On turbulence: deciphering a renormalization flow out of an elliptic curve, II

TL;DR

This paper explores a novel approach to understanding turbulence by modeling scale-dependent states with ninth-degree polynomials derived from elliptic curves, analyzing their associated L functions and bifurcation behaviors.

Contribution

It introduces a new modeling framework linking turbulence to elliptic curve L functions and investigates their bifurcation and statistical correlation properties.

Findings

Significant negative correlation between escape rates and L function values at z=1+0i.

Bifurcation diagrams of L functions reveal complex dynamical behaviors.

Statistical tests support the consistency of the elliptic curve-based turbulence model.

Abstract

Reaching for a better understanding of turbulence, a line of investigation was followed, its main presupposition being that each scale dependent state, in a general renormalization flow, is a state that can be modeled using a class of ninth degree polynomials. These polynomials are deduced from the Weierstrass models of a certain kind of elliptic curves. As the consequences of this presupposition unfolded, leading to the numerical study of a few samples of elliptic curves, the L functions associated with these later were considered. Their bifurcation diagrams were observed and their escape rates were determined. The consistency of such an approach was put to a statistical test, measuring the rank correlation between escape rates and values taken by these L functions on the point z=1+0i. In the most significant case, the rank correlation coefficient found, r_s, was about r_s=-0.78, with an associated p-value of an order of magnitude close to the (-69) power of 10.