Scaling laws of diffusion and time intermittency generated by coherent structures in atmospheric turbulence

Abstract

Abstract. We investigate the time intermittency of turbulent transport associated with the birth-death of self-organized coherent structures in the atmospheric boundary layer. We apply a threshold analysis on the increments of turbulent fluctuations to extract sequences of rapid acceleration events, which is a marker of the transition between self-organized structures.The inter-event time distributions show a power-law decay ψ(τ ) ∼ 1/τ µ , with a strong dependence of the power-law index µ on the threshold.A recently developed method based on the application of event-driven walking rules to generate different diffusion processes is applied to the experimental event sequences. At variance with the power-law index µ estimated from the inter-event time distributions, the diffusion scaling H , defined by X 2 ∼ t 2H , is independent from the threshold. From the analysis of the diffusion scaling it can also be inferred the presence of different kind of events, i.e. genuinely transition events and spurious events, which all contribute to the diffusion process but over different time scales. The great advantage of event-driven diffusion lies in the ability of separating different regimes of the scaling H . In fact, the greatest H , corresponding to the most anomalous diffusion process, emerges in the long time range, whereas the smallest H can be seen in the short time range if the time resolution of the data is sufficiently accurate.The estimated diffusion scaling is also robust under the change of the definition of turbulent fluctuations and, under the assumption of statistically independent events, it corresponds to a self-similar point process with a well-defined power-law index µ D ∼ 2.1, where D denotes that µ D is derived from the diffusion scaling. We argue that this renewal point process can be associated to birth and death of coherent structures and to turbulent transport near the ground, where the contribution of turbulent coherent structures becomes dominant.

Scaling laws of turbulence intermittency in the atmospheric boundary layer: the role of stability

“…However, this rule is less accurate as it is affected by the presence of noise, which can be related to the experimental data and instrumentation, but also to the thresholding technique [5]. On the contrary, the AJ rule gives a well-defined anomalous scaling H ∼ 0.9.…”

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

“…On the contrary, it has been proved that the EDDiS approach is able to separate different regimes of both diffusion scalings δ and H, but only for the Asymmetric Jump (AJ) and Symmetric Jump (SJ) walking rules (see Appendix Appendix A) [15,17,9]. This is a crucial property when noise affects the recorded time series.…”

“…This is related to the time evolution of the rate of event production r(t), which is essentially the mean number of events per time unit [8,10,17]. In general, the rate is not constant between two events, and it is renewed at its initial value in correspondence of each event occurrence.…”

“…Actually, two contribution are sufficient to explain a mistaken multi-scaling behavior: a genuine complex sequence superposed to secondary events related to short-time effects. In particular, the presence of a normal scaling in the short-time range of the AJ diffusion process mark the presence of noisy secondary events [16,17] . It is well known that the normal scaling corresponds to a complexity index µ > 3 (see Appendix A), which is always a power-law decay, but this range of µ is considered outside the long-range regime, as it admits a finite correlation time for both stationary and aged correlation functions [61].…”

“…There are several examples of complex systems displaying a fractal intermittent behavior: ecological systems [22], neural dynamics [23], blinking quantum dots [24,25,26], social dynamics [27], brain information processing [28,29,30,16,31,32,18,19,33,1,3,4], atmospheric turbulence [34,17,35,9], earthquakes [36], single particle tracking in cell biology [37], molecular biology [20].…”