arXiv subjects

Yongyun Hwang

Publications and source records attributed to Yongyun Hwang.

At least 19 recordsLinked to original sources

arXiv2026

Navier-Stokes-driven analysis of mean and fluctuating wall shear stress in turbulent channel flow

We propose a Navier-Stokes-driven analysis of the mean and fluctuating wall shear stress (WSS) applied to turbulent channel flow data from direct numerical simulations at friction Reynolds numbers up to $Re_τ\approx 2000$. Starting from the streamwise momentum equation, we derive exact integral equations that relate the square plane-average and the square fluctuating WSS to wall-normal integrals of terms combining shear with acceleration, shear with pressure-radient, and shear with viscous diffusion. The square plane-average WSS can be well approximated by the product of plane-average shear and plane-average acceleration integrated over the buffer layer with corrections from the mean pressure gradient which diminish as the reciprocal of the Reynolds number. The square fluctuating WSS is similarly well approximated by the shear-acceleration and shear-pressure-gradient covariances integrated over the buffer layer, but the latter increases in magnitude with Reynolds number and is therefore not negligible. The acceleration fluctuations around the plane-average acceleration consist of a local Eulerian fluctuating acceleration, an advective acceleration and a term which gives rise a turbulence production contribution to the shear-acceleration covariance. By Taylor's frozen turbulence hypothesis the Eulerian acceleration and the streamwise mean advection part of the advective acceleration cancel each other. The shear-acceleration covariance is characterised by a near-wall peak which results from turbulence production and, more specifically, sweeps.

physics.flu-dyn↗

arXiv2026

Multiscale quasi time-periodic coherent structures in shear flows

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as complex as quasi-time-periodic solutions. Approximations of these states can be computed efficiently using a quasi-linear model, consistent with the large-Reynolds-number asymptotic analysis. The quasi-linear structure is key to producing multiscale critical layers that generate vortices obeying Taylor frozen-flow hypothesis.

physics.flu-dyn↗

arXiv2025

Turbulent transport for wall shear stress fluctuations

Statistical structure and the underlying energy budget of wall shear stress fluctuations are studied in both Poiseulle and Couette flows with emphasis on its streamwise component. Using a dimensional analysis and direct numerical simulation data, it is shown that the spectra of streamwise wall dissipation for $λ\lesssim 1000 δ_ν$ are asymptotically invariant with the Reynolds number ($Re$), whereas those for $λ\gtrsim δ$ decay with $Re$ (here, $λ$ is a nominal wall-parallel wavelength, and $δ_ν$ and $δ$ are the viscous inner and outer length scales, respectively). The wall dissipation increases with $Re$ due to the increasing contribution of the spectra at $1000 δ_ν\lesssim λ\lesssim δ$. The subsequent analysis of the energy budget shows that the near-wall motions associated with these wall dissipation spectra are mainly driven by turbulent transport and are `inactive' in the sense that they contain very little Reynolds shear stress (or turbulence production). As such, turbulent transport spectra near the wall are also found to share the same $Re$-scaling behaviour with wall dissipation, and this is observed in the spectra of both the wall-normal and inter-scale turbulent transports. The turbulent transport underpinning the increase of wall dissipation with $Re$ is characterised by energy fluxes towards the wall, together with inverse energy transfer from small to large length scales along the wall-parallel directions.

physics.flu-dyn↗

arXiv2025

Structural Anisotropy Stabilises Asymmetric Beating in Instability Driven Filaments

Asymmetries and anisotropies are widespread in biological systems, including in the structure and dynamics of cilia and eukaryotic flagella. These microscopic, hair-like appendages exhibit asymmetric beating patterns that break time-reversal symmetry needed to facilitate fluid transport at the cellular level. The intrinsic anisotropies in ciliary structure can promote preferential beating directions, further influencing their dynamics. In this study, we employ numerical simulation and bifurcation analysis of a mathematical model of a filament driven by a follower force at its tip to explore how intrinsic curvature and direction-dependent bending stiffnesses impact filament dynamics. Our results show that while intrinsic curvature is indeed able to induce asymmetric beating patterns when filament motion is restricted to a plane, this beating is unstable to out of plane perturbations. Furthermore, we find that a 3D whirling state seen for isotropic filament dynamics can be suppressed when sufficient asymmetry or anisotropy are introduced. Finally, for bending stiffness ratios as low as 2, we demonstrate that combining structural anisotropy with intrinsic curvature can stabilise asymmetric beating patterns, highlighting the crucial role of anisotropy in ciliary dynamics.

cond-mat.soft↗

arXiv2025

A Comparison of Instabilities and Dynamic States in Active Filament Models

Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature typically involve combinations of follower-forces, compressive tangential forces, along the filament, and an opposite force on the fluid that generates an effective surface flow. In this paper, we present a comparative dynamical systems study of active filament models examining the differences in dynamic states that occur when actuation is through follower forces alone, or the effect of surface flows is also included. We consider cases where actuation is applied only at the filament tip, or distributed uniformly along the filament length. By varying actuation strength, we show that the first bifurcations that provide the transition between the upright, whirling and beating states appear in all models. At higher values of actuation, when beating becomes unstable, however, qualitative differences between the models emerge. Those with distributed actuation produce a single, time-dependent state, which for the surface flow model is reminiscent of a rotating helix that periodically changes handedness and rotation direction. Tip actuation, however, yields complex transitions that ultimately produce a chaotic state. We link the differences in dynamics between tip and distributed actuation to differences in their respective internal stress distributions, differences which appear as early as the first bifurcation where they affect the shapes of the unstable modes.

physics.flu-dyn↗

arXiv2025

State-dependent convergence of Galerkin-based reduced-order models for Couette flow

In this study, we explore the effect of basis functions on the performance and convergence of the Galerkin projection-based reduced-order model (ROM) in the minimal flow unit of Couette flow. POD (proper orthogonal decomposition) modes obtained from direct numerical simulation and controllability and balanced truncation modes from the linearised Navier-Stokes equations (LNSE) with different base flows (laminar base flow and turbulent mean flow) and an eddy viscosity model are considered. In the neighbourhood of the laminar base state, the ROMs based on the modes from the LNSE with the laminar base flow and molecular viscosity are found to perform very well as they are able to capture the linear stability of the laminar base flow for each plane Fourier component only with a single degree of freedom. In particular, the ROM based on the balanced truncation modes models the linear dynamics involving transient growth around the laminar base flow most effectively, consistent with previous studies. In contrast, for turbulent state, the ROM based on POD modes is found to reproduce its statistics and coherent dynamics most effectively. The ROMs based on the modes from the LNSE with turbulent mean flow and an eddy viscosity model performs better compared to any other ROMs using the modes from the LNSE. These observations suggest that the performance and convergence of a ROM are highly state-dependent. In particular, this state dependence is strongly correlated with the information and dynamics that each of the basis functions contains. Discussions supporting these observations are also provided in relation to the flow physics involved and the form of coherent structures in Couette flow.

physics.flu-dyn↗

arXiv2024

Bifurcations and nonlinear dynamics of the follower force model for active filaments

Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental cellular processes. As they move, motor proteins exert compressive forces on the filaments to which they are attached, leading to buckling and a subsequent range of dynamics. The follower force model, in which a single compressive force is imposed at the filament tip, is the standard and most basic model for an elastic filament, such as a microtubule, driven by a motor protein. Depending on the force value, one can observe different states including whirling, beating and writhing, though the bifurcations giving rise to these states are not completely understood. In this paper, we utilise techniques from computational dynamical systems to determine and characterise these bifurcations. We track emerging time-periodic branches and identify new, quasiperiodic states. We investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model.

physics.bio-ph↗

arXiv2024

The origin of wall-shear stress fluctuations in wall-bounded turbulence

The origin of wall shear-stress fluctuations in wall turbulence was studied through energy dissipation at the wall. While confirming the universality in wall dissipation at small inner scales, the dissipation at larger scales is a consequence of near-wall scale interactions. In particular, the energy transport from the universal small to larger scale strengthens with Reynolds number due to the growing number of intermediate scales associated with the log layer. We anticipate that these insights broadly apply to all canonical wall-bounded turbulence for sufficiently high Reynolds numbers.

physics.flu-dyn↗

arXiv2024

Multi-scale invariant solutions in plane Couette flow: a reduced-order model approach

Plane Couette flow at Re=1200 (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this system, the computation of invariant solutions that are physically representative of the turbulent state has been understood to be challenging. To address this challenge, our approach is to employ an accurate reduced-order model with 600 degrees of freedom (Cavalieri & Nogueira, {Phys. Rev. Fluids}, vol. 7, 2022, L102601). Using the two-scale energy budget and the temporal cross-correlation of key observables, it is first demonstrated that the model contains most of the multi-scale physical processes identified recently (Doohan et al., J. Fluid Mech., vol. 913, 2021, A8): i.e. the large- and small-scale self-sustaining processes, the energy cascade for turbulent dissipation, and an energy-cascade mediated small-scale production mechanism. Invariant solutions of the reduced-order model are subsequently computed, including 96 equilibria and 43 periodic orbits. It is found that none of the computed equilibrium solutions are able to reproduce an accurate energy balance associated with the multi-scale dynamics of turbulent state. Incorporation of unsteadiness into invariant solutions is seen to be essential for a sensible description of the multi-scale turbulent dynamics and the related energetics, at least in this type of flow, as periodic orbits with a sufficiently long period are mainly able to describe the complex spatiotemporal dynamics associated with the known multi-scale phenomena.

physics.flu-dyn↗

arXiv2023

Near-wall turbulence intensity as $Re_τ\rightarrow \infty$

In this study, asymptotic scaling of near-wall streamwise turbulence intensity $\overline{u'u'}/u_τ^2$ ($u_τ$ is the friction velocity) is theoretically explored. The three scalings previously proposed are first reviewed with their derivation and physical justification: 1) $\overline{u'u'}/u_τ^2 \sim \ln Re_τ$ ($Re_τ$ is the friction velocity); 2) $\overline{u'u'}/u_τ^2 \sim 1/U_\infty^+$ ($U_\infty^+$ is the inner-scaled freestream velocity in boundary layer); 3) $\overline{u'u'}/u_τ^2 \sim Re_τ^{-1/4}$. A new analysis is subsequently developed based on velocity spectrum, and two possible scenarios are identified based on the asymptotic behaviour of the outer-scaling part of the near-wall velocity spectrum. In the former case, the outer-scaling part of the spectrum is assumed to reach a non-zero constant as $Re_τ\rightarrow \infty$, and it results in the scaling of $\overline{u'u'}/u_τ^2 \sim \ln Re_τ$, both physically and theoretically consistent with the classical attached eddy model. In the latter case, a sufficiently rapid decay of the outer-scaling part of the spectrum with $Re_τ$ is assumed due to the effect of viscosity, such that $\overline{u'u'}/u_τ^2 < \infty$ for all $Re_τ$. The following analysis yields $\overline{u'u'}/u_τ^2 \sim 1/\ln Re_τ$, asymptotically consistent with the scaling of $\overline{u'u'}/u_τ^2 \sim 1/U_\infty^+$. The scalings are further verified with the existing simulation and experimental data and those from a quasilinear approximation (Holford \emph{et al.}, 2023, \texttt{arXiv:2305.15043}), the spectra of which all appear to favour $\overline{u'u'}/u_τ^2 \sim 1/\ln Re_τ$, although new datasets for $Re_τ\gtrsim O(10^4)$ would be necessary to conclude this issue.

physics.flu-dyn↗

arXiv2023

A data-driven quasi-linear approximation for turbulent channel flow

A data-driven implementation of a quasi-linear approximation is presented, extending a minimal quasi-linear approximation (MQLA) (Hwang & Ekchardt, J. Fluid Mech., 2020, 894:A23) to incorporate non-zero streamwise Fourier modes. A data-based approach is proposed, matching the two-dimensional wavenumber spectra for a fixed spanwise wavenumber between a direct numerical simulation (DNS) (Lee & Moser, J. Fluid Mech., 2015, 774:395-415) and that generated by the eddy viscosity-enhanced linearised Navier-Stokes equations at $Reτ \simeq 5200$. Leveraging the self-similar nature of the energy-containing part in the DNS velocity spectra, a universal self-similar streamwise wavenumber weight is determined for the linearised fluctuation equations at $Re_τ \simeq 5200$. This data-driven quasi-linear approximation (DQLA) offers qualitatively similar findings to the MQLA, with quantitative improvements in the turbulence intensities and additional insights from the streamwise wavenumber spectra. By comparing the one-dimensional streamwise wavenumber spectra and two-dimensional spectra to DNS results, the limitations of the presented framework are discussed, mainly pertaining to the lack of the streak instability (or transient growth) mechanism and energy cascade from the linearised model. The DQLA is subsequently employed over a range of Reynolds numbers up to $Re_τ = 10^5$. Overall, the turbulence statistics and spectra produced by the DQLA scale consistently with the available DNS and experimental data, with the Townsend-Perry constants displaying a mild Reynolds dependence (Hwang, Hutchins & Marusic, J. Fluid Mech., 2022, 933:A8). The scaling behaviour of the turbulence intensity profiles deviates away from the classic $\ln(Re_τ)$ scaling, following the inverse centreline velocity scaling for the higher Reynolds numbers.

physics.flu-dyn↗

arXiv2022

A local approximation model for macroscale transport of biased active Brownian particles in a flowing suspension

A dilute suspension of motile microorganisms subjected to a strong ambient flow, such as algae in the ocean, can be modelled as a population of non-interacting, orientable active Brownian particles (ABPs). Using the Smoluchowski equation (i.e. Fokker-Planck equation in space and orientation), one can describe the non-trivial transport phenomena of ABPs such as taxis and shear-induced migration. This work transforms the Smoluchowski equation into a transport equation, in which the drifts and dispersions can be further approximated as a function of the local flow field. The new model can be applied to any global flow field due to its local nature, unlike previous methods such as those utilising the generalised Taylor dispersion theory. The transformation shows that the overall drift includes both the biased motility of individual particles in the presence of taxis and the shear-induced migration in the absence of taxis. In addition, it uncovers other new drifts and dispersions caused by the interactions between the orientational dynamics and the passive advection-diffusion of ABPs. Finally, the performance of this model is assessed using examples of gyrotactic suspensions, where the proposed model is demonstrated to be most accurate when the biased motility of particles (i.e. taxis) is weak.

physics.flu-dyn↗

arXiv2021

Generalised quasilinear approximations of turbulent channel flow: Part 2. Spanwise scale interactions

Continuing from Part 1 (Hernández \emph{et al.}, \emph{arXiv:2108.12395}, 2021), a generalized quasilinear (GQL) approximation is studied in turbulent channel flow using a flow decomposition defined with spanwise Fourier modes: the flow is decomposed into a set of low-wavenumber spanwise Fourier modes and the rest high-wavenumber modes. This decomposition leads to the nonlinear low-wavenumber group that supports the self-sustaining process within the given integral length scales, whereas the linearised high-wavenumber group is not able to do so, unlike the GQL models in Part 1 which place a minimal mathematical description for the self-sustaining process across all integral scales. Despite the important physical difference, it is shown that the GQL models in this study share some similarities with those in Part 1: i.e. the reduced multi-scale behaviour and anisotropic turbulent fluctuations. Furthermore, despite not being able to support the self-sustaining process in the high-wavenumber group, the GQL models in the present study are found to reproduce some key statistical features in the high-wavenumber group solely through the `scattering' mechanism proposed by previous studies. Finally, using the nature of the GQL approximation, a set of numerical experiments suppressing certain triadic nonlinear interactions are further carried out. This unveils some key roles played by the certain types of triadic interactions including energy cascade and inverse energy transfer in the near-wall region. In particular, the inhibition of inverse energy transfer in the spanwise direction leads to suppression of the near-wall positive turbulent transport at large scales.

physics.flu-dyn↗

arXiv2021

Generalised quasilinear approximations of turbulent channel flow: Part 1. Streamwise nonlinear energy transfer

A generalised quasilinear (GQL) approximation (Marston \emph{et al.}, \emph{Phys. Rev. Lett.}, vol. 116, 104502, 2016) is applied to turbulent channel flow at $Re_τ\simeq 1700$ ($Re_τ$ is the friction Reynolds number), with emphasis on the energy transfer in the streamwise wavenumber space. The flow is decomposed into low and high streamwise wavenumber groups, the former of which is solved by considering the full nonlinear equations whereas the latter is obtained from the linearised equations around the former. The performance of the GQL approximation is subsequently compared with that of a QL model (Thomas \emph{et al.}, \emph{Phys. Fluids.}, vol. 26, no. 10, 105112, 2014), in which the low-wavenumber group only contains zero streamwise wavenumber. It is found that the QL model exhibits a considerably reduced multi-scale behaviour at the given moderately high Reynolds number. This is improved significantly by the GQL approximation which incorporates only a few more streamwise Fourier modes into the low-wavenumber group, and it reasonably well recovers the distance-from-the-wall scaling in the turbulence statistics and spectra. Finally, it is proposed that the energy transfer from the low to the high-wavenumber group in the GQL approximation, referred to as the `scattering' mechanism, depends on the neutrally stable leading Lyapunov spectrum of the linearised equations for the high wavenumber group. In particular, it is shown that if the threshold wavenumber distinguishing the two groups is sufficiently high, the scattering mechanism can completely be absent due to the linear nature of the equations for the high-wavenumber group.

physics.flu-dyn↗

arXiv2020

A sequence of transcritical bifurcations in a suspension of gyrotactic microswimmers in vertical pipe

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 numbers of steady axisymmetric axially uniform solutions to such a system (Bees, M. A. & Croze, O. A., 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 Richardson number increases. Linear stability, weakly nonlinear and fully nonlinear analyses are performed, revealing that each of the solutions arises from the destabilisation of uniform suspension. The discrete number 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. Except the one arising at the lowest Richardson number, all of the solutions found are unstable, implying that they would play a role in the transient dynamics in the route from a uniform suspension to the fully-developed gyrotactic pattern.

physics.flu-dyn↗

arXiv2020

Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe

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.

physics.flu-dyn↗

arXiv2020

Finding extremal periodic orbits with polynomial optimisation, with application to a nine-mode model of shear flow

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] 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 Newton-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.

math.DS↗

arXiv2019

Instability of tilted shear flow in a strongly stratified and viscous medium

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, J. Fluid Mech., vol. 699, 2012, pp. 174-197). 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. To support this claim, the asymptotic regime where this equation would be strictly valid is subsequently discussed in relation to previous arguments on the proper vertical length scale. Furthermore, the absolute and convective instability analysis of parallel wake is performed, revealing qualitatively good agreement with the experimental result. The low-Froude-number mode is found to be stabilised on increasing Froude number, as is in the experiment. 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. It modifies the inflectional instability and is also associated with the paradoxically stabilising buoyancy on increasing Froude number. Lastly, we proposed some possible behaviours of the base flow when the tilting angle changes, and they may provide a better approximation to produce the behaviour consistent with the experiment.

physics.flu-dyn↗