Measuring the effect of spatial dimension on hydrodynamic turbulence using direct numerical simulation
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arXiv
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| Format: | Preprint |
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2025
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| author | Ho, Richard D. J. G. Clark, Daniel Armua, Andres Yang, Xichao Brener, Daniel J. Berera, Arjun |
| author_facet | Ho, Richard D. J. G. Clark, Daniel Armua, Andres Yang, Xichao Brener, Daniel J. Berera, Arjun |
| contents | We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, $λ$, decrease with dimension, and $λ< 0$ for all simulations in six-dimensions up to $Re = 40$. These six-dimensional simulations display non-Gaussian statistics and other behavior similar to well developed turbulence despite their lack of chaos. Further, we find that small scale perturbations do not extend to the largest scales and that this terminal scale between correlation and decorrelation shrinks with dimension. We theorize that this change is related to the increased rate of vortex stretching. We find the interplay between turbulent and chaotic properties changes with increasing dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring the effect of spatial dimension on hydrodynamic turbulence using direct numerical simulation Ho, Richard D. J. G. Clark, Daniel Armua, Andres Yang, Xichao Brener, Daniel J. Berera, Arjun Fluid Dynamics High Energy Physics - Theory Chaotic Dynamics We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, $λ$, decrease with dimension, and $λ< 0$ for all simulations in six-dimensions up to $Re = 40$. These six-dimensional simulations display non-Gaussian statistics and other behavior similar to well developed turbulence despite their lack of chaos. Further, we find that small scale perturbations do not extend to the largest scales and that this terminal scale between correlation and decorrelation shrinks with dimension. We theorize that this change is related to the increased rate of vortex stretching. We find the interplay between turbulent and chaotic properties changes with increasing dimension. |
| title | Measuring the effect of spatial dimension on hydrodynamic turbulence using direct numerical simulation |
| topic | Fluid Dynamics High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2512.00449 |