Two-dimensional turbulence with local interactions: statistics of the condensate

TL;DR

This paper investigates the statistical properties of a condensate in two-dimensional turbulence with local interactions, using a quasi-geostrophic model, revealing universal symmetry-breaking mechanisms and the influence of locality on small-scale dynamics.

Contribution

It provides the first analytical and numerical study of the condensate in a local quasi-geostrophic model, highlighting symmetry breaking and locality effects.

Findings

Analytical expressions for mean flow and correlation functions.

Validation of results through numerical simulations.

Identification of universal symmetry-breaking mechanisms.

Abstract

Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic equation, observed here for the first time. We obtain analytical results for the mean flow and the two-point, second-order correlation functions, and validate them numerically. The condensate state requires parity+time-reversal symmetry breaking. We demonstrate distinct universal mechanisms for the even and odd correlators under this symmetry. We find that the model locality is imprinted in the small scale dynamics, which the condensate spatially confines.