Statistical analysis of local turbulent energy fluctuations

Abstract

Time–frequency energy fluctuations of turbulent experimental velocity signals for Re_λ≃10 and 800, are analysed using orthogonal wavelet transform. Some statistical properties of the energy bursts are analysed and discussed. The probability distribution functions (PDFs) of the energy amplitude fluctuations are investigated at different scales. Such PDFs show that the so-called non-intermittent and intermittent regions are characterized by quite different behaviour. Analysis of the wavelet coefficient scaling relations, averaged under suitable conditioning, reveals that the most energetic events localized in time and scale are responsible for the structure function (or wavelet coefficients) scaling anomalies related to intermittency. It is shown that the statistical properties which are correlated with the mechanism of the energy cascade from large to small scales are characterized by a universal behaviour. On the other hand, when the chosen statistical indicators are related to the characteristic size of turbulent structures, no universality is achieved, and a strong dependence upon the turbulent generator and Re_λ is observed. This is demonstrated by analysis of the statistics of time delays between successive events which show non-universal PDFs. The mean delay between successive intermittent events is also Re_λ dependent and increases for increasing Re_λ.