On two-dimensionalization of three-dimensional turbulence in shell models

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case

Comparison of Pareto and tapered Pareto distributions for environmental phenomena

The Pareto distribution is often used to describe environmental phenomena such as the sizes of earthquakes or wildfires, or the interevent times or distances between such environmental disturbances. Because it is heavy-tailed, the Pareto distribution, or power-law distribution as it is occasionally called, suggests that a higher frequency of extremely large values occur compared to other, more familiar distributions such as the normal, exponential, or uniform. However, an alternative distribution called the tapered Pareto has been shown in some cases to fit as well or better to data than the Pareto distribution, and the tapered Pareto distribution is not heavy-tailed, suggesting a far lower frequency of extreme events. Even with rather large datasets, it is often quite difficult to distinguish which of these distributions is preferable, as they only differ markedly in the extreme upper tail where few, if any, observations are recorded. This article reviews the evidence and arguments related to these two competing distributions, especially in the context of earthquakes and wildfires