A covariant approach to relativistic large-eddy simulations: The fibration picture

TL;DR

This paper introduces a covariant framework for large-eddy simulations in relativistic turbulence, addressing the challenges of space-time splitting and proposing a new closure scheme with demonstrated stability.

Contribution

It develops a novel covariant filtering approach using spacetime fibration and Fermi coordinates, and proposes a stable closure model for relativistic turbulent flows.

Findings

Derived resolved equations with effective dissipative terms.

Introduced a new closure scheme inspired by relativistic fluid modeling.

Proved the linear stability of the proposed closure model.

Abstract

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how "effective" dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.