Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Azimi, Sajjad; Schneider, Tobias

doi:10.1017/jfm.2019.1067

Cited by 5 publications

(3 citation statements)

References 29 publications

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“…Jiménez & Simens 2001;Viswanath 2007;Gibson et al 2009;Willis, Short & Cvitanović 2016;Doohan, Willis & Hwang 2019), using techniques such as computational-domain confinement in the near-wall region and over-damped large-eddy simulation in the logarithmic layer (Yang, Willis & Hwang 2019) and in the outer region (Rawat et al 2015;Hwang, Willis & Cossu 2016). In particular, a number of previously computed invariant solutions have been found to scale in inner units (Deguchi 2015;Eckhardt & Zammert 2018;Yang et al 2019;Azimi & Schneider 2020). In recent years, efforts have also been made to extend the dynamical systems approach to multi-scale turbulence, including a multi-scale equilibrium solution of Rayleigh-Bénard convection (Motoki, Kawahara & Shimizu 2021) and a periodic orbit that captures the energy cascade in three-dimensional body-forced turbulence (van Veen, Vela-Martín & Kawahara 2019).…”

Section: Introductionmentioning

confidence: 99%

“…In particular, a number of previously computed invariant solutions have been found to scale in inner units (Deguchi 2015; Eckhardt & Zammert 2018; Yang et al. 2019; Azimi & Schneider 2020). In recent years, efforts have also been made to extend the dynamical systems approach to multi-scale turbulence, including a multi-scale equilibrium solution of Rayleigh–Bénard convection (Motoki, Kawahara & Shimizu 2021) and a periodic orbit that captures the energy cascade in three-dimensional body-forced turbulence (van Veen, Vela-Martín & Kawahara 2019).…”

Section: Introductionmentioning

confidence: 99%

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The state space and travelling-wave solutions in two-scale wall-bounded turbulence

et al. 2022

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The computation of invariant solutions and the visualisation of the associated state space have played a key role in the understanding of transition and the self-sustaining process in wall-bounded shear flows. In this study, an extension of this approach is sought for a turbulent flow which explicitly exhibits multi-scale behaviour. The minimal unit of multi-scale near-wall turbulence, which resolves two adjacent spanwise integral length scales of motion, is considered using a shear stress-driven flow model (Doohan, Willis & Hwang J. Fluid Mech., vol. 913, 2021, A8). The edge state, 26 travelling waves and two periodic orbits are computed, which represent either the large- or small-scale self-sustaining processes. Given that the spanwise length scales are not widely separated here, it could be envisaged that turbulent trajectories visit these solutions in the state space. Considering the 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 detailed analysis reveals that this is due to the lack of scale interaction processes captured by the invariant solutions, including the mean–fluctuation interaction, the energy cascade in the streamwise wavenumber space and the cascade-driven energy production discovered recently. There is a single solution that resembles turbulence much more than the others, which captures two-scale energetics and a scale interaction process involving energy feeding from small to large spanwise scales through the subharmonic sinuous streak instability mode. Based on these observations, it is conjectured that the state space view of turbulent trajectories wandering between solutions would need suitable refinement to model multi-scale turbulence, when each solution does not represent multi-scale processes of turbulence. In particular, invariant solutions that are inherently multi-scale would be required.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

et al. 2022

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“…One of the most notable successes in continuing recurrent solutions to higher is the computation of attached eddies (Eckhardt & Zammert 2018; Doohan, Willis & Hwang 2019; Yang, Willis & Hwang 2019; Azimi & Schneider 2020) and their bulk analogues (Deguchi 2015; Eckhardt & Zammert 2018) in a variety of canonical three-dimensional (3-D) shear flows. In wall units, these solutions become independent of , just like the wall-bounded fully developed turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

Exact coherent structures in fully developed two-dimensional turbulence

Zhigunov,

Grigoriev

2023

J. Fluid Mech.

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This paper reports several new classes of unstable recurrent solutions of the two-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions are in many ways analogous to recurrent solutions of the Navier–Stokes equation which are often referred to as exact coherent structures. In particular, we find that recurrent solutions of the Euler equation are dynamically relevant: they faithfully reproduce large-scale flows in simulations of turbulence at very high Reynolds numbers. On the other hand, these solutions have a number of properties which distinguish them from their Navier–Stokes counterparts. First of all, recurrent solutions of the Euler equation come in infinite-dimensional continuous families. Second, solutions of different types are connected, e.g. an equilibrium can be smoothly continued to a travelling wave or a time-periodic state. Third, and most important, they are only weakly unstable and, as a result, fully developed turbulence mimics some of these solutions remarkably frequently and over unexpectedly long temporal intervals.

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Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders

Page,

Holey,

Brenner

et al. 2024

J. Fluid Mech.

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Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$ . ‘Latent Fourier analysis’ (Page et al., Phys. Rev. Fluids6, 2021, p. 034402) reveals a detached class of bursting dynamics at $Re=40$ which merge with the low-dissipation dynamics as $Re$ is increased to $100$ and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At $Re=400$ , the UPOs discovered at lower $Re$ move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier projections identify an associated ‘large-scale’ UPO which we believe to be a finite- $Re$ continuation of a solution to the Euler equations.

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Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

Cited by 5 publications

References 29 publications

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

Exact coherent structures in fully developed two-dimensional turbulence

Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders

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