Holographic Turbulence in a Large Number of Dimensions

TL;DR

This paper explores how relativistic hydrodynamics simplifies in many spatial dimensions, enabling analysis of turbulent flows and their geometric relations using holographic theories with truncated derivative expansions.

Contribution

It demonstrates that holographic theories in large dimensions satisfy specific restrictions, leading to simplified hydrodynamic equations and enabling detailed turbulence analysis.

Findings

Hydrodynamic equations simplify significantly at large dimensions.

Turbulent flows in 2D and 3D are analyzed using these simplified models.

The relation between turbulence and geometric data is elucidated.

Abstract

We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large number of dimensions satisfy the aforementioned restrictions and their dynamics are captured by hydrodynamics with a naturally truncated derivative expansion. Using analytic and numerical techniques we analyze two and three-dimensional turbulent flow of such fluids in various regimes and its relation to geometric data.