Kinetic energy budget of the largest scales in turbulent pipe flow

So-called very-large-scale motions (VLSM) have been observed in turbulent pipe flows recently. It was discovered that they carry a substantial fraction of turbulent kinetic energy. However, the question how they gain and loose their energy from other scales has not been rigorously studied yet. Hence, the present study is intended to investigate how energy is transferred toward and away from the very-large scales. The inter- and intrascale energy flux in turbulent pipe flow is analyzed by means of the (u′zuz′)-budget equation of the two-dimensionally filtered streamwise fluctuating velocity field uz′ obtained from a direct numerical simulation at Reτ=1500. We show that the largest scales of motion gain their energy in the logarithmic layer through the production term of the low-pass filtered budget equation. In contrast to the small-scale energy transfer near the wall, no mean backscattering of energy is observed toward VLSM. Instantaneous flow field realizations as well as conditional averages, on the contrary, show backscattering into negative ejecting VLSM up to y+=200, which is overcompensated by even stronger forward scattering from positive sweeping VLSM. This behavior opposes the small-scale energy transfer near the wall, where backscattering is associated with high-speed sweeping motions.

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Kinetic energy budget of the largest scales in turbulent pipe flow