Shear instability and entropy generation in heavy-ion collisions

Abstract

An instability, known as Kelvin-Helmholtz instability (shear instability), well known in fluid theory and plasma physics is studied in heavy-ion collisions to study the process of entropy generation. The source of this instability is the transverse gradient of longitudinal velocity which is quite likely to arise when the collisions are somewhat peripheral (noncentral). Relativistic equations describing this instability are derived here. A set of coupled partial differential equations in three dependent and three independent variables are obtained. It is difficult to solve them analytically. In order to get a qualitative idea, we have solved the nonrelativistic version of the above equations with some approximations. We find that in the boost-invariant unperturbed state the growth rate of this instability competes with damping due to the boost-invariant expansion of the unperturbed system. We also analyze low-energy nuclear collisions, where there is no boost invariance, using a simple equilibrium flow with shear.