Turbulent fluctuations around Bjorken flow

TL;DR

This paper investigates the evolution of local fluctuations around Bjorken flow in heavy ion collisions, revealing that under certain conditions, these fluctuations can exhibit turbulent behavior governed by non-linear equations similar to Navier-Stokes.

Contribution

It introduces a framework to analyze local fluctuations in relativistic heavy ion collisions using non-linear equations akin to classical fluid turbulence models.

Findings

Perturbations at different rapidities decouple quickly.

Effective two-dimensional Navier-Stokes equations describe fluctuations.

Conditions for turbulence onset are discussed.

Abstract

We study the evolution of local event-by-event deviations from smooth average fluid dynamic fields, as they can arise in heavy ion collisions from the propagation of fluctuating initial conditions. Local fluctuations around Bjorken flow are found to be governed by non-linear equations whose solutions can be characterized qualitatively in terms of Reynolds numbers. Perturbations at different rapidities decouple quickly, and satisfy (after suitable coordinate transformations) an effectively two-dimensional Navier-Stokes equation of non-relativistic form. We discuss the conditions under which non-linearities in these equations cannot be neglected and turbulent behavior is expected to set in.