Quantum field approach to relativistic turbulence

Abstract

The goal of this work is apply field theory methods to discuss turbulence in relativistic real fluids. We shalltake as representtive model an Israel-Stewart framework, where the conservation laws for the energy-momentum tensor are supplemented by a Cattaneo-Maxwell equation for its viscous part, which relaxes to its Landau-Lifshitz value. We assume the parameters of the model scale with the peed of light $c$ in such a way that as $c\to\infty$ the fluid becomes an incompressible fluid obeying the Navier-Stokes equations. We find that for finite $c$ each mode of the fluid behaves as an overdamped oscillator with two decaying rates, one that converges to the K41 value and another that diverges when $c\to\infty$. There are therefore two basic flow patterns, one where the fast decaying modes are absent, and which repreduces Kolmogorov turbulence, and another made only of fast decaying modes. We point out the scaling relations that allow the latter flow pattern to sustain an entropy cascade.