Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon
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| Format: | Preprint |
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2025
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| _version_ | 1866909844228800512 |
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| author | Du, Jia Tian, Yu Zhang, Hongbao |
| author_facet | Du, Jia Tian, Yu Zhang, Hongbao |
| contents | We 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 numerically construct dynamical and spatially inhomogeneous turbulent black holes in the asymptotically $\mathrm{AdS}_4$ spacetime by solving the full nonlinear equations of motion in the Bondi-Sachs formalism. The inverse energy cascade and the corresponding energy spectrum of both decaying and driven turbulence are analyzed. The scalar driving leads to a compressible energy dominated flow, and the corresponding scaling power laws agree well with previous simulations of two-dimensional turbulence in compressible fluids. Furthermore, we take a direct estimate of the fractal structure of the turbulent black hole, obtaining a fractal dimension $D\approx2.65$, which matches the result from simulating the boundary conformal fluid. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon Du, Jia Tian, Yu Zhang, Hongbao High Energy Physics - Theory General Relativity and Quantum Cosmology We 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 numerically construct dynamical and spatially inhomogeneous turbulent black holes in the asymptotically $\mathrm{AdS}_4$ spacetime by solving the full nonlinear equations of motion in the Bondi-Sachs formalism. The inverse energy cascade and the corresponding energy spectrum of both decaying and driven turbulence are analyzed. The scalar driving leads to a compressible energy dominated flow, and the corresponding scaling power laws agree well with previous simulations of two-dimensional turbulence in compressible fluids. Furthermore, we take a direct estimate of the fractal structure of the turbulent black hole, obtaining a fractal dimension $D\approx2.65$, which matches the result from simulating the boundary conformal fluid. |
| title | Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.12198 |