On scaling and statistical geometry in passive scalar turbulence

TL;DR

This paper investigates the multiscaling behavior of passive scalar turbulence at large scales, proposing a new formalism to predict scaling exponents and exploring their geometric origins.

Contribution

It introduces a general formalism for predicting large-scale scaling exponents in passive scalar turbulence, highlighting mechanisms beyond statistical conservation laws.

Findings

Multiscaling can occur at large scales without conservation laws.

A formalism for explicit predictions of scaling exponents is developed.

Geometric origins of scaling behavior are discussed at different scales.

Abstract

We show that the statistics of a turbulent passive scalar at scales larger than the pumping may exhibit multiscaling due to a weaker mechanism than the presence of statistical conservation laws. We develop a general formalism to give explicit predictions for the large scale scaling exponents in the case of the Kraichnan model and discuss their geometric origin at small and large scale.