Relationship between large-scale structures and near-wall turbulence: a theory and implications

Sergei Chernyshenko
Imperial College

The growth of the energy of large-scale motions in the boundary layer as the Reynolds number increases poses a challenge for extrapolating results of direct numerical simulations and of wind-tunnel experiments to the high-Reynolds-number conditions characteristic of typical flight regimes. A theory will be outlined making this extrapolation noticeably easier. The theory is based on the conjecture that in the near-wall region the effect of large-scale motions is restricted to replacing the wall units based on the mean skin friction with the wall units based on the large-scale-filtered skin friction. This simple conjecture, together with the assumption that the amplitude of the large-scale is relatively small, leads to a number of predictions. For example, it allows to give, in terms of the mean velocity profile and the mean rms profile, explicit expressions for the empirical modulation and superposition coefficients, obtained by Mathis, Hutchins & Marusic (JFM 2011) from experiments and numerical calculations. Implications for the physics of turbulent flows and for the effect of the Reynolds number on the turbulent skin friction reduction by various techniques will be discussed.

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