Near-wall Streaks Research Articles

Overdamped large-eddy simulations of turbulent pipe flow up to Reτ = 1500

We present results from large-eddy simulations (LES) of turbulent pipe flow in a computational domain of 42 radii in length. Wide ranges of shear the Reynolds number and Smagorinsky model parameter are covered, 180 ≤ Reτ ≤ 1500 and 0.05 ≤ Cs ≤ 1.2, respectively. The aim is to asses the effect of Cs on the resolved flow field and turbulence statistics as well as to test whether very large scale motions (VLSM) in pipe flow can be isolated from the near-wall cycle by enhancing the dissipative character of the static Smagorinsky model with elevated Cs values. We found that the optimal Cs to achieve best agreement with reference data varies with Reτ and further depends on the wall normal location and the quantity of interest. Furthermore, for increasing Reτ, the optimal Cs for pipe flow LES seems to approach the theoretically optimal value for LES of isotropic turbulence. In agreement with previous studies, we found that for increasing Cs small-scale streaks in simple flow field visualisations are gradually quenched and replaced by much larger smooth streaks. Our analysis of low-order turbulence statistics suggests, that these structures originate from an effective reduction of the Reynolds number and thus represent modified low-Reynolds number near-wall streaks rather than VLSM. We argue that overdamped LES with the static Smagorinsky model cannot be used to unambiguously determine the origin and the dynamics of VLSM in pipe flow. The approach might be salvaged by e.g. using more sophisticated LES models accounting for energy flux towards large scales or explicit anisotropic filter kernels.

Turbulence intensities in large-eddy simulation of wall-bounded flows.

A persistent problem in wall-bounded large-eddy simulations (LES) with Dirichlet no-slip boundary conditions is that the near-wall streamwise velocity fluctuations are overpredicted, while those in the wall-normal and spanwise directions are underpredicted. The problem may become particularly pronounced when the near-wall region is underresolved. The prediction of the fluctuations is known to improve for wall-modeled LES, where the no-slip boundary condition at the wall is typically replaced by Neumann and no-transpiration conditions for the wall-parallel and wall-normal velocities, respectively. However, the turbulence intensity peaks are sensitive to the grid resolution and the prediction may degrade when the grid is refined. In the present study, a physical explanation of this phenomena is offered in terms of the behavior of the near-wall streaks. We also show that further improvements are achieved by introducing a Robin (slip) boundary condition with transpiration instead of the Neumann condition. By using a slip condition, the inner energy production peak is damped, and the blocking effect of the wall is relaxed such that the splatting of eddies at the wall is mitigated. As a consequence, the slip boundary condition provides an accurate and consistent prediction of the turbulence intensities regardless of the near-wall resolution.

Sustainment of Oscillations in Localized Turbulent Structures in Pipes

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically investigated. In the phase space this solution corresponds to the limiting state of the solution which evolves along the separatrix dividing the regions of attraction of the solutions corresponding to the laminar and turbulent flow regimes. Relative simplicity of the spatial and temporal behavior of the limiting solution on the separatrix makes it possible to investigate it in detail. In particular, the nonlinear mechanism of the onset of streamwise vortices responsible for sustainment of near-wall streaks whose instability ensures the presence of fluctuations is revealed.

Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall

ABSTRACTCompressible turbulent channel flow over a wavy surface is investigated by direct numerical simulations using high-resolution finite difference schemes. The Reynolds number considered in the present paper is 3380 based on the bulk velocity, the channel half-width and the kinetic viscosity at the wall. Four test cases are simulated and analysed at Mam = 0.33, 0.8, 1.2, 1.5 based on the bulk velocity and the speed of sound at the wall. We mainly focus on the curvature and the Mach number effects on the compressible turbulent flows. Numerical results show that although the wavy wall has effects on the mean and fluctuation quantities, log law still exists in the distribution of the wave-averaged streamwise velocity if the roughness effects are taken into consideration in the scaling of it. Near-wall streaks are broken by the wavy surface and near-wall quasi-streamwise vortices mostly begin at the upslope of the wave and pass over the crest of it. The wavy wall makes the turbulence more active and the flow easier to be blended. From the viewpoint of turbulent kinetic budgets, curvature effects strengthen both the diffusion terms and the dissipation terms. At the same time, they change the properties of the compressibility-related terms and promote more inner energy transferring into turbulent kinetic energy. As the Mach number increases, the reattachment of the mean flow is delayed, which indicates the mean separation bubble becomes larger. Concerning the near-wall coherent structures, the vortices are more sparsely distributed with the increasing of the Mach number. For the supersonic cases, shock waves appear. Though they have little effects on the mean turbulent quantities, they change the structures of the flow fields and induce local separations at the upper wall of the channel.

Preferential particle concentration in wall-bounded turbulence with zero skin friction

Inertial particles dispersed in turbulence distribute themselves unevenly. Besides their tendency to segregate near walls, they also concentrate preferentially in wall-parallel planes. We explore the latter phenomenon in a tailor-made flow with the view to examine the homogeneity and anisotropy of particle clustering in the absence of mean shear as compared with conventional, i.e., sheared, wall turbulence. Inertial particles with some different Stokes numbers are suspended in a turbulent Couette-Poiseuille flow, in which one of the walls moves such that the shear rate vanishes at that wall. The anisotropies of the velocity and vorticity fluctuations are therefore qualitatively different from those at the opposite non-moving wall, along which quasi-coherent streaky structures prevail, similarly as in turbulent pipe and channel flows. Preferential particle concentration is observed near both walls. The inhomogeneity of the concentration is caused by the strain-vorticity selection mechanism, whereas the anisotropy originates from coherent flow structures. In order to analyse anisotropic clustering, a two-dimensional Shannon entropy method is developed. Streaky particle structures are observed near the stationary wall where the flow field resembles typical wall-turbulence, whereas particle clusters near the moving friction-free wall are similar to randomly oriented clusters in homogeneous isotropic turbulence, albeit with a modest streamwise inclination. In the absence of mean-shear and near-wall streaks, the observed anisotropy is ascribed to the imprint of large-scale flow structures which reside in the bulk flow and are global in nature.

Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall

We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier–Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney–Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk $Re=2800$ and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties.

Changes in the boundary-layer structure at the edge of the ultimate regime in vertical natural convection

In thermal convection for very large Rayleigh numbers ($Ra$), the thermal and viscous boundary layers are expected to undergo a transition from a classical state to an ultimate state. In the former state, the boundary-layer thicknesses follow a laminar-like Prandtl–Blasius–Polhausen scaling, whereas in the latter, the boundary layers are turbulent with logarithmic corrections in the sense of Prandtl and von Kármán. Here, we report evidence of this transition via changes in the boundary-layer structure of vertical natural convection (VC), which is a buoyancy-driven flow between differentially heated vertical walls. The numerical dataset spans $Ra$ values from $10^{5}$ to $10^{9}$ and a constant Prandtl number value of $0.709$. For this $Ra$ range, the VC flow has been previously found to exhibit classical state behaviour in a global sense. Yet, with increasing $Ra$, we observe that near-wall higher-shear patches occupy increasingly larger fractions of the wall areas, which suggest that the boundary layers are undergoing a transition from the classical state to the ultimate shear-dominated state. The presence of streaky structures – reminiscent of the near-wall streaks in canonical wall-bounded turbulence – further supports the notion of this transition. Within the higher-shear patches, conditionally averaged statistics yield a logarithmic variation in the local mean temperature profiles, in agreement with the log law of the wall for mean temperature, and an $Ra^{0.37}$ effective power-law scaling of the local Nusselt number. The scaling of the latter is consistent with the logarithmically corrected $1/2$ power-law scaling predicted for ultimate thermal convection for very large $Ra$. Collectively, the results from this study indicate that turbulent and laminar-like boundary layer coexist in VC at moderate to high $Ra$ and this transition from the classical state to the ultimate state manifests as increasingly larger shear-dominated patches, consistent with the findings reported for Rayleigh–Bénard convection and Taylor–Couette flows.

Recovery of a supersonic turbulent boundary layer after an expansion corner

Supersonic turbulent flows at Mach 2.7 over expansion corners with deflection angles of 0° (flat plate), 2°, and 4° have been studied using direct numerical simulation. Distributions of skin friction, pressure, velocity, and boundary layer growth show that the turbulent boundary layer experiences a recovery from a non-equilibrium to an equilibrium state downstream of the expansion corner. Analysis of velocity profiles indicates that the streamwise velocity undergoes a reduction in the near-wall region even though the velocity in the core part of the boundary layer is accelerated after the expansion corner. Growth of the boundary layer was evaluated and a higher shape factor was found in the expansion cases. Turbulence was found to be mostly suppressed downstream of the corner, and throughout the recovery region, even though turbulence is regenerated in the near-wall region. The expansion ramp increases the near-wall streak spacing compared to a flat plate, and turbulent kinetic energy profiles and budgets exhibit a characteristic two-layer structure. Near-wall turbulence recovers to a balance between the local production and dissipation equilibrium more quickly in the inner layer than in the outer layer. The two-layer structure is due to a history effect of turbulence decay in the outer part of the boundary layer downstream of the expansion corner, with limited momentum and energy exchange between the inner layer and the main stream.

The influence of shear-dependent rheology on turbulent pipe flow

Direct numerical simulations of turbulent pipe flow of power-law fluids at $Re_{\unicode[STIX]{x1D70F}}=323$ are analysed in order to understand the way in which shear thinning or thickening affects first- and second-order flow statistics including turbulent kinetic energy production, transport and dissipation in such flows. The results show that with shear thinning, near-wall streaks become weaker and the axial and azimuthal correlation lengths of axial velocity fluctuations increase. Viscosity fluctuations give rise to an additional shear stress term in the mean momentum equation which is negative for shear-thinning fluids and which increases in magnitude as the fluid becomes more shear thinning: for an equal mean wall shear stress, this term increases the mean velocity gradient in shear-thinning fluids when compared to a Newtonian fluid. Consequently, the mean velocity profile in power-law fluids deviates from the law of the wall $U_{z}^{+}=y^{+}$ in the viscous sublayer when traditional near-wall scaling is used. Consideration is briefly given to an alternative scaling that allows the law of wall to be recovered but which results in loss of a common mean stress profile. With shear thinning, the mean viscosity increases slightly at the wall and its profile appears to be approximately logarithmic in the velocity log layer. Through analysis of the turbulent kinetic energy budget, undertaken here for the first time for generalised Newtonian fluids, it is shown that shear thinning decreases the overall turbulent kinetic energy production but widens the wall-normal region where it is generated. Additional dissipation terms in the mean flow and turbulent kinetic energy budget equations arise from viscosity fluctuations; with shear thinning, these result in a net decrease in the total viscous dissipation. The overall effect of shear thinning on the turbulent kinetic energy budget is found to be largely confined to the inner layers, $y^{+}\lesssim 60$.

The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers.

The present work is based on our recent discovery of a new class of exact coherent structures generated near the edge of quite general boundary layer flows. The structures are referred to as free-stream coherent structures and were found using a large Reynolds number asymptotic approach to describe equilibrium solutions of the Navier-Stokes equations. In this paper, first we present results for a new family of free-stream coherent structures existing at relatively large wavenumbers. The new results are consistent with our earlier theoretical result that such structures can generate larger amplitude wall streaks if and only if the local spanwise wavenumber is sufficiently small. In a Blasius boundary layer, the local wavenumber increases in the streamwise direction so the wall streaks can typically exist only over a finite interval. However, here it is shown that they can interact with wall curvature to produce exponentially growing Görtler vortices through the receptivity process by a novel nonparallel mechanism. The theoretical predictions found are confirmed by a hybrid numerical approach. In contrast with previous receptivity investigations, it is shown that the amplitude of the induced vortex is larger than the structures in the free-stream which generate it.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.

Spanwise modulation effects of local body force on downstream turbulence growth around two-dimensional hump

Flow characteristics under flow-separation control by the spanwise-modulated body force of a plasma actuator around a two-dimensional hump are numerically investigated. When the Reynolds number is set to Reh=16000, the incoming flow contains much disturbance and a near-wall streak structure appears around the hump. The local body force induces stable streamwise velocity to form a streak-like profile artificially. Under the forcing, turbulence fluctuations increase downstream, with resulting in early flow reattachment. These changes alter the momentum balance around the hump. Particularly, the wall-normal pressure gradient and velocity fluctuation terms in the momentum equation are modified. This somewhat suggests a relation between increases in wall-normal gradient terms and the flow reattachment profile under the control. In addition, the turbulence growth depends on the spanwise modulation wavelength of the forcing. The most effective wavelength among those tested here is λz=0.08, normalized by the hump height, which is λz+=150 in local viscous wall units. This viscous scale corresponds to that of a streak structure appearing around a two-dimensional hump.

Turbulent Couette–Poiseuille flow with zero wall shear

A particular pressure-driven flow in a plane channel is considered, in which one of the walls moves with a constant speed that makes the mean shear rate and the friction at the moving wall vanish. The Reynolds number considered based on the friction velocity at the stationary wall (uτ,S) and half the channel height (h) is Reτ,S = 180. The resulting mean velocity increases monotonically from the stationary to the moving wall and exhibits a substantial logarithmic region. Conventional near-wall streaks are observed only near the stationary wall, whereas the turbulence in the vicinity of the shear-free moving wall is qualitatively different from typical near-wall turbulence. Large-scale-structures (LSS) dominate in the center region and their spanwise spacing increases almost linearly from about 2.3 to 4.2 channel half-heights at this Reτ,S. The presence of LSS adds to the transport of turbulent kinetic energy from the core region towards the moving wall where the energy production is negligible. Energy is supplied to this particular flow only by the driving pressure gradient and the wall motion enhances this energy input from the mean flow. About half of the supplied mechanical energy is directly lost by viscous dissipation whereas the other half is first converted from mean-flow energy to turbulent kinetic energy and thereafter dissipated.

Convergence of numerical simulations of turbulent wall-bounded flows and mean cross-flow structure of rectangular ducts

Convergence criteria for direct numerical simulations of turbulent channel and duct flows are proposed. The convergence indicator for channels is defined as the deviation of the nondimensional total shear-stress profile with respect to a linear profile, whereas the one for the duct is based on a nondimensional streamwise momentum balance at the duct centerplane. We identify the starting ( $$T_{S}$$ ) and averaging times ( $$T_{A}$$ ) necessary to obtain sufficiently converged statistics, and also find that optimum convergence rates are achieved when the spacing in time between individual realizations is below $$\Delta t^{+}=17$$ . The in-plane structure of the flow in turbulent ducts is also assessed by analyzing square ducts at $$Re_{\tau ,c} \simeq 180$$ and 360 and rectangular ducts with aspect ratios 3 and 10 at $$Re_{\tau ,c} \simeq 180$$ . Identification of coherent vortices shows that near-wall streaks are located in all the duct cases at a wall-normal distance of $$y^{+} \simeq 40$$ as in Pinelli et al. (J Fluid Mech 644:107–122, 2010). We also find that large-scale motions play a crucial role in the streamline pattern of the secondary flow, whereas near-wall structures highly influence the streamwise vorticity pattern. These conclusions extend the findings by Pinelli et al. to other kinds of large-scale motions in the flow through the consideration of wider ducts. They also highlight the complex and multiscale nature of the secondary flow of second kind in turbulent duct flows.

LES investigation of the transport and decay of various-strengths wake vortices in ground effect and subjected to a turbulent crosswind

This study is concerned with the investigation of two-vortex systems (2VS) of various strengths that are released near the ground and evolve in the presence of a turbulent crosswind. We analyze the physics of the vortices interactions with the turbulent wind and with the ground during the rebound phase, and that lead to the fully developed turbulent flow and interactions. The transport and decay of the vortices are also analyzed. The turbulent wind itself is obtained by direct numerical simulation using a half channel flow. The flow is then supplemented with the 2VS, using vortices with a circulation distribution that is representative of vortices after roll-up of a near wake. The vortex strengths, Γ0, are such that ReΓ = Γ0/ν = 2.0 × 104 for the baseline; there is then a case with twice weaker vortices, and a case with twice stronger vortices. The simulations are run in wall-resolved Large Eddy Simulation (LES) mode. The baseline is in line with the wall-resolved LES study of a similar case [A. Stephan et al., “Aircraft wake-vortex decay in ground proximity—Physical mechanisms and artificial enhancement,” J. Aircr. 50(4), 1250–1260 (2013)]. They highlighted the significant effect that the near-wall streaks of the wind have on the development of instabilities in the secondary vortices, and the ensuing turbulence. Our analysis complements theirs by also showing the significant effect that the wind turbulent structures, away from the ground and that are stretched by the primary vortices, also have on the destabilization of the secondary vortices. Comparisons are also made with the most recent study [F. N. Holzäpfel et al., “Wind impact on single vortices and counter-rotating vortex pairs in ground proximity,” in 7th AIAA Atmospheric and Space Environments Conference, AIAA Aviation (American Institute of Aeronautics and Astronautics, 2015)], where ReΓ = 2.0 × 104 for all cases and where it is the wind intensity that is varied. Diagnostics on the vortex trajectories and circulation decay are provided, for the mean and for the envelopes of behaviour. The results are discussed and compared with the recent literature. In particular, for the case with relatively twice stronger wind relative to the vortices, the upwind vortex quickly looses its coherence when it comes closest to the ground and does not rebound; the physics of that are explained by a long wave instability excited by the turbulent wind. Finally, a case where the baseline wake is released at a lower altitude is also studied, to support an analysis on what is the proper length scale to use, and initial time, when comparing results of wakes released at different altitudes: indeed, when normalized using those quantities, the trajectory and decay curves of this case are seen to collapse very well with those of the baseline.

Gravity Effects on Fiber Dynamics in Wall Turbulence

The present study investigated gravity effects on the dynamical behavior of inertial fibers suspended in a vertical channel flow. Direct numerical simulations were performed to obtain the turbulent flow field and the fibers were modelled as prolate spheroidal point particles. For each of the four fiber classes, three different gravity configurations were considered: upward flow with gravity opposing, downward flow with aiding gravity, and channel flow in absence of gravity. Results for the fiber distribution and the translational and rotational fiber motion were reported. In the near-wall region, the presence of gravity resulted in an increased fiber density in the downward flow but a nearly uniform distribution of fibers in upward flow. However, the preferential clustering of fibers in near-wall low-speed streaks was unaffected by gravity. The mean wall-normal or drift velocity of the fibers was higher in the downward flow and lower in the upward flow as compared to the case with no gravity. The suppressed drift velocity in the upward flow resulted in a more uniform fiber distribution throughout the channel in contrast to the near-wall accumulation of fibers in the two other cases. Overall gravity turned out to have negligible effects on some of the statistics of the least inertial fibers whereas the inclusion of gravity had a strong impact for heavier fibers.

Experimental observation of hairpin auto-generation events in a turbulent boundary layer

Time-resolved tomographic particle image velocimetry experiments show that new hairpin vortices are generated within a fully developed and unperturbed turbulent boundary layer. The measurements are taken at a Reynolds number based on the momentum thickness of 2038, and cover the near-wall region below $y^{+}=140$, where $y^{+}$ is the wall-normal distance in wall units. Instantaneous visualizations of the flow reveal near-wall low-speed streaks with associated quasi-streamwise vortices, retrograde inverted arch vortices, hairpin vortices and hairpin packets. The hairpin heads are observed as close to the wall as $y^{+}=30$. Examples of hairpin packet evolution reveal the development of new hairpin vortices, which are created upstream and close to the wall in a manner consistent with the auto-generation model (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). The development of the new hairpin appears to be initiated by an approaching sweep event, which perturbs the shear layer associated with the initial packet. The shear layer rolls up, thereby forming the new hairpin head. The head subsequently connects to existing streamwise vortices and develops into a hairpin. The time scale associated with the hairpin auto-generation is 20–30 wall units of time. This demonstrates that hairpins can be created over short distances within a developed turbulent boundary layer, implying that they are not simply remnants of the laminar-to-turbulent transition process far upstream.

Coherent structures in a zero-pressure-gradient and a strongly decelerated boundary layer

Coherent structures in a strongly decelerated large-velocity-defect turbulent boundary layer (TBL) and a zero pressure gradient (ZPG) boundary layer are analysed by direct numerical simulation (DNS). The characteristics of the one-point velocity stastistics are also considered. The adverse pressure gradient (APG) TBL simulation is a new one carried out by the present authors. The APG TBL begins as a zero pressure gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain in the form of a very thin separation bubble. The one-point velocity statistics in the outer region of this large-defect boundary layer are compared to those of two other large-velocity-defect APG TBLs (one in dynamic equilibrium, the other in disequilibrium) and a mixing layer. In the upper half of the large-defect boundary layers, the velocity statistics are similar to those of the mixing layer. The dominant peaks of turbulence production and Reynolds stresses are located in the middle of the boundary layers. Three-dimensional spatial correlations of (u, u) and (u, v) show that coherence is lost in the streamwise and spanwise directions as the velocity defect increases. Near-wall streaks tend to disappear in the large-defect zone of the flow to be replaced by more disorganized u motions. Near-wall sweeps and ejections are also less numerous. In the outer region, the u structures tend to be shorter, less streaky, and more inclined with respect to the wall than in the ZPG TBL. The sweeps and ejections are generally bigger with respect to the boundary layer thickness in the large-defect boundary layer, even if the biggest structures are found in the ZPG TBL. Large sweeps and ejections that reach the wall region (wall-attached) are less streamwise elongated and they occupy less space than in the ZPG boundary layer. The distinction between wall-attached and wall-detached structures is not as pronounced in the large-defect TBL.

Particle transport in turbulent curved pipe flow

Direct numerical simulations (DNS) of particle-laden turbulent flow in straight, mildly curved and strongly bent pipes are performed in which the solid phase is modelled as small heavy spherical particles. A total of seven populations of dilute particles with different Stokes numbers, one-way coupled with their carrier phase, are simulated. The objective is to examine the effect of the curvature on micro-particle transport and accumulation. It is shown that even a slight non-zero curvature in the flow configuration strongly impact the particle concentration map such that the concentration of inertial particles with bulk Stokes number $0.45$ (based on bulk velocity and pipe radius) at the inner bend wall of mildly curved pipe becomes $12.8$ times larger than that in the viscous sublayer of the straight pipe. Near-wall helicoidal particle streaks are observed in the curved configurations with their inclination varying with the strength of the secondary motion of the carrier phase. A reflection layer, as previously observed in particle laden turbulent S-shaped channels, is also apparent in the strongly curved pipe with heavy particles. In addition, depending on the curvature, the central regions of the mean Dean vortices appear to be completely depleted of particles, as observed also in the partially relaminarised region at the inner bend. The turbophoretic drift of the particles is shown to be affected by weak and strong secondary motions of the carrier phase and geometry-induced centrifugal forces. The first- and second-order moments of the velocity and acceleration of the particulate phase in the same configurations are addressed in a companion paper by the same authors. The current data set will be useful for modelling particles advected in wall-bounded turbulent flows where the effects of the curvature are not negligible.

Inner–outer interactions of large-scale structures in turbulent channel flow

Direct numerical simulation data of turbulent channel flow ($Re_{{\it\tau}}=930$) are used to investigate the statistics of long motions of streamwise velocity fluctuations ($u$), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-$u$ structures are organized into longer streamwise extent (${>}3{\it\delta}$) in comparison to the positive-$u$ counterparts. Near the wall, the footprint of negative-$u$ structures is relatively narrow in comparison to the footprint of positive-$u$ structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations ($w$) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-$u$ structures generate relatively weak $w$ but intense negative-$u$ regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-$u$ upwell during the merging of the outer long scales – an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-$u$ structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-$u$ structures in the log region.

Drag-reduction in buoyant and neutrally-buoyant turbulent flows over super-hydrophobic surfaces in transverse orientation

The present study involves Direct Numerical Simulations (DNS) of a turbulent channel flow subject to passive-control of super-hydrophobic surfaces (SHS) employed in form of ridges/posts at the bottom-wall of the channel, oriented in transverse direction to the flow. The simulations have been carried out for a fixed friction Reynolds number Reτ=180 to investigate the effect of thermal forcing in tandem with SHS at a fixed friction Richardson number Riτ=15. It is observed that on decreasing the width to depth (w/d) ratio of the ridge topology, the drag-reduction increases and this reduction is found to be maximum for the topology of SHS posts. A key effect of this control is reduction in cross-flow fluctuations in the buffer-layer (i.e. 10<z+⩽50) which lead to generation of weaker and more stable low-speed streaks which results in reduction in bursting of these near-wall streaks. This eventually causes considerable reduction in turbulent kinetic energy (TKE) which leads to turbulent skin-friction drag reduction at the controlled wall generally of the order of 10–22%. Unstable-stratification of the SHS flow results in the wall-normal convection of turbulent-vorticity which enhances cross-flow fluctuations leading to an increase in Reynolds shear-stresses near to the bottom-wall. In total the effect of heating is found to mitigate the net-reduction produced in turbulent drag by 6–7% for different cases employing ridge/post topology.