Building up the elliptic flow: analytical insights

TL;DR

This paper provides an analytical model for the early development of elliptic flow in relativistic viscous hydrodynamics, linking theoretical predictions with empirical viscosity dependence formulas.

Contribution

It introduces an elliptic deformation of Gubser flow and analytically derives the momentum anisotropy evolution, enhancing understanding of elliptic flow formation.

Findings

Analytical expression for elliptic flow development over time

Connection established between flow anisotropy and viscosity

Validation of empirical viscosity dependence formula

Abstract

In this paper, we present a fully analytical description of the early-stage formation of elliptic flow in relativistic viscous hydrodynamics. We first construct an elliptic deformation of Gubser flow which is a boost invariant solution of the Navier-Stokes equation with a nontrivial transverse profile. We then analytically calculate the momentum anisotropy of the flow as a function of time and discuss the connection with the empirical formula by Bhalerao {\it et al.} regarding the viscosity dependence of elliptic flow.