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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2402.19158 |
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| _version_ | 1866929259464884224 |
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| author | Carbone, Maurizio Peterhans, Vincent J. Ecker, Alexander S. Wilczek, Michael |
| author_facet | Carbone, Maurizio Peterhans, Vincent J. Ecker, Alexander S. Wilczek, Michael |
| contents | Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for non-local pressure and viscous contributions. The fidelity of the resulting models depends on the accuracy of the underlying modeling assumptions. Here, we discuss an alternative data-driven approach leveraging machine learning to derive a velocity gradient model which captures its statistics by construction. We use a normalizing flow to learn the velocity gradient probability density function (PDF) from direct numerical simulation (DNS) of incompressible turbulence. Then, by using the equation for the single-time PDF of the velocity gradient, we construct a deterministic, yet chaotic, dynamical system featuring the learned steady-state PDF by design. Finally, utilizing gauge terms for the velocity gradient single-time statistics, we optimize the time correlations as obtained from our model against the DNS data. As a result, the model time realizations statistically closely resemble the time series from DNS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tailor-designed models for the turbulent velocity gradient through normalizing flow Carbone, Maurizio Peterhans, Vincent J. Ecker, Alexander S. Wilczek, Michael Fluid Dynamics Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for non-local pressure and viscous contributions. The fidelity of the resulting models depends on the accuracy of the underlying modeling assumptions. Here, we discuss an alternative data-driven approach leveraging machine learning to derive a velocity gradient model which captures its statistics by construction. We use a normalizing flow to learn the velocity gradient probability density function (PDF) from direct numerical simulation (DNS) of incompressible turbulence. Then, by using the equation for the single-time PDF of the velocity gradient, we construct a deterministic, yet chaotic, dynamical system featuring the learned steady-state PDF by design. Finally, utilizing gauge terms for the velocity gradient single-time statistics, we optimize the time correlations as obtained from our model against the DNS data. As a result, the model time realizations statistically closely resemble the time series from DNS. |
| title | Tailor-designed models for the turbulent velocity gradient through normalizing flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2402.19158 |