Intermittent fluctuations due to uncorrelated Lorentzian pulses

TL;DR

This paper models intermittent fluctuations as a superposition of uncorrelated Lorentzian pulses, revealing skewness-flatness relationships and probability densities with exponential tails, relevant to turbulence and plasma physics.

Contribution

It introduces a stochastic model for fluctuations composed of uncorrelated Lorentzian pulses, deriving moments and probability densities that match observed turbulent behaviors.

Findings

Skewness and flatness moments follow a parabolic relationship.

Probability density functions exhibit exponential tails.

Model captures intermittent fluctuations in turbulent fluids and plasmas.

Abstract

Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap, resulting in large skewness and flatness moments. The characteristic function and the lowest order moments are derived, revealing a parabolic relationship between the skewness and flatness moments. Numerical integration reveals the probability density functions in the case of exponential and Laplace distributed pulse amplitudes. This stochastic model describes the intermittent fluctuations and probability densities with exponential tails commonly observed in turbulent fluids and magnetized plasmas.