1. Questions about Viscosity
NCRH Frankfurt, April 2007
L.P. Csernai, University of Bergen

2. In this model the authors concluded that
In superstring theory, „based on analogy between black hole physics and equilibrium thermodynamics, ... there exist solutions called black branes,
which are black holes with translationally invariant horizons. ... these solutions can be extended to hydrodynamics, ... and black branes possess
hydrodynamic characteristics of ... fluids: viscosity, diffusion constants, etc.”
In this model the authors concluded that
η / s = 1 / 4π
And then they „speculate” that in general η / s > 1 / 4π or η / s > 1.
They argue that this is a lower limit especially for such strongly interacting systems where up to now there is no reliable estimate for viscosity, like the QGP. According to the authors the viscosity of QGP must be lower than that of classical fluids.

3. <=1
[Kovtun, et al., PRL 2005]

4. Why Perfect QGP Fluid Core + Hadron Gas Corona May Reproduce Data?
 : shear viscosity, s : entropy density
TH and Gyulassy (’05)‏
Kovtun,Son,Starinets(’05)‏
Absolute value of viscosity
Its ratio to entropy density !
Rapid increase of entropy density near Tc could validate hydro at RHIC/LHC
Deconfinement Signal ?!

6. Origin of the news:

9. Why viscosity ?
Viscosity leads to dissipation, it slows down, weakens, averages out flow phenomena, - helps to approach global equilibrium in a system. (No problem, the flow is present and strong in HI physics  viscosity is not too strong to eliminate the flow !!! )
Viscosity prevents random, irregular, turbulent motion and instabilities, makes the flow LAMINAR, i.e. well defined and coherent, while too low viscosity leads to instabilities and turbulence. (Yes, flow seems to be regular and systematic in HI reactions  viscosity is large enough !!! )
Strictly speaking: Perfect fluid is absolutely unstable ! [LL]

10. RT – instabilities in Tokamak
The figure above shows three- dimensional isosurfaces of the pressure as the instability develops along ridges dominantly aligned along the ambient magnetic field.

11. Stability, Reynolds number
- kinematic viscosity
- density
In an ideal fluid any small perturbation increases and leads to turbulent flow. For stability sufficiently large viscosity and/or heat conductivity are needed! Re 
(Calculations are also stabilized by numerical viscosity!)
- viscosity
- length
- velocity
Measured [Lijuan Ruan / STAR] scaling [A, E] of dimensionless v2 fluctuations , can be compared to constant Re contours. If the two are similar viscous effects are dominant in these fluctuations, and viscosity (or Re) can be extracted.
(If not, Initial State (IS) fluctuations and FD fluctuations should be separated: complex theroretical task.)

12. Re – studies in HICs
Theoretical [D. Molnar, U. Heinz, et al., ] η = 50 – 500 MeV/fm2c Re  10 – 100
Exp.: 50 – 800 MeV/nucleon energies 80’s [Bonasera, Schurmann, Csernai] scaling analysis of flow parameters. Re  7 – 8 ! (more dilute, more viscous matter)
In both cases η/s  (0.5 – 5) , This is a value large enough to keep the flow laminar in Heavy Ion Collisions !!!
NS – Star-quakes / Spin-up of rotation is observed  η finite

13. Stability, Reynolds number
Interesting and important: in RFD detonation fronts are stabilized by radiation and heat conductivity. E.g. : - Rocket propulsion - Implosion, fission- and fusion reactions - Heavy Ion reactions

14. Preventing turbulence
The instability of deflagration- (flame-) front is not desirable at supersonic fronts.
With increasing temperature the radiation becomes dominant and stabilizes the flame front.

15. (Kovtun, et al., PRL 2005)
With Kapusta and McLerran we have studied these results and assumptions and found that :
η vs. T has a typical decreasing and then increasing behaviour, due to classical reasons (Enskog’21)
η/s has a minimum exactly at the critical point in systems, which have a liquid-gas type of transition
η vs. T shows a characteristic behaviour in all systems near the critical point (not only in the case of He).

16. Viscosity vs. T has a minimum at the 1st order phase transition
Viscosity vs. T has a minimum at the 1st order phase transition. This might signal the phase transition if viscosity is measured. At lower energies this was done.

17. Viscosity – Momentum transfer
Via VOIDS
Via PARTICLES
Liquid
Gas

18. [Prakash, Venugopalan, .]
Helium (NIST)
QGP (Arnold, Moore, Yaffe)
This phenomenon can help us to detect experimentally the critical point:
η can be determined from (i) fluctuation of flow parameters and from (ii) scaling properties of flow parameters.
Water (NIST)

19. Viscosity at this meeting
Formulation of dissipative processes in RFD, the physical processes governing these processes and their stability L. Turko, A.K. Chaduri, T. Koide, P. Van, A. Muronga, ..
Fluid dynamical models and the role of viscosity, numerical and parametric, and lack of viscosity in really perfect fluid, ANALYTIC solutions I. Mishustin, T. Csorgo, M. Nagy, M. Chojnacki, U. Ornik, D. Strottman, I. Arsene, M. Gyulassy, B. Betz, E. Molnar, G. Denicol, P. Mota, …
Other subjects, important but not strongly related to viscosity, like freeze-out, initial states, role of EoS, …
All these are needed for experimental study of Vicsosity.

20. 1st measurement of viscosity
Roy Lacey et al. :
C. Nonaka – adiabatic expansion goes close to the CEP.
Low viscosity point can be reached in expansion
Using – Cs. & Cs.’s perfect FD model results, Tc, m.f.p, Cs, - η was estimated as η/s=0.09

21. The prediction is strongly based on model FD estimates.
This is unavoidable both in AE scaling in flow analyses and in v2 value estimates.
Thus, reliable 3d CRFD models are vital with known physical (parametric) and numerical (computational) viscosity.

22. Numerical viscosity
Shock test: asymptotic states are exactly known from an EoS.
Stationary shock profile should develop in a stable CRFD model Ls
M. Chojnacki – Mathematica [WR]

23. Estimate viscosity in a planar shock front: The front is standing in the calculational frame, and a stationary profile develops after some time, then
Measure this!
D. Strottman, P. Romatschke, U. Ornik, ..

24. Other questions related to numerical viscosity
Dissipation and entropy production may be eliminated by brute force in CFD. However,
Coarse graining, (finite cell size) eliminates SHORT wave-length flow patterns by averaging these out. The energy of these should be dissipated and transformed to heat.
If entropy increase is prevented (or forced to a given value), due to energy conservation, this extra energy is returned to the fluid in the form of LONG wavelength fluid motion! (see talk of Gabriel Denicol or instabilities in T. Mota’s talk.)
This can only be realistic if the physical process is such, that short wavelength fluctuations die out due to some other reason this other process is well represented by the method..

25. Other tests
We need analytic test cases for the given EoS!!! (Also viscous test cases!)
Both for viscosity and for forced entropy conservation do the test!
Shock waves, discontinuities
Harmonic waves, wavelength vs. cell size
Bjorken model, …
Unfortunately all these examples require non- confined boundary and initial conditions, thus different from a collision !