Bose-like condensation of Lagrangian particles and higher-order statistics in passive scalar turbulent advection

TL;DR

This paper uncovers a novel link between zero modes and instantons in passive scalar turbulence, suggesting Bose-like condensation of particles influences scalar gradient production and scaling behaviors.

Contribution

It introduces a new theoretical framework connecting zero modes and instantons via Bose-like condensation in scalar turbulence.

Findings

Scaling exponents grow asymptotically as log N in 2D.

Establishes a connection enabling computation of structure function exponents.

Proposes a many-body theory approach to turbulence statistics.

Abstract

We establish an hitherto hidden connection between zero modes and instantons in the context of the Kraichanan model for passive scalar turbulent advection, that relies on the hypothesis that the production of strong gradients of the scalar is associated with Bose-like condensation of Lagrangian particles. It opens the way to the computation of scaling exponents of the N-th order structure functions of the scalar by techniques borrowed from many-body theory. To lowest order of approximation, scaling exponents are found to increase asymptotically as log N in two dimensions.