Fluctuations around Bjorken flow and the onset of turbulent phenomena

Abstract

We study how fluctuations in fluid dynamic fields can be dissipated or amplified within the characteristic spatio-temporal structure of a heavy ion collision. The initial conditions for a fluid dynamic evolution of heavy ion collisions may contain significant fluctuations in all fluid dynamical fields, including the velocity field and its vorticity components. We formulate and analyze the theory of local fluctuations around average fluid fields described by Bjorken's model. For conditions of laminar flow, when a linearized treatment of the dynamic evolution applies, we discuss explicitly how fluctuations of large wave number get dissipated while modes of sufficiently long wave-length pass almost unattenuated or can even be amplified. In the opposite case of large Reynold's numbers (which is inverse to viscosity), we establish that (after suitable coordinate transformations) the dynamics is governed by an evolution equation of non-relativistic Navier-Stokes type that becomes essentially two-dimensional at late times. One can then use the theory of Kolmogorov and Kraichnan for an explicit characterization of turbulent phenomena in terms of the wave-mode dependence of correlations of fluid dynamic fields. We note in particular that fluid dynamic correlations introduce characteristic power-law dependences in two-particle correlation functions.

Longitudinal decorrelation of anisotropic flows in heavy-ion collisions at the CERN Large Hadron Collider

“…Much attention has now been paid to fluctuations of the anisotropic flows of final hadrons due to the fluctuations in the initial states of heavy-ion collisions, such as the fluctuations of nucleon positions and color charges inside colliding nuclei and multiplicities of initial parton production [10]. One of the most interesting consequences of initial-state fluctuations is the presence of elliptic flow in the most central nucleus-nucleus collisions, and finite odd harmonic flows in the final-state azimuthal distributions [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The elliptic, triangular and other higher-order harmonic flows have been measured in Au+Au collisions at RHIC and Pb+Pb collisions at the LHC [27][28][29].…”

Nonlinear waves in second order conformal hydrodynamics

“…These fluctuations may be produced by inhomogeneous initial conditions which, as pointed out in [10], are the result of quantum fluctuations in the densities of the two colliding nuclei and also in the energy deposition mechanism. These fluctuations and their phenomenological implications have been studied extensively [11][12][13][14][15] because they may be responsible for the angular correlations of particle emission observed in heavy-ion experiments. There are also hydrodynamic fluctuations [10], which are the result of finite particle number effects in a given fluid cell.…”

Nonlinear evolution of density and flow perturbations on a Bjorken background

“…[40]. Here, we recall the results relevant for the present work, and the approximations on which they are based, but we refer to Ref.…”

“…For vorticity fluctuations, two of us have argued some time ago that the time and length scales of a heavy-ion collision might be sufficient in order to see the onset of nonlinear or turbulent behavior [40]. On the other hand, within the current phenomenological picture density or compressional modes (sound waves) are much more important.…”