On the fine-scale intermittency of turbulence

This paper presents a simple theory for evaluating the several measures used to characterize the intermittency of fine-scale turbulence, and corroborates the theoretical results from comparison with experimental data, some of which are new. The basic analytical tool is the envelope of the narrow-bandpass-filtered turbulent signal, defined via its Hilbert transform and the analytic signal. The contribution of this paper is twofold. First, it correctly identifies the roles played by the filter characteristics (such as the bandwidth) in determining the intermittency factor, the width of the active regions (pulses) in narrow-bandpass-filtered turbulent signals, and the pulse frequency; it also reveals that all dynamical characteristics of the signal enter indirectly through the peak pulse frequency and the threshold setting. Secondly, the theory suggests that, in the far-dissipation range, the most important feature of signals exhibiting internal intermittency is the stronger-than-algebraic roll-off of the spectral density in that region; it is argued that this feature of turbulence essentially determines the peak pulse frequency in that region. The theory is incomplete in that it does not show how the threshold setting depends on the signal dynamics, but here the discussion is supplemented by experimental data.