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.

40 pages, 5 figures, published version

References in corpus (20)

• Glauber Modeling in High Energy Nuclear Collisions
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Triangular flow in hydrodynamics and transport theory
• Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200A$ GeV
• Translation of collision geometry fluctuations into momentum anisotropies in relativistic heavy-ion collisions
• Event-by-event hydrodynamics and elliptic flow from fluctuating initial state
• Resolving the HBT Puzzle in Relativistic Heavy Ion Collision
• Fluctuating initial conditions in heavy-ion collisions from the Glauber approach
• Initial condition for hydrodynamics, partonic free streaming, and the uniform description of soft observables at RHIC
• Turbulence in nonabelian gauge theory
• Free-streaming approximation in early dynamics of relativistic heavy-ion collisions
• On Kolmogorov Wave Turbulence in QCD
• Eccentricity fluctuations in an integrated hybrid approach: Influence on elliptic flow
• Eccentricity fluctuations and its possible effect on elliptic flow measurements
• Energy dependent growth of the nucleon and hydrodynamic initial conditions
• Fluid turbulence and eddy viscosity in relativistic heavy-ion collisions
• Evolution of Anisotropy of Parton System from Relativistic Heavy-Ion Collisions
• The Sound of the Little Bangs
• Relativistic Hydrodynamics at RHIC and LHC

Cited by in corpus (52)

• Chiral Magnetic and Vortical Effects in High-Energy Nuclear Collisions --- A Status Report
• Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions
• Heavy Ion Collisions: Achievements and Challenges
• Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics
• Polarization and Vorticity in the Quark Gluon Plasma
• Lambda Polarization in Peripheral Heavy Ion Collisions
• Flow Vorticity in Peripheral High Energy Heavy Ion Collisions
• Hydrodynamics of spin currents
• Elliptic and triangular flow anisotropy in deuteron-gold collisions at RHIC and proton-lead collisions at the LHC
• Chiral vortical wave and induced flavor charge transport in a rotating quark-gluon plasma
• Transverse-momentum fluctuations in relativistic heavy-ion collisions from event-by-event viscous hydrodynamics
• Chiral Magnetic Effects in Nuclear Collisions
• Longitudinal Decorrelation of Anisotropic Flows in Heavy-ion Collisions at the CERN Large Hadron Collider
• Mode-by-mode fluid dynamics for relativistic heavy ion collisions
• $\Lambda$ polarization in peripheral collisions at moderate relativistic energies
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Longitudinal fluctuations and decorrelations of anisotropic flows at the LHC and RHIC energies
• Vorticity in heavy-ion collisions at the JINR Nuclotron-based Ion Collider fAcility
• Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
• Holographic Heavy-Ion Collisions: Analytic Solutions with Longitudinal Flow, Elliptic Flow and Vorticity
• Probe of electromagnetic moments of the tau lepton in gamma-gamma collisions at the CLIC
• Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions
• New method for measuring longitudinal fuctuations and directed flow in ultrarelativistic heavy ion reactions
• Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
• Viscous potential flow analysis of peripheral heavy ion collisions
• Counting hot/cold spots in quark-gluon plasma
• A hydrodynamic approach to boost invariant free streaming
• How (non-) linear is the hydrodynamics of heavy ion collisions?
• Hydrodynamical noise and Gubser flow
• Hydro overview
• A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions
• Fully developed relativistic turbulence
• Morphology of High-Multiplicity Events in Heavy Ion Collisions
• Collective Flow Global Collective Flow in Heavy Ion Reactions from the Beginnings to the Future
• The Influence of Initial State Fluctuations on Heavy Quark Energy Loss in Relativistic Heavy-ion Collisions
• Fluctuations in Relativistic Causal Hydrodynamics
• A Hydrodynamic Approach to the Study of Anisotropic Instabilities in Dissipative Relativistic Plasmas
• A new relativistic hydrodynamics code for high-energy heavy-ion collisions
• Study of Rotating High Energy Systems with the Differential HBT Method
• Introductory Overview of Quark Matter 2012
• Meson turbulence at quark deconfinement from AdS/CFT
• Viscosity, wave damping and shock wave formation in cold hadronic matter
• Nonlinear waves in second order conformal hydrodynamics
• Field Theory Approaches to Relativistic Hydrodynamics
• Particle production and hadronization temperature in the massive Schwinger model
• Nonlinear evolution of density and flow perturbations on a Bjorken background
• Stimulation of static deconfined medium by multiple hard partons
• An Initial State with Shear in Peripheral Heavy Ion Collisions
• Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics
• Mode-by-mode hydrodynamics: ideas and concepts
• Dissipative type theories for Bjorken and Gubser flows
• Nonlinear Dynamics of Tensor Modes in Conformal Real Relativistic Fluids