## Publications

3 results found

Doohan P, Bengana Y, Yang Q,
et al., 2022, The state space and travelling-wave solutions in two-scale wall-bounded turbulence, *Journal of Fluid Mechanics*, Vol: 947, Pages: 1-36, ISSN: 0022-1120

The computation of invariant solutions and the visualisation of the associated state spacehave played a key role in the understanding of transition and the self-sustaining processin wall-bounded shear flows. In this study, an extension of this approach is sought for aturbulent flow which explicitly exhibits multi-scale behaviour. The minimal unit of multiscale near-wall turbulence, which resolves two adjacent spanwise integral length scalesof motion, is considered using a shear stress-driven flow model (Doohan et al., J. FluidMech., vol. 913, 2021, A8). The edge state, twenty-six travelling waves and two periodicorbits are computed, which represent either the large- or small-scale self-sustainingprocesses. Given that the spanwise length scales are not widely separated here, it could beenvisaged that turbulent trajectories visit these solutions in the state space. Consideringthe intra- and inter-scale dynamics of the flow, numerous phase portraits are examined,but the turbulent state is not found to approach any of these solutions. A detailedanalysis reveals that this is due to the lack of scale interaction processes captured bythe invariant solutions, including the mean-fluctuation interaction, the energy cascade inthe streamwise wavenumber space and the cascade-driven energy production discoveredrecently. There is a single solution that resembles turbulence much more than the others,which captures two-scale energetics and a scale interaction process involving energyfeeding from small to large spanwise scales through the subharmonic sinuous streakinstability mode. Based on these observations, it is conjectured that the state space viewof turbulent trajectories wandering between solutions would need suitable refinement tomodel multi-scale turbulence, when each solution does not represent multi-scale processesof turbulence. In particular, invariant solutions that are inherently multi-scale would berequired.

Bengana Y, Yang Q, Tu G,
et al., 2022, Exact coherent states in plane Couette flow under spanwise wall oscillation, *Journal of Fluid Mechanics*, Vol: 947, ISSN: 0022-1120

A set of several exact coherent states in plane Couette flow is computed under spanwise wall oscillation control, with a range of wall oscillation amplitudes and periods (Aw,T). It is found that the wall oscillation generally stabilises the upper branch of the equilibrium solutions and achieves the corresponding drag reduction, while it influences modestly the lower branch. The stabilisation effect is found to increase with the oscillation amplitude with an optimal time period around T+≈100. The exact coherent states reproduce some key dynamical behaviours of streaks observed in previous studies, while exhibiting the rich coherent structure dynamics that cannot be extracted from a phase average of turbulent states. Visualisation of state portraits shows that the size of the state space supporting turbulent solution is reduced by the spanwise wall oscillation, and the upper-branch equilibrium solutions become less repelling, with many of their unstable manifolds being stabilised. This change of the state space dynamics leads to a significant reduction in lifetime of turbulence. Finally, the main stabilisation mechanism of the exact coherent states is found to be the suppression of the lift-up effect of streaks, explaining why previous linear analyses have been so successful for turbulence stabilisation modelling and the resulting drag reduction.

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

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