title: Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence.
abstract: We study the statistical properties of return intervals r between successive energy dissipation rates above a certain threshold Q in three-dimensional fully developed turbulence. We find that the distribution function P(Q)(r) scales with the mean return interval R(Q) as P(Q)(r)=R(Q)(-1)f(r/R(Q)) for R(Q) is an element of [50,500], where the scaling function f(x) has two power-law regimes. The scaling behavior is statistically validated by the Cramér-von Mises criterion. The return intervals are short-term and long-term correlated and possess multifractal nature. The Hurst index of the return intervals decays exponentially against R(Q), predicting that rare extreme events with R(Q)-->infinity are also long-term correlated with the Hurst index H(infinity)=0.639. These phenomenological findings have potential applications in risk assessment of extreme events at very large R(Q).
authors.affiliation: School of Business, East China University of Science and Technology, Shanghai, China.
authors.forename: Chuang
authors.initials: C
authors.lastname: Liu
authors.forename: Zhi-Qiang
authors.initials: ZQ
authors.lastname: Jiang
authors.forename: Fei
authors.initials: F
authors.lastname: Ren
authors.forename: Wei-Xing
authors.initials: WX
authors.lastname: Zhou
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D008962:Models, Theoretical; D017711:Nonlinear Dynamics