On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914097960845312 |
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| author | Fu, Chengzhang Jolly, Michael S. Kumar, Anuj Martinez, Vincent R. |
| author_facet | Fu, Chengzhang Jolly, Michael S. Kumar, Anuj Martinez, Vincent R. |
| contents | Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument to derive an energy spectrum that scales as $κ^{2β/3-3}$ where $β$ controls the regularity of the velocity ($β=1$ in the special case of the SQG). Direct numerical simulations indicate that this fits better than $κ^{β/3-3}$ which was derived in earlier work. Guided by earlier work on the 2D Navier-Stokes equations, we prove a certain condition implies a direct cascade of enstrophy, as well as an upper bound on the enstrophy dissipation rate, and sharp bounds on a dissipation wavenumber. The dependence of these rigorous results on the two parameters is demonstrated numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations Fu, Chengzhang Jolly, Michael S. Kumar, Anuj Martinez, Vincent R. Fluid Dynamics Analysis of PDEs 35Q30, 76F02, 76F25 Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument to derive an energy spectrum that scales as $κ^{2β/3-3}$ where $β$ controls the regularity of the velocity ($β=1$ in the special case of the SQG). Direct numerical simulations indicate that this fits better than $κ^{β/3-3}$ which was derived in earlier work. Guided by earlier work on the 2D Navier-Stokes equations, we prove a certain condition implies a direct cascade of enstrophy, as well as an upper bound on the enstrophy dissipation rate, and sharp bounds on a dissipation wavenumber. The dependence of these rigorous results on the two parameters is demonstrated numerically. |
| title | On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations |
| topic | Fluid Dynamics Analysis of PDEs 35Q30, 76F02, 76F25 |
| url | https://arxiv.org/abs/2510.15077 |