveling wave is investigated by combined use of the Floquet analysis, direct numerical simulation, and singular value decomposition analysis. Results show that stability highly depends on the phase speed of the traveling wave; most disturbances become highly unstable when the phase speed is around 40% of the centerline velocity, while streamwise streaktype threedimensional disturbances become stabilized with transient growth suppressed when the phase speed exceeds the centerline velocity for both subcritical and supercritical Reynolds numbers. This destabilization is interpreted by investigation of wave interactions. An upstreamtraveling wave, which reduces mean drag, does not stabilize the flow.

Turbulent dispersion from line sources in grid turbulence
View Description Hide DescriptionProbability density function (PDF) calculations are reported for the dispersion from line sources in decaying grid turbulence. The calculations are performed using a modified form of the interaction by exchange with the conditional mean (IECM) mixing model. These flows pose a significant challenge to statistical models because the scalar length scale (of the initial plume) is much smaller than the turbulence integral scale. Consequently, this necessitates incorporating the effects of molecular diffusion in order to model laboratory experiments. Previously, Sawford [Flow Turb. Combust.72, 133 (2004)] performed PDF calculations in conjunction with the IECM mixing model,modeling the effects of molecular diffusion as a random walk in physical space and using a mixing time scale empirically fit to the experimental data of Warhaft [J. Fluid Mech.144, 363 (1984)]. The resulting transport equation for the scalar variance contains a spurious production term. In the present work, the effects of molecular diffusion are instead modeled by adding a conditional mean scalar drift term, thus avoiding the spurious production of scalar variance. A laminar wake model is used to obtain an analytic expression for the mixing time scale at small times, and this is used as part of a general specification of the mixing time scale. Based on this modeling, PDF calculations are performed, and comparison is made primarily with the experimental data of Warhaft on single and multiple line sources and with the previous calculations of Sawford. A heated mandoline is also considered with comparison to the experimental data of Warhaft and Lumley [J. Fluid Mech.88, 659 (1978)]. This establishes the validity of the proposed model and the significant effect of molecular diffusion on the decay of scalar fluctuations. The following are the significant predictions of the model. For the line source, the effect of the source size is limited to early times and can be completely accounted for by simple transformations. The peak centerline ratio of the rms to the mean of the scalar increases with the Reynolds number (approximately as ), whereas this ratio tends to a constant (approximately 0.4) at large times independent of . In addition, the model yields a universal longtime decay exponent for the temperature variance.

Discrete conservation principles in largeeddy simulation with application to separation control over an airfoil
View Description Hide DescriptionAn unstructuredgrid largeeddy simulation(LES) technique is used to investigate the turbulent flow separation over an airfoil with and without syntheticjet control. Numerical accuracy and stability on arbitrary shaped mesh elements at high Reynolds numbers are achieved using a finitevolume discretization of the incompressible Navier–Stokes equations based on higherorder conservation principles—i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Two different stall configurations, which consist of flow over a NACA 0015 airfoil at and angles of attack, are simulated at Reynolds number of based on the airfoil chord length and freestream velocity. In the case of angle of attack where flow separates around a midchord location, LES results show excellent agreement with the experimental data for both uncontrolled and controlled cases. LES confirms the experimental finding that synthetic jets, which are produced through a slot across the entire span on suction surface at 12% chord location, effectively delay the onset of flow separation and cause a significant increase in the lift coefficient. In the case of angle of attack where flow separates near the leading edge, LES predicts reasonable results comparable to experimental data when grid resolution is sufficient to predict the separated shear layer. In this case, the syntheticjet actuation at 12% chord location is found marginally effective in controlling leadingedge separation.

Time evolving simulations as a tentative reproduction of the Reynolds experiments on flow transition in circular pipes
View Description Hide DescriptionTime developing numerical simulations of the Navier–Stokes equations in circular pipes can be performed to make an attempt to reproduce Reynolds’ 1883 experiments [Philos. Trans. R. Soc. London174, 935 (1883)]. However, it should be demonstrated that these simulations are equivalent to space developing simulations. For Reynolds it was rather difficult to estimate exactly the inlet conditions. With high probability these were different from a Poiseuille profile with superimposed clean disturbances, the conditions often assigned in stability and transitional studies. To be close to the Reynolds experiment, in the present study, a turbulent field has been assigned as the initial condition. The lowest transitionReynolds numbers have been evaluated by decreasing the Reynolds numbers, and determining, by pressure gradient time history, and flow visualizations when the turbulent flow survives. This paper, in honor of John Kim, who used direct numerical simulation to understand the role of the near wall structures in turbulent plane channels, shows that the flow remains turbulent only when the near wall structures survive.

Direct intervention of hairpin structures for turbulent boundarylayer control
View Description Hide DescriptionDirect intervention of largescale, outerlayer structures of a turbulent boundary layer has been carried out by counteracting the upwash motion of hairpin vortices with jets issued from a nozzle placed outside the boundary layer. The methodology of this turbulent boundarylayer control is similar in concept to the opposition control of nearwall turbulence, where the induced velocity field of vortical motion during the turbulence activities is opposed by suction and blowing at the wall. Unlike wallbased turbulence control techniques whose time and length scales reduce with an increase in the Reynolds number, scales of the proposed control are those of the outer layer, making this control technique highly practical. Here we show some results from a direct intervention of hairpin structures in a turbulent boundary layer, demonstrating that this is a promising technique for turbulence control.

Variations of von Kármán coefficient in canonical flows
View Description Hide DescriptionThe overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity. The composite profile incorporates , , and as the varying parameters and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers. The von Kármán coefficient in channel flow is smaller than the wellestablished value for zero pressure gradient turbulent boundary layers of 0.384, while in pipe flows it is consistently higher. In contrast, the estimates of the wake parameter are the smallest for channel flows and largest for boundary layers. Further, the Superpipe data are reanalyzed to reveal that is a better value for the von Kármán constant in pipe flow. The collective behavior of in boundary layers, pipes, and channels reveals that the von Kármán coefficient is not universal and exhibits dependence not only on the pressure gradient but also on the flow geometry.

Subsonic jet noise reduction by fluidic control: The interaction region and the global effect
View Description Hide DescriptionA microjet arrangement comprising both penetration (or immersion) and convergence (jets oriented such that two jets of a pair interact with one another) is used to control a subsonic turbulent jet with a view to noise reduction. The acoustic effect of the socalled fluidevron system is comparable to chevrons and nonconverging microjets as far as the noise reduction is concerned. Detailed experimental measurements are performed for a main jet with Mach and Reynolds numbers of 0.3 and , respectively. A direct numerical simulation study is performed for a model, plane mixinglayer problem using the immersedboundary method, in order to help understand the topological features of the fluidevron–mixinglayer interaction. In terms of modifications produced in the flow, two relatively distinct regions are identified: the nearnozzle region, , where the dynamics are dominated by the fluidevron–mainjet interaction, and the region , where the jet recovers many of the uncontrolledjet flow characteristics, but with globally reduced turbulence levels and a longer potential core. The flow structure produced in the nearnozzle region is found to comprise an ejection of fluid from the main jet; the ejection process leads to very high fluctuation levels. This highly turbulent fluid, on being reassimilated by the mixinglayer downstream of the interaction point, has a spectacular local impact on turbulent kinetic energy production and on the entrainment: the former is reduced by 70%, and the latter boosted by 30% over the range . The impact of the flow control on the integral scales of the turbulence is assessed, as these are central to acousticanalogybased source models. A significant reduction is found in the radial integral scales, and these are then weighted by the local fluctuation energy in order to assess the impact of the control on the source mechanisms of the flow (considered in the context of Lighthill’s formulation of the problem). Considerable reductions are shown between the base line and controlledflows in terms of these energyweighted space scales.
 Top

 LETTERS


Critical mass and a new periodic fourring vortex wake mode for freely rising and falling spheres
View Description Hide DescriptionIn this letter, we study the dynamics and vortex wakes of spheres rising or falling freely through a fluid. Since this problem was first considered by Newton in 1726, the conditions under which a sphere will vibrate are still not understood clearly. In our experiments, all falling spheres (where the relative density, ) descend rectilinearly. Although previous studies conclude that all rising spheres vibrate, we find instead that there exists a critical value of the relative density (for example, , for Reynolds numbers 400–500) above which there is a significant regime where rising spheres do not vibrate. Lighter spheres undergo largeamplitude periodic oscillations, confined to a single vertical plane. We discover a new mode of vortex formation comprising four vortex rings formed in each cycle, distinct from previous vortex modes for fixed and tethered bodies.
