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Turbulence in Two-Dimensional Relativistic Hydrodynamic Systems with a Lattice Boltzmann Model

Using a Lattice Boltzmann hydrodynamic computational modeler to simulate relativistic fluid systems we explore turbulence in two-dimensional relativistic flows. We first a give a pedagogical description of the phenomenon of turbulence and its characteristics in a two-dimensional system. The classical Lattice Boltzmann Method and its extension to relativistic fluid systems is then described. The model is tested against a system incorporating a random stirring force in k-space and then applied to a realistic sample of graphene. Part I: We investigate the relativistic adaptation of the Lattice Boltzmann Method reproducing a turbulent, two-dimensional, massless hydrodynamic system with a zero-averaged stirring force randomly generated in momentum space. The numeric formulation is evaluated and the flow characteristics produced are compared to properties of classical turbulence. The model can reasonably be expected to offer quantitative simulations of charged fluid flows in two-dimensional relativistic fluid systems. Part II: At low Reynolds numbers, the wind flow in the wake of a single wind turbine is generally not turbulent. However, turbines in wind farms affect each other's wakes so that a turbulent flow can arise. An analogue of this effect for the massless charge carrier flow around obstacles in graphene is outlined. We use a relativistic hydrodynamic simulation to analyze the flow in a sample containing impurities. Depending on the density of impurities in the sample, we indeed find evidence for a potentially turbulent flow and discuss experimental consequences.