1 / 24

Viscous hydrodynamics

Viscous hydrodynamics. with shear and bulk viscosity. Huichao Song. The Ohio State University. Supported by DOE. in collaboration with Ulrich Heinz. DPF 2009. July 27-July 31, Detroit, MI. 07/30/2009. What is viscosity. Shear viscosity –measures the resistance to flow.

pprewitt
Download Presentation

Viscous hydrodynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Viscous hydrodynamics with shear and bulk viscosity Huichao Song The Ohio State University Supported by DOE in collaboration with Ulrich Heinz DPF 2009 July 27-July 31, Detroit, MI 07/30/2009

  2. What is viscosity Shear viscosity –measures the resistance to flow the ability of momentum transfer Bulk viscosity –measure the resistance to expansion -volume viscosity Determines the dynamics of compressible fluid

  3. The QGP viscosity shear viscosity: Kubo formulas: bulk viscosity: Shear viscosity: uncertainty principle requires a lower limit for -weakly coupled QCD: Arnold, Moore & Yaffe, 00,03 -lattice SU(3) gluon dynamics : Meyer, PRD 07 -strongly coupled AdS/CFT prediction : D.T. Son et al. ‘01,’05 Bulk viscosity: zero for classical massless particles, reaches a peak near -weakly coupled QCD prediction: Arnold, Dogan & Moore, PRD06 -lattice SU(3) gluon dynamics : Meyer, PRL08 -LET+ assum. of spectral fun. + Lattice data: Kharzeev, et al. 07-08 -strongly coupled AdS/CFT prediction: Buchel, 07 Gubser, et al . 0806 .. To extract the QGP viscosity from experimental data, we need viscous hydrodynamics

  4. Viscous hydro with shear & bulk viscosity Conservation laws: Evolution equations for shear pressure tensor and bulk presurre: (2nd order shear-bulk -mixing term (Muronga, Rischke) not included.)

  5. Numerical Results Shear viscosity: Bulk viscosity: HRG QGP Min. AdS/CFT prediction Relaxation times: (see later)

  6. Shear viscosity vs. bulk viscosity (I) Same initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only Local temperature -Shear viscosity:decelerate cooling process in early stage accelerate cooling process in middle and late stages -Bulk viscosity: deceleratecooling process

  7. Shear viscosity vs. bulk viscosity (II) Same Initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only radial flow spectra -shear viscosity: increases radial flow, results in flatter spectra -bulk viscosity: decreases radial flow, results in steeper spectra

  8. Shear viscosity vs. bulk viscosity (III) Same Initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only Elliptical flow v2 -v2 is sensitive to both shear and bulk viscosity

  9. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected

  10. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected (a) Change the flow profile during hydro evolution bulk viscosity effects: (b) Additional spectra correction along freeze-out surface Song & Heinz: v2 will decrease, flow corrections only (a),, at freeze-out Monnai & Hirano: v2 will increase,spectra corrections only(b), ideal hydro for evolution

  11. Bulk Viscosity -relaxation time effects

  12. Bulk viscous v2 suppression: -- Smaller vs.largerrelaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

  13. is insensitive to different initializations of Effects from initialization of (I) Smaller relaxation time -When is small , -after (several relaxation times), viscous pressure loses memory of initial cond.

  14. is sensitive to different initializations of Effects from initialization of (II) largerrelaxation time -When is larger , -after (several relaxation times), viscous pressure loses memory of initial cond.

  15. Effects from initialization of (III) Smaller vs.largerrelaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

  16. Multiplicity scaling of v2/ε --Effects from system size and collision energy

  17. Multiplicity scaling of v2/εEOS I - at fixed , the curves are slightly above the ones Song & Heinz PRC 08 ideal hydro v2 scaling line full I-S eqn Ideal hydrodynamics: multiplicity scaling of v2/ε is weakly broken: - freeze-out condition introduces time scale, breaking scale invariance of id. hydro eqns. - Initial profiles for Cu+Cu and Au+Au systems are not identical after a rescaling Viscous hydrodynamics: additional scale breakingby shear viscosity, resulting in fine structure of v2/ε: - for similar initial energy density, Cu+Cu curves are slightly below the Au+Au curves Viscous effects are larger for smaller systems and lower collision energies

  18. Multiplicity scaling of v2/ε EOS L - to reproduce slope of v2/ε vs. (1/S)dN/dy, a better description of the highly viscous hadronic stage is needed: T-dependent , viscous hydro + hadron cascade Song & Heinz PRC 08 hydro region full I-S eqn dilute gases - experimental data show qualitatively similar fine ordering as viscous hydro prediction - the experimental v2/ε vs. (1/S)dN/dy scaling (slope and fine structure) is another good candidate to constrain) • this requires, however, experimental and theoretical improvements:reduced error bars, • accounting for T-dependence of near Tc, modeling hadronic phase with realistic cascade

  19. A Short Summary - is sensitive to - multiplicity scaling of is a good candidate to extract the QGP viscosity: - larger viscous effects in smaller systems and at lower collision energies -When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected -More theoretical inputs are needed for bulk viscosity: - relaxation time - initialization for bulk pressure - bulk viscosity of hadronic phase, etc

  20. Thank You

  21. EOS EOS

  22. Viscous hydro in 2+1-dimension 3+1 2+1 coordinates Bjorken approximation: --the transport equations for energy momentum tensor are explicit written as: -shear tensor decelerate longitudinal expansion, but accelerate transverse expansion -bulk pressure decelerates both longitudinal & transverse expansion (bulk pressure effectively softens the EoS near the QCD phase transition)

  23. --shear viscosity only Viscous hydro: a short summary for shear viscosity -2+1-d viscous hydro code individually developed by different groups: Romatsche & Romatschke (INT), Song & Heinz (OSU), Dusling & Teaney (Stony) Huovinen & Molnar (Purdue), Chaudhuri (Kolkata, India) -v2 at RHIC is sensitive to even the minimum shear viscosity entropy ratio -v2 suppression from different groups ranges from 20% to 70% -the above discrepancy was largely resolved by investigating effects from system size, EoS and different forms of I-S eqns. used Song & Heinz, PRC 78 (2008) 20% 70% -Code checking within the TECHQM collaboration: TECHQM webpage -The first attempt to extract QGP shear viscosity from RHIC data: Luzum & Romatschke, PRC 78 (2008)

  24. - is insensitive to different initializations of Effects from initialization of Song & Heinz, PLB08 & PRC 77(2008) vs. -after ~1fm/c (several relaxation times), viscous pressure loses memory of initial cond. -Effects on entropy production: ~20%

More Related