Anomalous scaling exponents and coherent structures in high Re fluid turbulence

Abstract

The scaling exponents of the velocity structure functions are predicted by a simple model based on the probability density function (PDF) of the local turbulent kinetic energy fluctuations with no hypotheses on the shape of the most intermittent coherent structures. The energy fluctuations are presumed to be induced by statistically independent coherent structures and, therefore, are characterized by exponential-like PDFs. Accounting also for the scaling of the energy with the scale, a recursive formula is obtained which permits the calculation of the scaling exponents of the velocity structure functions. The predicted exponents are checked to be in good agreement with previous theoretical and experimental results. The main hypotheses behind the present approach are also validated by analyzing experimental velocity time series acquired in a jet flow at moderately high Reλ. It is also shown that present approach allows the calculation of the scaling exponents also in cases of nonhomogeneous turbulence.