Statistical theory of isotropic turbulence Part IV: multiscales and cascade

TL;DR

This paper analyzes the multiscale cascade process in isotropic turbulence using a new Sedov-type solution, revealing chaotic behavior and similarities with logistic map dynamics through explicit scale analysis.

Contribution

It introduces a novel scale analysis method to visualize and understand the cascade process, highlighting its chaotic and multiscale nature in isotropic turbulence.

Findings

Visual evidence of Richardson cascade

Identification of period-doubling bifurcations

Chaotic behavior in turbulence cascade

Abstract

This paper is the forth part of our series of work, is devoted to the analysis on the multiscales and cascade aspects of the statistical theory of isotropic turbulence based on the new Sedov-type solution. In this paper, we use the explicit map method to analyse the nonlinear dynamical behaviour for cascade in isotorpic turbulence. This deductive scale analysis is shown to provide the first visual evidence of the celebrated Richardson cascade, and reveals in partcular its multiscale character. The results also indicate that the energy cascading process has remarkable similarities with the determinisitic construction rules of the logistic map. Cascade of period-doubling bifurcations have been seen in this isotropic turbuent systems that exhibit chaotic behaviour. The 'cascade' appears as an infinite sequence of period-doubling bifurcations.