Analogies between Scaling in Turbulence, Field Theory and Critical Phenomena

TL;DR

This paper explores two analogies linking turbulence to field theory, one related to critical phenomena with an infrared fixed point, and another akin to quantum chromodynamics with an ultraviolet fixed point.

Contribution

It introduces two novel analogies connecting turbulence behavior with different types of fixed points in field theory, expanding understanding of turbulence through theoretical physics.

Findings

Turbulence can be modeled using field theories with different fixed points.

Critical phenomena analogy involves an infrared attractive fixed point.

Quantum chromodynamics analogy involves an ultraviolet attractive fixed point.

Abstract

We discuss two distinct analogies between turbulence and field theory. In one analogue, the field theory has an infrared attractive renormalization-group fixed point and corresponds to critical phenomena. In the other analogue, the field theory has an ultraviolet attractive fixed point, as in quantum chromodynamics.