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.
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Studying fluid flows with auxiliary functions and LMIsat the IFAC World Congress, held in Yokohama, Japan on 8-14th July 2023.
Bounding time averages: a road to solving the problem of turbulenceat Institut de Mathématiques de Bordeaux, Bordeaux, May 4, 2023.
Bounding time averagesand
How quasi-steady is the modulation of near-wall turbulence by large-scale structures?(with Yunjiu Yang).
Auxiliary functionals: a path to solving the problem of turbulenceat The Seminar in the Analysis and Methods of PDE (SIAM PDE) on March 4, 2021. Links to the abstract and the video.
Accelerating time averagingat 73rd Annual Meeting of the APS Division of Fluid Dynamics, November 22, 2020: abstract and video.
Accelerating time averaging using auxiliary functionsat the Aerodynamics and Flight Mechanics group seminar, University of Southampton, on 6 February 2019
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).
Questions concerning quasi-steady mechanism of the Reynolds number, pressure gradient, and geometry effect on drag reductionat the Workshop on Active Drag Reduction, Aachen, Germany, 15-16 March 2018.
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