Entropy flow of a perfect fluid in (1+1) hydrodynamics

Abstract

Using the formalism of the Khalatnikov potential, we derive exact general formulae for the entropy flow dS/dy, where y is the rapidity, as a function of temperature for the (1+1) relativistic hydrodynamics of a perfect fluid. We study in particular flows dominated by a sufficiently long hydrodynamic evolution, and provide an explicit analytical solution for dS/dy. We discuss the theoretical implications of our general formulae and some phenomenological applications for heavy-ion collisions.Comment: 17 pages, 2 figures, to appear in Phys.Rev.

Systematic study of exact solutions in second-order conformal hydrodynamics

“…Many other solutions of ideal hydrodynamics have been found in the literature, mostly in the context of studies of QGP/heavy-ion physics [3][4][5][6][7][8][9][10][11][12][13][14]. These analytical solutions provide us with good physical intuition into the problem and they can also serve as a test of numerical hydrodynamic codes.…”

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

“…After these multiplications, the product (Aχ) has the same dimension as x and t, namely, the dimension of length. Because of the invariance of t and x with respect to different choices of A, the Khalatnikov solution can be written in many equivalent, and equally valid, forms, with A=1 in [2-5, 7-10, 16], or A=1/T 0 in [17][18][19][25][26][27]. There is freedom in the choice of A to partition the length dimension of (Aχ) between A and χ, or equivalently, to define χ in terms of t and x by writing the Legendre transform equation (4.10) of Belenkij and Landau [2,4] in a more general form with an explicit T 0 as…”

“…The generalization of the analytical solutions of Landau hydrodynamics to a general equation of state with a different speed of sound c s can be found in Ref. [25] and is summarized in Appendix A. It is necessary to take note of the typographical errors in the original articles of Belenkij and Landau [2][3][4] and the change of notations.…”

Non-boost-invariant solution of relativistic hydrodynamics in1+3dimensions

“…We shall work in the coordinates (8) and solve the hydrodynamic equations in the form (2) and (3). Solutions {û µ ,ε} are then transformed back to Minkowski space via the formulas…”

“…To accommodate this, there have been a number of attempts to interpolate the two solutions [4][5][6][7][8][9][10][11]. However, all of these works essentially deal with 1+1-dimensional hydrodynamics implicitly assuming, rather unrealistically, that the colliding nuclei have infinite transverse extent.…”