Relativistic Hydrodynamics I Wojciech Florkowski Institute of - - PowerPoint PPT Presentation

▶
relativistic hydrodynamics i
SMART_READER_LITE
LIVE PREVIEW

Relativistic Hydrodynamics I Wojciech Florkowski Institute of - - PowerPoint PPT Presentation

Aug 16, 2022 600 likes •899 views

Relativistic Hydrodynamics I Wojciech Florkowski Institute of Theoretical Physics, Jagiellonian University, Krakw, Poland March 2, 2020 Traditional and modern concepts of hydrodynamics Global vs. local equilibrium, perfect fluid

slide-1
SLIDE 1

Relativistic Hydrodynamics I

Wojciech Florkowski Institute of Theoretical Physics, Jagiellonian University, Kraków, Poland March 2, 2020

slide-2
SLIDE 2
  • Traditional and modern concepts of

hydrodynamics

  • Global vs. local equilibrium, perfect fluid
  • Relativistic Navier-Stokes hydrodynamics

Eckart 1940 Landau and Lifshitz 1959

  • Israel and Stewart, 1970-1979,

BRSSS 2008,

  • ther kinetic-theory formulations ~2010
  • Insights from kinetic theory
  • Anisotropic hydrodynamics 2010
  • Gradient expansion
  • Hydrodynamics with spin
  • first-order causal and stable hydrodynamics,

2020

  • Summary & conclusions
slide-3
SLIDE 3
slide-4
SLIDE 4
slide-5
SLIDE 5

modern POV:

slide-6
SLIDE 6

equation of state, kinetic coefficients (viscosities), …

slide-7
SLIDE 7
  • F. Becattini, P. Braun-Munzinger, W. Broniowski, J. Cleymans, WF, M. Gażdzicki, J. Rafelski, H. Satz, J. Stachel, ….
slide-8
SLIDE 8
slide-9
SLIDE 9
slide-10
SLIDE 10
slide-11
SLIDE 11
slide-12
SLIDE 12
slide-13
SLIDE 13

Thermodynamic identities: Switching to densities (convenient in hydro): Perfect-fluid hydrodynamics: First line represents entropy conservation While the second one is a relativistic Euler fluid equation:

slide-14
SLIDE 14

Entropy current (a direct consequence of previous definitions) Non-equilibrium entropy current (Israel-Stewart formalism, still close to local equilibrium)

Four-temperature vector Chemical potential scaled by temperature

slide-15
SLIDE 15

Tensor decompositions (with respect to the flow vector

Particle/baryon current Energy-momentum tensor:

slide-16
SLIDE 16

Eckart vs. Landau-Lifschitz (hydro) frames, V=0 or W=0

Non-equilibrium entropy current (Israel-Stewart formalism, still close to local equilibrium)

Heat-flux four-vector

slide-17
SLIDE 17

Entropy productio ion

slide-18
SLIDE 18

Using hydrodynamic equations in the leading order (perfect-fluid equations) one gets: Using hydrodynamic equations in the leading order (perfect-fluid equations) one gets:

slide-19
SLIDE 19

Bas asic ic kin inetic ic coeffic icie ients

slide-20
SLIDE 20

Entropy is positive if: with positive kinetic/transport coefficients heat conductivity, bulk viscosity, shear viscosity:

slide-21
SLIDE 21
slide-22
SLIDE 22
slide-23
SLIDE 23
slide-24
SLIDE 24
slide-25
SLIDE 25
slide-26
SLIDE 26
slide-27
SLIDE 27
slide-28
SLIDE 28