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Effect of large-scale motions on near-wall turbulence

Direct numerical simulations of turbulent flows can be done only at moderate Reynolds numbers Re. Experiment on near-wall turbulence is also limited to moderate Re, because at high Re the viscous sublayer becomes too thin to be resolved by existing instruments. As a result, industry is concerned with results obtained within academia not being transferrable to high Re typical of flight regime. Until recently, the hope of overcoming this difficulty was based on the idea of the universality (Re-independence) of near-wall turbulence. This hope suffered a serious blow with the discovery of a second, "outer", peak of the energy spectra at large Re, suggesting that at high Re more turbulence kinetic energy is contained in large-scale structures than in the near-wall region. Recent results on the modulation of the near-wall turbulence by large-scale structures, however, recreated the hope, since if the effect of large scales is limited to modulation then moderate-Re results can be used at high Re with appropriate processing.

Fig.1. The scheme for the extrapolating medium-Re DNS and experimental results to the high-Re flight conditions.

The plan is illustrated in the figure with a reference to a formula described in the paper by I. Marusic, R. Mathis, and N. Hutchins, "Predictive model for wall-bounded turbulent flow", Science 329 (5988), 193-196, 2010. First one performs experiments or direct numerical simulations at moderate Re to determine the universal, Re-independent, functions, and then uses these universal functions in combination with in-flight large-scale-only measurements to predict the statistical properties of the flow at flight conditions. The theoretical foundations for this approach are outlined in the paper by S. Chernyshenko, I. Marusic, and R. Mathis, "Quasi-steady description of modulation effects in wall turbulence", , 2012. The latest developments are summarised in the talk, the videorecord of which is linked below.

More information:

• A recent talk at the Workshop IV: Turbulence in Engineering Applications, Mathematics of Turbulence Program, IPAM, UCLA, 9 November 2014, Relationship between large-scale structures and near-wall turbulence: theory and implications (about 81 Mb zip archive).

Timeline:

• Gave a talk (slides) Progress on bounds for dissipation in flows of general geometry reinforces the need for methods applicable to stochastic PDE at the , May 11, 2026, Oxford.
• Gave a talk on A small step on the road to solving the problem of turbulence: a rigorous bound for dissipation in flows past walls of general shape (slides) at Imperial College Department of Mathematics Fluid Dynamics seminar, March 6, 2026.
• Gave a talk at seminar, Lille, France, 12 December 2025.
• Gave a plenary talk at , Aligarh (U.P), India, 20-23 December 2024.
• Attended the at the , Germany 28 July - 2 August 2024.
• Gave a talk on at the .
• Gave a talk on Bounding time averages: a road to solving the problem of turbulence at Institut de Mathématiques de Bordeaux, Bordeaux, May 4, 2023.
• Gave a talk on at Institut Pprime, Bordeaux on May 3, 2023.
• Talk at Department of Engineering, University of Cambridge, 4 November 2022, as part of the CUED Fluids seminar series, video: Joint work with Owen Tutty and Hanying Yang.
• On August 15, 2022, gave (online) an invited talk "On the path to solving the problem of turbulence" at the
• On July 22, 2022, gave (online) a talk "Bounds for time averages: towards solving the problem of turbulence" at the
• In January-April 2022 was a long-term participant of the . Gave two talks: and .
• Gave a talk Auxiliary functionals: a path to solving the problem of turbulence at on March 4, 2021. Links to and .
• Gave a talk on at IPAM, Wednesday, January 13, 2021, as part of the workshop on Transport and Mixing in Complex and Turbulent Flows. Great talks, all recorded, highly recommended.
• Gave a talk Accelerating time averaging at 73rd Annual Meeting of the APS Division of Fluid Dynamics, November 22, 2020: and video.
• 2020: the virus ... living online ... most of the year working on additional administration and teaching related to the pandemic ...
• Gave a talk at , Snowbird, Utah, U.S, May 19 - 23, 2019.
• Gave a keynote lecture at the workshop , The Fields Institute, Toronto, April 15-18, 2019.
• Gave a talk at 26-29 March 2019, Haus der Kirche, Bad Herrenalb, Germany.
• Gave a seminar talk on Accelerating time averaging using auxiliary functions at the Aerodynamics and Flight Mechanics group seminar, University of Southampton, on 6 February 2019
• Visited the in September 13-30, 2018.
• Attended , London, August 29-31, 2018, with a talk Large-scale motions for the QSQH theory (with Chi Zhang).
• Gave a talk on Questions concerning quasi-steady mechanism of the Reynolds number, pressure gradient, and geometry effect on drag reduction at the Aachen, Germany, 15-16 March 2018.
• Gave a lecture course , with Giovanni Fantuzzi providing exercise sessions, at

 

Sergei Chernyshenko