Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box
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| Format: | Preprint |
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2026
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| _version_ | 1866908921016352768 |
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| author | Layton, William Raghunathan, Nanda Nechingal |
| author_facet | Layton, William Raghunathan, Nanda Nechingal |
| contents | Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box Layton, William Raghunathan, Nanda Nechingal Numerical Analysis 76FO2, 35Q30 Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not. |
| title | Energy dissipation rates of ensemble eddy viscosity models of turbulence: the periodic box |
| topic | Numerical Analysis 76FO2, 35Q30 |
| url | https://arxiv.org/abs/2603.28340 |