Work

Holographic turbulence and numerical estimate of the fractal dimension of the turbulent horizon

Year: 2026

Type: article

Abstract: A bstract We numerically study two-dimensional turbulence driven by a scalar operator within the framework of the AdS/CFT correspondence, where the external driving source is used to sustain a quasi-steady turbulent state. We propose a simple and efficient evolution scheme within the Bondi-Sachs formalism. Applying this scheme to numerically solve the full nonlinear equations of motion, we obtain a turbulent black hole in asymptotically AdS 4 spacetime. The inverse energy cascade and the corresponding energy spectrum of both decaying and driven dual turbulence are analyzed. The scalar driving leads to a compressible-energy-dominated flow, and the corresponding power law scaling, E ( k ) ∝ k −1.79 , agrees well with previous simulations of two-dimensional turbulence in weakly coupled compressible fluids in fluid dynamics. This differs from the Kolmogorov –5/3 scaling law. Furthermore, we perform a direct numerical estimate of the fractal structure of the turbulent black hole, obtaining a fractal dimension D ≈ 2.65, which suggests an interesting universality in the fractal dimension.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep09(2026)002

Authors: Jia Du, Yu Tian, Hongbao Zhang

Institutions: University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing Normal University

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Awards: G2747297955, G4482933530, G4571021586, G5811165953, G6898621578