Publications
76 results found
Lakshmi MV, Fantuzzi G, Fernández-Caballero JD, et al., 2020, Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow, SIAM Journal on Applied Dynamical Systems, Vol: 19, Pages: 763-787, ISSN: 1536-0040
Tobasco et al. [Phys. Lett. A, 382:382–386, 2018] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Netwon–Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.
Hwang Y, 2019, Mesolayer of attached eddies in turbulent channel flow, Physical Review Fluids, Vol: 1, ISSN: 2469-990X
Recent experimental measurements have reported that the outer peak of the streamwisewavenumber spectra of the streamwise velocity depends on the Reynolds number. Starting fromthis puzzling observation, here it is proposed that the wall-parallel velocity components of eachof the energy-containing motions in the form of Towsnend’s attached eddies exhibit inner-scalingnature in the region close to the wall. Some compelling evidence on this proposition has been presentedwith a careful inspection of scaling of velocity spectra from DNS, a linear analysis with aneddy viscosity, and the recently computed statistical structure of the self-similar energy-containingmotions in the logarithmic region. This observation suggests that the viscous wall effect wouldnot be negligible at least below the peak wall-normal location of each of the energy-containingmotions in the logarithmic and outer regions, reminiscent of the concept of the ‘mesolayer’ previouslyobserved in the mean momentum balance. It is shown that this behavior emerges due to aminimal form of scale interaction, modeled by the eddy viscosity in the linear theory, and enablesone to explain the Reynolds-number-dependent behavior of the outer peak as well as the near-wallpenetration of the large-scale outer structures in a consistent manner. Incorporation of this viscouswall effect to Townsend’s attached eddies, which were originally built with an inviscid approximationat the wall, also reveals that the self-similarity of the wall-parallel velocity components of theenergy-containing motions would be theoretically broken in the region close to the wall.
Doohan P, Willis A, Hwang Y, 2019, Shear stress-driven flow: the state space of near-wall turbulence as Reτ →∞, Journal of Fluid Mechanics, Vol: 874, Pages: 606-638, ISSN: 0022-1120
An inner-scaled, shear stress-driven flow is considered as a model of independentnear-wall turbulence as Reτ → ∞. In this limit, the model is applicable to the nearwall region and the lower part of the logarithmic layer of various parallel shear flows,including turbulent Couette flow, Poiseuille flow and Hagen-Poiseuille flow. The modelis validated against damped Couette flow and there is excellent agreement between thevelocity statistics and spectra for y+ < 40. A near-wall flow domain of similar size tothe minimal unit is analysed from a dynamical systems perspective. The edge and fifteeninvariant solutions are computed, the first discovered for this flow configuration. Throughcontinuation in the spanwise width L+z, the bifurcation behaviour of the solutions overthe domain size is investigated. The physical properties of the solutions are exploredthrough phase portraits, including the energy input and dissipation plane, and streak,roll and wave energy space. Finally, a Reynolds number is defined in outer units and thehigh-Re asymptotic behaviour of the equilibria is studied. Three lower branch solutionsare found to scale consistently with vortex-wave interaction (VWI) theory, with waveforcing localising around the critical layer.
Maretvadakethope S, Keaveny EE, Hwang Y, 2019, The instability of gyrotactically trapped cell layers, Publisher: CAMBRIDGE UNIV PRESS
Maretvadakethope S, Keaveny E, Hwang Y, 2019, The instability of gyrotactically-trapped cell layers, Journal of Fluid Mechanics, Vol: 868, ISSN: 0022-1120
Several metres below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of bottom-heavy swimming algae cells, especially in flows where the vorticity varies linearly with depth (Durham et al., Science, vol. 323(5917), 2009, pp. 1067–1070). Using a continuum model for dilute microswimmer suspensions, we report that an instability of a gyrotactically trapped cell layer can arise in a pressure-driven plane channel flow. The linear stability analysis reveals that the equilibrium cell-layer solution is hydrodynamically unstable due to negative microswimmer buoyancy (i.e. a gravitational instability) over a range of biologically relevant parameter values. The critical cell concentration for this instability is found to be Nc≃104 cells cm−3 , a value comparable to the typical maximum cell concentration observed in thin layers. This result indicates that the instability may be a potential mechanism for limiting the layer’s maximum cell concentration, especially in regions where turbulence is weak, and motivates the study of its nonlinear evolution, perhaps, in the presence of turbulence.
Yang Q, Willis A, Hwang Y, 2019, Exact coherent states of attached eddies in channel flow, Journal of Fluid Mechanics, Vol: 862, Pages: 1029-1059, ISSN: 0022-1120
A new set of exact coherent states in the form of a travelling wave is reported in plane channel flow. They are continued over a range in Re from approximately 2600 up to 30 000, an order of magnitude higher than those discovered in the transitional regime. This particular type of exact coherent states is found to be gradually more localised in the near-wall region on increasing the Reynolds number. As larger spanwise sizes L + z are considered, these exact coherent states appear via a saddle-node bifurcation with a spanwise size of L + z ' 50 and their phase speed is found to be c + ' 11 at all the Reynolds numbers considered. Computation of the eigenspectra shows that the time scale of the exact coherent states is given by h/Ucl in channel flow at all Reynolds numbers, and it becomes equivalent to the viscous inner time scale for the exact coherent states in the limit of Re → ∞. The exact coherent states at several different spanwise sizes are further continued to a higher Reynolds number, Re = 55 000, using the eddy-viscosity approach (Hwang & Cossu, Phys. Rev. Lett., vol. 105, 2010, 044505). It is found that the continued exact coherent states at different sizes are self-similar at the given Reynolds number. These observations suggest that, on increasing Reynolds number, new sets of self-sustaining coherent structures are born in the near-wall region. Near this onset, these structures scale in inner units, forming the near-wall self-sustaining structures. With further increase of Reynolds number, the structures that emerged at lower Reynolds numbers subsequently evolve into the self-sustaining structures in the logarithmic region at different length scales, forming a hierarchy of self-similar coherent structures as hypothesised by Townsend (i.e. attached eddy hypothesis). Finally, the energetics of turbulent flow is discussed for a consistent extension of these dynamical systems notions to high Reynolds numbers.
Ibrahim J, Yang Q, Doohan P, et al., 2019, Phase-space dynamics of opposition control in wall-bounded turbulent flows, Journal of Fluid Mechanics, Vol: 861, Pages: 29-54, ISSN: 0022-1120
We investigate the nonlinear phase-space dynamics of plane Couette flow and plane Poiseuille flow under the action of opposition control at low Reynolds numbers in domains close to the minimal unit. In Couette flow, the effect of the control is analysed by focussing on a pair of non-trivial equilibrium solutions. It is found that the control only slightly modifies the statistics, turbulent skin friction and phase-space projection of the lower-branch equilibrium solution, which, in this case, is in fact identical to the edge state. On the other hand, the upper-branch equilibrium solution and mean turbulent state are modified considerably when the control is applied. In phase space, they gradually approach the lower-branch equilibrium solution on increasing the control amplitude, and this results in an elevation of the critical Reynolds number at which the equilibrium solutions first occur via a saddle-node bifurcation. It is also found that the upper-branch equilibrium solution is stabilised by the control. In Poiseuille flow, we study an unstable periodic orbit on the edge state and find that it, too, is modified very little by opposition control. We again observe that the turbulent state gradually approaches the edge state in phase space as the control amplitude is increased. In both flows, we find that the control significantly reduces the fluctuating strength of the turbulent state in phase space. However, the reduced distance between the turbulent trajectory and the edge state yields a significant reduction in turbulence lifetimes for both Couette and Poiseuille flow. This demonstrates that opposition control greatly increases the probability of the trajectory escaping from the turbulent state, which takes the form of a chaotic saddle.
Pausch M, Yang Q, Hwang Y, et al., 2019, Quasilinear approximation for exact coherent states in parallel shearflows, Fluid Dynamics Research, Vol: 51, ISSN: 0169-5983
In the quasilinear approximation to the Navier–Stokes equation a minimal set of nonlinearities that is able to maintain turbulent dynamics is kept. For transitional Reynolds numbers, exact coherent structures provide an opportunity for a detailed comparison between full direct numerical solutions of the Navier–Stokes equation with their quasilinear approximation. We show here, for both plane Couette flow and plane Poiseuille flow, that the quasilinear approximation is able to reproduce many properties of exact coherent structures. For higher Reynolds numbers differences in the stability properties and the friction values for the upper branch appear that are connected with a reduction in the number of downstream wavenumbers in the quasilinear approximation. The results show the strengths and limitations of the quasilinear approximation and suggest modelling approaches for turbulent flows.
Doohan P, Marensi E, Willis AP, et al., 2019, Two-scale interaction in near-wall turbulence
The temporal dynamics of a two-scale near-wall flow are investigated, with a particular emphasis on nonlinear turbulent transport between the scales. The energy balance equations at each scale are derived, and their statistics and dynamics are analysed. The temporal dynamics of the energy-containing eddies at each scale follow the self-sustaining process, based on the interaction between streaks and quasi-streamwise vortices. It is shown that the turbulent production term correlates well with the lift-up effect and the pressure transport term correlates well with streak instability, at both large and small scales. Across the wall-normal domain, the dominant scale interaction process is the cascade of energy from large to small scales and it is most active during the late stages of streak breakdown. However, very close to the wall, energy transfer from small to large scales occurs highly intermittently and it leads to the formation of large-scale wall-parallel velocity structures. In the presentation, the full dynamics of the two-scale interaction system will be discussed in detail.
Yang Q, Hwang Y, 2019, Modulation of attached exact coherent states under spanwise wall oscillation
The drag reduction deterioration by spanwise wall oscillation control is explored in this study. When the outer scale motions are absent from the domain, the optimal wall oscillation period is fixed in wall units, i.e., T+ ≃ 100, in perfect agreement with the convection time scale of the near-wall structures. A set of wall-normal localised exact coherent states under the modulation of spanwise wall oscillation are obtained. The saddle-node point of the bifurcation curves move towards higher Reynolds numbers until T+ ~ 100, beyond which the solution can not be continued. The drag reduction of wall oscillation on logarithmic exact coherent states is negligible at T+ ≃ 100, and this is the same for logarithmic eddies in long but narrow domains. However, substantial drag reduction is still achievable for isolated logarithmic eddies at larger oscillation periods, and the optimal periods tend to scale in a domain width related time scale, i.e., Lz/uτ , which is consistent with the bursting period of minimum logarithmic attached eddies, i.e., 2 ~ 3Lz/uτ . As the spanwise wall oscillation control only target eddies at a single period, this might be one reason that the optimal oscillation period varies with Reynolds number.
Dunstan J, Lee K, Hwang Y, et al., 2018, Evaporation-driven convective flows in suspensions of non-motile bacteria, Physical Review Fluids, Vol: 13, ISSN: 2469-990X
We report a novel form of convection in suspensions of the bioluminescent marine bacterium Photobacterium phosphoreum. Suspensions of these bacteria placed in a chamber open to the air create persistent luminescent plumes most easily visible when observed in the dark. These flows are strikingly similar to the classical bioconvection pattern of aerotactic swimming bacteria, which create an unstable stratification by swimming upwards to an air-water interface, but they are a puzzle since the strain of P. phosphoreum used does not express flagella and therefore cannot swim. When microspheres were used instead of bacteria, similar flow patterns were observed, suggesting that the convective motion was not driven by bacteria but instead by the accumulation of salt at the air-water interface due to evaporation of the culture medium. Even at room temperature and humidity, and physiologically relevant salt concentrations, the water evaporation was found to be sufficient to drive convection patterns. To prove this hypothesis, experiments were complemented with a mathematical model that aimed to understand the mechanism of plume formation and the role of salt in triggering the instability. The simplified system of evaporating salty water was first studied using linear stability analysis, and then with finite element simulations. A comparison between these three approaches is presented. While evaporation-driven convection has not been discussed extensively in the context of biological systems, these results suggest that the phenomenon may be broadly relevant, particularly in those systems involving microorganisms of limited motility.
Cho M, Hwang Y, Choi H, 2018, Scale interactions and spectral energy transfer in turbulent channel flow, Journal of Fluid Mechanics, Vol: 854, Pages: 474-504, ISSN: 0022-1120
Spectral energy transfer in a turbulent channel flow is investigated at Reynolds number Re ≃1700 , based on the wall shear velocity and channel half-height, with a particular emphasis on full visualization of triadic wave interactions involved in turbulent transport. As in previous studies, turbulent production is found to be almost uniform, especially over the logarithmic region, and the related spanwise integral length scale is approximately proportional to the distance from the wall. In the logarithmic and outer regions, the energy balance at the integral length scales is mainly formed between production and nonlinear turbulent transport, the latter of which plays the central role in the energy cascade down to the Kolmogorov microscale. While confirming the classical role of the turbulent transport, the triadic wave interaction analysis unveils two new types of scale interaction processes, highly active in the near-wall and the lower logarithmic regions. First, for relatively small energy-containing motions, part of the energy transfer mechanisms from the integral to the adjacent small length scale in the energy cascade is found to be provided by the interactions between larger energy-containing motions. It is subsequently shown that this is related to involvement of large energy-containing motions in skin-friction generation. Second, there exists a non-negligible amount of energy transfer from small to large integral scales in the process of downward energy transfer to the near-wall region. This type of scale interaction is predominant only for the streamwise and spanwise velocity components, and it plays a central role in the formation of the wall-reaching inactive part of large energy-containing motions. A further analysis reveals that this type of scale interaction leads the wall-reaching inactive part to scale in the inner units, consistent with the recent observation. Finally, it is proposed that turbulence production and pressure–strain spectra supp
Maretvadakethope S, Keaveny E, Hwang Y, 2018, Gyrotactic trapping can be hydrodynamically unstable, Pages: 39-40
Thin layers of motile phytoplankton are observed in the coastal ocean, meters below the surface, and they often exhibit high ecological activities. In a recent study by Durham et al (2009, Science, 323:1067-1070), it was proposed that, for bottom-heavy motile phytoplank-ton (e.g. Chlamydomonas), such thin layers can be formed by 'gyrotactic trapping'. Here, we perform a linear stability analysis of the layer formed by this mechanism, and show that it can be hydrodynamically unstable if the cell concentration is sufficiently high. The present result implies that the gyrotactic trapping may not be a robust mechanism in the formation of the thin layers of phytoplankton.
Yang Q, Willis AP, Hwang Y, 2017, Energy production and self-sustained turbulence at the Kolmogorov scale inCouette flow, Journal of Fluid Mechanics, Vol: 834, Pages: 531-554, ISSN: 0022-1120
Several recent studies have reported that there exists a self-similar form of invariant solutions down to the Kolmogorov microscale in the bulk region of turbulent Couette flow. While their role in a fully developed turbulent flow is yet to be identified, here we report that there exists a related mechanism of turbulence production at the Kolmogorov microscale in the bulk region of turbulent Couette flow by performing a set of minimal-span direct numerical simulations up to friction Reynolds number . This mechanism is found to essentially originate from the non-zero mean shear in the bulk region of the Couette flow, and involves eddy turn-over dynamics remarkably similar to the so-called self-sustaining process (SSP) and/or vortex–wave interaction (VWI). A numerical experiment that removes all other motions except in the core region is also performed, which demonstrates that the eddies at a given wall-normal location in the bulk region are sustained in the absence of other motions at different wall-normal locations. It is proposed that the self-sustaining eddies at the Kolmogorov microscale correspond to those in uniform shear turbulence at transitional Reynolds numbers, and a quantitative comparison between the eddies in uniform shear and near-wall turbulence is subsequently made. Finally, it is shown that turbulence production by the self-sustaining eddies at the Kolmogorov microscale is much smaller than that of full-scale simulations, and that the difference between the two increases with Reynolds number.
de Giovanetti M, Sung HJ, Hwang Y, 2017, Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions, Journal of Fluid Mechanics, Vol: 832, Pages: 483-513, ISSN: 0022-1120
It has often been proposed that the formation of large-scale motion (or bulges) is aconsequence of successive mergers and/or growth of near-wall hairpin vortices. In thepresent study, we report our direct observation that large-scale motion is generated byan instability of an ‘amplified’ streaky motion in the outer region (i.e. very-large-scalemotion). We design a numerical experiment in turbulent channel flow up to Reτ '2000where a streamwise-uniform streaky motion is artificially driven by body forcing inthe outer region computed from the previous linear theory (Hwang & Cossu, J. FluidMech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is foundthat an energetic streamwise vortical structure emerges at a streamwise wavelength ofλx/h '1–5 (h is the half-height of the channel). The application of dynamic modedecomposition and the examination of turbulence statistics reveal that this structureis a consequence of the sinuous-mode instability of the streak, a subprocess of theself-sustaining mechanism of the large-scale outer structures. It is also found that thestatistical features of the vortical structure are remarkably similar to those of the largescalemotion in the outer region. Finally, it is proposed that the largest streamwiselength of the streak instability determines the streamwise length scale of very-largescalemotion.
Cassinelli A, de Giovanetti M, Hwang Y, 2017, Streak instability in near-wall turbulence revisited, Journal of Turbulence, Vol: 18, Pages: 443-464, ISSN: 1468-5248
The regeneration cycle of streaks and streamwise vortices plays a central role in the sustainment of near-wall turbulence. In particular, the streak breakdown phase in the regeneration cycle is the core process in the formation of the streamwise vortices, but its current understanding is limited particularly in a real turbulent environment. This study is aimed at gaining fundamental insight into the underlying physical mechanism of the streak breakdown in the presence of background turbulent fluctuation. We perform a numerical experiment based on direct numerical simulation, in which streaks are artificially generated by a body forcing computed from previous linear theory. Upon increasing the forcing amplitude, the artificially driven streaks are found to generate an intense fluctuation of the wall-normal and spanwise velocities in a fairly large range of amplitudes. This cross-streamwise velocity fluctuation shows its maximum at λ+ x ≈ 200 − 300 (λ+ x is the inner-scaled streamwise wavelength), but it only appears for λ+ x ≲ 3000 − 4000. Further examination with dynamic mode decomposition reveals that the related flow field is composed of sinuous meandering motion of the driven streaks and alternating cross-streamwise velocity structures, clearly reminiscent of sinuous-mode streak instability found in previous studies. Finally, it is shown that these structures are reasonably well aligned along the critical layer of the secondary instability, indicating that the surrounding turbulence does not significantly modify the inviscid inflectional mechanism of the streak breakdown via streak instability and/or streak transient growth.
Cossu C, Hwang Y, 2017, Self-sustaining processes at all scales in wall-boundedturbulent shear flows, Royal Society of London. Philosophical Transactions A. Mathematical, Physical and Engineering Sciences, Vol: 375, ISSN: 1364-503X
We collect and discuss the results of our recentstudies which show evidence of the existence ofa whole family of self-sustaining motions in wallboundedturbulent shear flows with scales rangingfrom those of buffer-layer streaks to those of largescaleand very-large-scale motions in the outer layer.The statistical and dynamical features of this familyof self-sustaining motions, which are associated withstreaks and quasi-streamwise vortices, are consistentwith those of Townsend’s attached eddies. Motionsat each relevant scale are able to sustain themselvesin the absence of forcing from larger- or smaller-scalemotions by extracting energy from the mean flow viaa coherent lift-up effect. The coherent self-sustainingprocess is embedded in a set of invariant solutions ofthe filtered Navier-Stokes equations which take intofull account the Reynolds stresses associated with theresidual smaller-scale motions.
Hwang Y, 2017, The mesolayer of attached eddies in wall-bounded turbulent flows
It has recently been reported that the outer peak in the secondorder statistics of the streamwise velocity depends on the Reynolds number. Starting from this puzzling observation, here I propose that the streamwise velocity component of each of the energy-containing motions in the form of Towsnend's attached eddies exhibit innerscaling nature in the region close to the wall (see figure 1). Some compelling evidence on this proposition has been presented with a careful inspection of scaling of velocity spectra from direct numerical simulations and a linear analysis with an eddy viscosity. It is shown that this behavior can emerge due to inhomogeneous turbulent dissipation in the wall-normal direction, and also enables one to explain the Reynolds-number-dependent behavior of the outer peak as well as the near-wall penetration of the large-scale outer structures in a consistent manner. Extension of this concept to Townsend's attached eddy hypothesis further reveals that the selfsimilarity in the streamwise velocity of the attached eddies would be theoretically broken in the region close to the wall.
de Giovanetti M, Hwang Y, Choi H, 2016, Skin-friction generation by attached eddies in turbulent channel flow, Journal of Fluid Mechanics, Vol: 808, Pages: 511-538, ISSN: 1469-7645
Despite a growing body of recent evidence on the hierarchical organization of the selfsimilarenergy-containing motions in the form of Townsend’s attached eddies in wallboundedturbulent flows, their role in turbulent skin-friction generation is currentlyknown very little. In this paper, the contribution of each of these self-similar energycontainingmotions to turbulent skin friction is explored up to Reτ ≃ 4000. Threedifferent approaches are employed to quantify the skin-friction generation by the motions,the spanwise length scale of which is smaller than a given cut-off wavelength: 1) FIKidentity in combination with the spanwise wavenumber spectra of the Reynolds shearstress; 2) confinement of the spanwise computational domain; 3) artificial damping ofthe motions to be examined. The near-wall motions are found to continuously lose theirrole in skin-friction generation on increasing the Reynolds number, consistent with theprevious finding at low Reynolds numbers. The largest structures given in the form ofvery-large-scale and large-scale motions are also found to be of limited importance: dueto a non-trivial scale-interaction process, their complete removal yields only 5 ∼ 8% ofskin-friction reduction at all the Reynolds numbers considered, although they are foundto be responsible for 20 ∼ 30% of total skin friction at Reτ ≃ 2000. Application of all thethree approaches consistently reveals that the largest amount of skin friction is generatedby the self-similar motions populating the logarithmic region. It is further shown thatthe contribution of these motions to turbulent skin friction gradually increases with theReynolds number, and that these coherent structures are eventually responsible for mostof turbulent skin-friction generation at sufficiently high Reynolds numbers.
Hwang Y, Willis AP, Cossu C, 2016, Invariant solutions of minimal large-scale structures in turbulent channel flow for Reτ up to 1000, Journal of Fluid Mechanics, Vol: 802, ISSN: 1469-7645
Understanding the origin of large-scale structures in high Reynolds number wall turbulencehas been a central issue over a number of years. Recently, Rawat et al. (J.Fluid Mech., 2015, 782, p515) have computed invariant solutions for the large-scalestructures in turbulent Couette flow at Reτ ≃ 128 using an over-damped LES with theSmagorinsky model to account for the effect of the surrounding small-scale motions.Here, we extend this approach to an order of magnitude higher Reynolds numbers inturbulent channel flow, towards the regime where the large-scale structures in the formof very-large-scale motions (long streaky motions) and large-scale motions (short vorticalstructures) energetically emerge. We demonstrate that a set of invariant solutions canbe computed from simulations of the self-sustaining large-scale structures in the minimalunit (domain of size Lx = 3.0h streamwise and Lz = 1.5h spanwise) with midplanereflection symmetry at least up to Reτ ≃ 1000. By approximating the surrounding smallscales with an artificially elevated Smagorinsky constant, a set of equilibrium states arefound, labelled upper- and lower-branch according to their associated drag. It is shownthat the upper-branch equilibrium state is a reasonable proxy for the spatial structureand the turbulent statistics of the self-sustaining large-scale structures.
Hwang Y, Bengana Y, 2016, Self-sustaining process of minimal attached eddies in turbulent channel flow, Journal of Fluid Mechanics, Vol: 795, Pages: 708-738, ISSN: 1469-7645
It has been recently shown that the energy-containing motions (i.e. coherent structures) in turbulent channel flow exist in the form of Townsend’s attached eddies by a numerical experiment which simulates the energy-containing motions only at a prescribed spanwise length scale using their self-sustaining nature (Hwang, J. Fluid Mech., vol. 767, 2015, pp. 254–289). In the present study, a detailed investigation of the self-sustaining process of the energy-containing motions at each spanwise length scale (i.e. the attached eddies) in the logarithmic and outer regions is carried out with an emphasis on its relevance to ‘bursting’, which refers to an energetic temporal oscillation of the motions (Flores & Jiménez, Phys. Fluids, vol. 22, 2010, 071704). It is shown that the attached eddies in the logarithmic and outer regions, composed of streaks and quasi-streamwise vortical structures, bear the self-sustaining process remarkably similar to that in the near-wall region: i.e. the streaks are significantly amplified by the quasi-streamwise vortices via the lift-up effect; the amplified streaks subsequently undergo a ‘rapid streamwise meandering motion’, reminiscent of streak instability or transient growth, which eventually results in breakdown of the streaks and regeneration of new quasi-streamwise vortices. For the attached eddies at a given spanwise length scale λz between λ+z≃100 and λz≃1.5h , the single turnover time period of the self-sustaining process is found to be Tuτ/λz≃2 ( uτ is the friction velocity), which corresponds well to the time scale of the bursting. Two additional numerical experiments, designed to artificially suppress the lift-up effect and the streak meandering motions, respectively, reveal that these processes are essential ingredients of the self-sustaining process of the attached eddies in the logarithmic and outer regions, consistent with several previous theoret
Hwang Y, 2016, Statistics of single self-sustaining attached eddy in a turbulent channel, Pages: 391-398, ISSN: 1382-4309
A Numerical experiment that isolates the motions at a given spanwise length scale is performed based on previous observation on the self-sustaining nature of the eddies in the logarithmic and the wake outer regions [7, 8]. It is shown that the statistics of the isolated self-sustaining motions at a given spanwise length scale are strikingly similar to those of the single attached eddy postulated by Townsend and Perry [1, 2, 5, 6], demonstrating the existence of the attached eddies in turbulent channel flow. Inspecting one-dimensional spectra also leads to build a complete form of the self-similarity of the streamwise length scale and the wall-normal location of all the coherent structures known, including near-wall streaks, quasi-streamwise vortices, very-large-scale motions, and large-scale motions.
Rawat S, Cossu C, Hwang Y, et al., 2015, On the self-sustained nature of large-scale motions in turbulent Couette flow, Journal of Fluid Mechanics, Vol: 782, Pages: 515-540, ISSN: 1469-7645
Hogan B, Babataheri A, Hwang Y, et al., 2015, Characterizing cell adhesion by using micropipette aspiration, Biophysical Journal, Vol: 109, Pages: 209-219, ISSN: 1542-0086
Gouget CLM, Hwang Y, Barakat AI, 2015, Model of cellular mechanotransduction via actin stress fibers, Biomechanics and Modeling in Mechanobiology, Vol: 15, Pages: 331-344, ISSN: 1617-7959
Hwang Y, 2015, Statistical structure of self-sustaining attached eddies in turbulent channel flow, Journal of Fluid Mechanics, Vol: 767, Pages: 254-289, ISSN: 1469-7645
The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend’s attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend’s attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length
Bengana Y, Hwang Y, 2015, Minimal dynamics of self-sustaining attached eddies in a turbulent channel
Very recently, we have performed a numerical experiment designed to simulate only the energy-containing motions at a prescribed spanwise length scale using their self-sustaining nature (Hwang, 2015). The computed statistical structure of each of the energy containing-motions have been found to be self-similar with respect to the spanwise length scale, proportional to the distance from the wall. More importantly, the statistical structure was found to be remarkably similar to that given in the original theory of Townsend, demonstrating the existence of the attached eddies as energy-containing motions contributing to the logarithmic layer. In this work, we extend the previous work to explore the dynamical self-similarity of each of the attached eddies. It is shown that each of the attached eddies exhibit the so-called 'self-sustaining process' composed of 1) streak amplification via the lift-up effect, 2) streak breakdown via the secondary instability, 3) nonlinear regeneration of streamwise vortical structure. This process occurs self-similarly with respect to the spanwise length scale of each of the attached eddies and results in the time scale given by Tut/Lz ≃ 2 ∼ 3.
Hwang Y, Kumar P, Barakat AI, 2014, Intracellular regulation of cell signaling cascades: how location makes a difference, JOURNAL OF MATHEMATICAL BIOLOGY, Vol: 69, Pages: 213-242, ISSN: 0303-6812
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Hwang Y, Pedley TJ, 2014, Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel, Journal of Fluid Mechanics, Vol: 749, Pages: 750-777, ISSN: 1469-7645
Hwang Y, 2014, Structural sensitivities of soft and steep nonlinear global modes in spatially developing media, European Journal of Mechanics B - Fluids, Vol: 49, Pages: 322-334, ISSN: 0997-7546
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