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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", arXiv:1203.3714, 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:

• Attended the Oberwolfach Workshop 2431 - Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms, and Applications at the Mathematisches Forschungsinstitut Oberwolfach, Germany 28 July - 2 August 2024.
• Gave a talk on Studying fluid flows with auxiliary functions and LMIs at the IFAC World Congress, held in Yokohama, Japan on 8-14th July 2023.
• 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 QSQH theory of scale interaction in near-wall turbulence: the essence, evolution, and the current state 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: "Accelerating time averaging by adding a Lie derivative of an auxiliary function". 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 International Symposium on Turbulence in Memory of Chou Pei-Yuan's 120th anniversary of birth (IST2022).
• On July 22, 2022, gave (online) a talk "Bounds for time averages: towards solving the problem of turbulence" at the Harbin Institute of Technology Fluid Mechanics Seminar.
• In January-April 2022 was a long-term participant of the Isaac Newton Institute Programme "Mathematical aspects of turbulence: where do we stand?". Gave two talks: Bounding time averages and How quasi-steady is the modulation of near-wall turbulence by large-scale structures? (with Yunjiu Yang).
• Gave a talk Auxiliary functionals: a path to solving the problem of turbulence at The Seminar in the Analysis and Methods of PDE (SIAM PDE) on March 4, 2021. Links to the abstract and the video.
• Gave a talk on Extension of QSQH theory to all velocity components, abstract and video, 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: abstract 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 SIAM Conference on Applications of Dynamical Systems (DS19), , Snowbird, Utah, U.S, May 19 - 23, 2019.
• Gave a keynote lecture at the workshop Scientific Computing Across Scales: Extreme Events and Criticality in Fluid Mechanics, The Fields Institute, Toronto, April 15-18, 2019.
• Gave a talk at European Drag Reduction and Flow Control Meeting 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 Peking University State Key Laboratory for Turbulence and Complex System in September 13-30, 2018.
• Attended EeroMech Colloquim 598 Coherent structures in wall-bounded turbulence: new directions in a classic problem, 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 Workshop on Active Drag Reduction, Aachen, Germany, 15-16 March 2018.
• Gave a lecture course The problem of turbulence: bounding solutions to equations of fluid mechanics & other dynamical systems, with Giovanni Fantuzzi providing exercise sessions, at The 6th Bremen Winter School Dynamical systems and turbulence, March 12-16, 2018.

 

Sergei Chernyshenko