## Publications

51 results found

Fung L, Bearon RN, Hwang Y, 2021, A local approximation model for macro-scale transport of biased active Brownian particles in a flowing suspension, *Journal of Fluid Mechanics*, ISSN: 0022-1120

A dilute suspension of motile micro-organisms subjected to a strong ambientflow, such as algae in the ocean, can be modelled as a population ofnon-interacting, orientable active Brownian particles (ABPs). Using theSmoluchowski equation (i.e. Fokker-Planck equation in space and orientation),one can describe the non-trivial transport phenomena of ABPs such as taxes andshear-induced migration. This work transforms the Smoluchowski equation into atransport equation, in which the drifts and dispersions can be furtherapproximated as a function of the local flow field. The new model can beapplied to any global flow field due to its local nature, unlike previousmethods such as those utilising the generalised Taylor dispersion theory. Thetransformation shows that the overall drift includes both the biased motilityof individual particles in the presence of taxis and the shear-inducedmigration in the absence of taxis. In addition, it uncovers other new driftsand dispersions caused by the interactions between the orientational dynamicsand the passive advection/diffusion of ABPs. Finally, the performance of thismodel is assessed using examples of gyrotactic suspensions, where the proposedmodel is demonstrated to be most accurate when the biased motility of particles(i.e. taxis) is weak.

Basso R, Hwang Y, Assi G,
et al., 2021, Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate, *Journal of Fluid Mechanics*, Vol: 928, Pages: 1-32, ISSN: 0022-1120

This paper investigates the origin of flow-induced instabilities and their sensitivities ina flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linearstability and sensitivity problem is formulated in the Eulerian frame by considering thegeometric nonlinearity arising from the rotational motion of the cylinder which is notpresent in the stationary or purely translating stability methodology. This nonlinearityneeds careful and consistent treatment in the linearised problem particularly whenconsidering the Eulerian frame or reference adopted in this study and not so widelyconsidered. Two types of instabilities arising from the fluid-structure interaction arefound. The first type of the instabilities is the stationary symmetry-breaking mode, whichwas well reported in previous studies. This instability exhibits a strong correlation withthe length of the recirculation zone. A detailed analysis of the instability mode andits sensitivity reveals the importance of the flow near the tip region of the plate for thegeneration and control of this instability mode. The second type is an oscillatory torsionalflapping mode, which has not been well reported. This instability typically emerges whenthe length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode,it is not so closely correlated with the length of the recirculation zone. The sensitivityanalysis however also reveals the crucial role played by the flow near the tip region inthis instability. Finally, it is found that many physical features of this instability arereminiscent of those of the flapping (or flutter instability) observed in a flow over aflexible plate or a flag, suggesting that these instabilities share the same physical origin.

Hwang Y, Hutchins N, Marusic I, 2021, The logarithmic variance of streamwise velocity and k−1 conundrum in wall turbulence, *Journal of Fluid Mechanics*, ISSN: 0022-1120

The logarithmic dependence of streamwise turbulence intensity has repeatedly beenobserved in recent experimental and direct numerical simulation data. However, itsspectral counterpart, a well-developed k−1spectrum (k is the spatial wavenumber ina wall-parallel direction), has not been convincingly observed from the same data. Inthe present study, we revisit the spectrum-based attached eddy model of Perry andco-workers, who proposed the emergence of k−1spectrum in the inviscid limit, forsmall but finite z/δ and for finite Reynolds numbers (z is the wall-normal co-ordinateand δ the outer length scale). In the upper logarithmic layer (or inertial sublayer),a reexamination reveals that the intensity of the spectrum must vary with the wallnormal location at order of z/δ, consistent with the early observation argued with‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated,demonstrating that the existence of a well-developed k−1spectrum is not a necessarycondition for the approximate logarithmic wall-normal dependence of turbulence intensity– a more general condition is the existence of pre-multiplied power-spectral intensity ofO(1) for O(1/δ) < k < O(1/z). Furthermore, it is shown that the Townsend-Perryconstant must weakly be dependent on the Reynolds number. Finally, the analysis issemi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wallcorrection for the turbulence intensity is subsequently proposed. All the predictions ofthe proposed model and the related analyses/assumptions are validated with high-fidelityexperimental data (Samie et al., J. Fluid Mech., 2018, vol. 851, pp. 391–415).

Jin D, Hwang Y, Kampf N,
et al., 2021, Direct measurement of the viscoelectric effect in water, *Proceedings of the National Academy of Sciences of USA*, ISSN: 0027-8424

The viscoelectric effect concerns the increase in viscosity of a polar liquid in an electric field due to its interaction with the dipolar molecules, and was first determined for polar organic liquids more than 80 years ago. For the case of water, however, the most common polar liquid, direct measurement of the viscoelectric effect is challenging and has not to date been carried out, despite its importance in a wide range of electrokinetic and flow effects. In consequence, estimates of its magnitude for water vary by more than 3 orders of magnitude. Here we measure the viscoelectric effect in water directly using a surface force balance (SFB), by measuring the dynamic approach of two molecularly-smooth surfaces with a controlled, uniform electric field between them across highly-purified water. As the water is squeezed out of the gap between the approaching surfaces, viscous damping dominates the approach dynamics; this is modulated by the viscoelectric effect under the uniform transverse electric field across the water, enabling its magnitude to be directly determined as a function of the field. We find a value for this magnitude which differs respectively by 1 and by 2 orders of magnitude from its highest and lowest previously estimated values.

Fung L, Hwang Y, 2021, Instability of tilted shear flow in a strongly stratified and viscous medium, *IUTAM Bookseries*, Vol: 38, Pages: 379-389, ISSN: 1875-3507

It is well known that stratification can stabilise shear flow. In a vertical shear flow, the Miles-Howard’s criterion firmly indicates that flow should be stable if the local Richardson number is greater than one fourth. However, if shear is tilted with a non-zero angle from vertical, an instability can arise even under very strong stratification, and such an instability was recently observed in a titled wake flow at low Reynolds number (Meunier 2012, J. Fluid Mech., 699:174). In the present study, we showed that in the limit of low Froude number and low Reynolds number, the linearised equations of motion could be reduced to the Orr-Sommerfeld equation on the horizontal plane, except the viscous term that contains vertical dissipation. Based on this equation, it is demonstrated that the low-Froude-number mode would be a horizontal inflectional instability, and should remain two dimensional at small tilting angles. It is further shown that the emergence of small vertical velocity at finite Froude number modifies the horizontal inflectional instability and leads to paradoxically stabilising buoyancy force on increasing Froude number. Finally, an absolute instability analysis is performed, revealing qualitatively good agreement with the experimental result.

Doohan P, Willis A, Hwang Y, 2021, Minimal multi-scale dynamics of near-wall turbulence, *Journal of Fluid Mechanics*, Vol: 913, ISSN: 0022-1120

Recent numerical experiments have shown that the temporal dynamics of isolated energy-containing eddies in the hierarchy of wall-bounded turbulence are governed by the self-sustaining process (SSP). However, high-Reynolds-number turbulence is a multi-scale phenomenon and exhibits interaction between the structures of different scales, but the dynamics of such multi-scale flows are poorly understood. In this study, the temporal dynamics of near-wall turbulent flow with two integral length scales of motion are investigated using a shear stress-driven flow model (Doohan et al., J. Fluid Mech., vol. 874, 2019, pp. 606–638), with a focus on identifying scale interaction processes through the governing equations and relating these to the SSPs at each scale. It is observed that the dynamics of the energy cascade from large to small scales is entirely determined by the large-scale SSP and the timing of the corresponding inter-scale turbulent transport coincides with the large-scale streak breakdown stage. Furthermore, the characteristic time scales of the resulting small-scale dissipation match those of the large-scale SSP, indicative of non-equilibrium turbulent dissipation dynamics. A new scale interaction process is identified, namely that the transfer of wall-normal energy from large to small scales drives small-scale turbulent production via the Orr mechanism. While the main outcome of this driving process appears to be the transient amplification of localised small-scale velocity structures and their subsequent dissipation, it also has an energising effect on the small-scale SSP. Finally, the feeding of energy from small to large scales is impelled by the small-scale SSP and coincides with the small-scale streak instability stage. The streamwise feeding process seems to be related to the subharmonic sinuous streak instability mode in particular and leads to the formation of the wall-reaching part of high-speed large-scale streaks.

Skouloudis N, Hwang Y, 2021, Scaling of turbulence intensities up to Reτ=10^6 with a resolvent-based quasi-linear approximation, *Physical Review Fluids*, Vol: 6, ISSN: 2469-990X

A minimal form of quasilinear approximation (QLA), recently proposed with a stochastic forcing and proper orthogonal decomposition modes [Hwang and Ekchardt, J. Fluid Mech. 894, A23 (2020)], has been extended by employing a resolvent framework. A particular effort is made to reach an extremely high Reynolds number by carefully controlling the approximation without loss of the general scaling properties in the spectra, while setting out the main limitations and accuracy of the proposed QLA with possibility of further improvement. The QLA is subsequently applied to turbulent channel flow up to Reτ=106 (Reτ is the friction Reynolds number). While confirming that the logarithmic wall-normal dependence in streamwise and spanwise turbulence intensities robustly appears, it reveals some nontrivial difference from the scaling of the classical attached eddy model based on inviscid flow assumption. First, the spanwise wave number spectra do not show any clearly visible inverse-law behavior due to the viscous wall effect prevailing in a significant portion of the lower part of the logarithmic layer. Second, the near-wall peak streamwise and spanwise turbulence intensities are found to deviate from lnReτ scaling for Reτ≳104. Importantly, the near-wall streamwise turbulence intensity is inversely proportional to 1/U+cl (U+cl is the inner-scaled channel centreline velocity), consistent with the scaling obtained from an asymptotic analysis of the Navier-Stokes equations [Monkewitz and Nagib, J. Fluid Mech. 783, 474 (2015)]. The same behavior was also observed for the streamwise turbulence intensity in the logarithmic region, as was predicted with the asymptotic analysis. Finally, the streamwise turbulence intensity in the logarithmic region is found to become greater than the near-wall one at Reτ≃O(105). It is shown that this behavior originates from the near-wall spectra associated with large-scale inactive motions, the intensity of which gradually decays as R

Jiao Y, Hwang Y, Chernyshenko S, 2021, The Orr mechanism in transition of parallel shear flow, *Physical Review Fluids*, Vol: 6, ISSN: 2469-990X

The Orr mechanism is revisited to understand its precise role in the transition of plane Couette flow. By considering homogeneous shear flow and plane Couette flow, it is identified that the Orr mechanism induces a lift-up effect which significantly amplifies spanwise velocity. An optimal perturbation analysis for an individual velocity component reveals that the amplification of spanwise velocity is most active at the streamwise length comparable to the given spanwise length of the perturbation. The relevance of this mechanism to transition is subsequently examined in plane Couette flow. To this end, a set of initial conditions, which combines the optimal perturbation for spanwise velocity with the one for all the velocity components, is considered by varying their amplitudes. Two representative transition scenarios are found: oblique and streak transitions. In the former, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the latter, its role is limited only to the streak breakdown at the late stage of transition. As such, the oblique transition offers a route to turbulence energetically more efficient than the streak transition, at least for the cases examined in the present paper. Finally, the oblique transition is found to share many physical similarities with the transition by the minimal seed.

Hernandez C, Hwang Y, 2020, Spectral energetics of a quasilinear approximation in uniform shear turbulence, *Journal of Fluid Mechanics*, Vol: 604, Pages: A11-1-A11-26, ISSN: 0022-1120

The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the meanare fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascadeis shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. It is also found that the streamwise wave number spectra of turbulent transport, obtained with the classical Reynolds decomposition, statistically characterizes the instability of the linearised fluctuation equations. Further supporting evidence of this claim is presented by carrying out a numerical experiment, in which the QL model with single streamwise Fourier mode is found to generate the strongest turbulence for Lx/Lz= 1∼3, consistent with previous findings (Lx and Lz are the streamwise and spanwise computational domains, respectively). Finally, the QL model is shown to completely ignore the role of slow pressure in the fluctuations, resulting in a significant damage of pressure-strain transport at all length scales. This explains the anisotropic turbulence of the QL model throughout the entire wavenumber space as well as the inhibited nonlinear regeneration of streamwise vortices in the self-sustaining process.

Hwang Y, Myoungkyu L, 2020, The mean logarithm emerges with self-similar energetics, *Journal of Fluid Mechanics*, Vol: 903, Pages: R6-1-R6-11, ISSN: 0022-1120

The attached eddy hypothesis of Townsend (The structure of turbulent shear flow, 1956,Cambridge U. Press) states that the logarithmic mean velocity would admit self-similarenergy-containing eddies which scales with the distance from the wall. Over the pastdecade, there has been significant amount of evidence supporting the hypothesis, placingit to be the central platform for the statistical description of the general organisationof coherent structures in wall-bounded turbulent shear flows. Nevertheless, the mostfundamental question, namely why the hypothesis has to be true, remains unansweredover many decades. Under the assumption that the integral length scale is proportionalto the distance from the wally, in the present study, we analytically demonstrate thatthe mean velocity is a logarithmic function ofyif and only if the energy balance atintegral length scale is self-similar with respect toy, providing a theoretical groundfor the attached eddy hypothesis. The analysis is subsequently verified with the datafrom direct numerical simulation of incompressible channel flow at the friction ReynoldsnumberReτ'5200 (Lee & Moser,J. Fluid Mech., vol. 774, 2015, 395–415).

Fung L, Bearon R, Hwang Y, 2020, Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe, *Journal of Fluid Mechanics*, Vol: 902, Pages: 1-34, ISSN: 0022-1120

In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218-220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the Generalised Taylor Dispersion (GTD) theory and the Fokker-Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration, at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker-Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.

Fung L, Hwang Y, 2020, A sequence of transcritical bifurcations in a suspension of gyrotactic microswimmers in vertical pipe, *Journal of Fluid Mechanics*, Vol: 902, Pages: R2-1-R2-11, ISSN: 0022-1120

Kessler (Nature, vol. 313, 1985, pp. 218–220) first showed that plume-like structures spontaneously appear from both stationary and flowing suspensions of gyrotactic microswimmers in a vertical pipe. Recently, it has been shown that there exist multiple steady, axisymmetric and axially uniform solutions to such a system (Bees & Croze, Proc. R. Soc. A, vol. 466, 2010, pp. 2057–2077). In the present study, we generalise this finding by reporting that a countably infinite number of such solutions emerge as the Richardson number increases. Linear stability, weakly nonlinear and fully nonlinear analyses are performed, revealing that each of the solutions arises from the destabilisation of a uniform suspension. The countability of the solutions is due to the finite flow domain, while the transcritical nature of the bifurcation is because of the cylindrical geometry, which breaks the horizontal symmetry of the system. It is further shown that there exists a maximum threshold of achievable downward flow rate for each solution if the flow is to remain steady, as varying the pressure gradient can no longer increase the flow rate from the solution. All of the solutions found are unstable, except for the one arising at the lowest Richardson number, implying that they would play a role in the transient dynamics in the route from a uniform suspension to the fully developed gyrotactic pattern.

Hwang Y, Eckhardt B, 2020, Attached eddy model revisited using a minimal quasi-linear approximation, *Journal of Fluid Mechanics*, Vol: 894, ISSN: 0022-1120

Townsend’s model of attached eddies for boundary layers is revisited within a quasi-linear approximation. The velocity field is decomposed into a mean profile and fluctuations. While the mean is obtained from the nonlinear equations, the fluctuations are modelled by replacing the nonlinear self-interaction terms with an eddy-viscosity-based turbulent diffusion and stochastic forcing. Under this particular approximation, the resulting fluctuation equations remain linear, enabling solutions to be superposed, the same theoretical idea used in the original attached eddy model. By leveraging this feature, the stochastic forcing is determined self-consistently by solving an optimisation problem which minimises the difference between the Reynolds shear stresses from the mean and fluctuation equations, subject to a constraint that the averaged Reynolds shear-stress spectrum is sufficiently smooth in the spatial wavenumber space. The proposed quasi-linear approximation is subsequently applied to channel flow for Reynolds number Re𝜏 ranging from 500 to 20 000. The best result is obtained when the Reynolds stress is calculated by retaining only the two leading proper orthogonal decomposition modes, which further filters out the modelling artefact caused by the unphysical stochastic forcing. In this case, the resulting turbulence intensity profile and energy spectra exhibit the same qualitative behaviour as direct numerical simulation (DNS) data throughout the entire wall-normal domain, while reproducing the early theoretical predictions of the original attached eddy model within a controlled approximation to the Navier–Stokes equations. Finally, the proposed quasi-linear approximation reveals that the peak streamwise and spanwise turbulence intensities may deviate slightly from the logarithmic scaling with the Reynolds number for Re𝜏 ≳ 10 000, and the supporting evidence is presented using the existing DNS data.

Fung L, Hwang Y, 2020, Linear instability of tilted parallel shear flow in a strongly stratified and viscous medium, *JMST Advances*, Vol: 2, Pages: 37-51, ISSN: 2524-7905

A linear stability analysis is performed on a tilted parallel wake in a strongly stratified fluid at low Reynolds numbers. A particular emphasis of the present study is given to the understanding of the low-Froude-number mode observed by the recent experiment (Meunier in J Fluid Mech 699:174–197, 2012). In the limit of low Froude number, the linearised equations of motion can be reduced to the Orr–Sommerfeld equation on the horizontal plane, except the viscous term that contains vertical dissipation. Based on this equation, it is proposed that the low-Froude-number mode would be a horizontal inflectional instability and should remain two-dimensional at small tilting angles as long as the Reynolds number is sufficiently low. To support this claim, the asymptotic regime where this analysis is strictly valid is subsequently discussed in relation to previous work on the proper vertical length scale. The absolute and convective instability analysis of parallel wake is further performed, showing qualitatively good agreement with the experimental result. The low-Froude-number mode is found to be stabilised on increasing Froude number, as in the experiment. It is shown that the emergence of small vertical velocity at finite Froude number, the size of which is proportional to the square of Froude number, plays the key role in the stabilisation by modifying the inflectional instability and paradoxically creating stabilising buoyancy effect with the increase of Froude number.

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.

Smitha M, 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.

Maretvadakethope S, Keaveny EE, Hwang Y, 2019, The instability of gyrotactically trapped cell layers

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, 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.

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

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.

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.

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