On spectral scaling laws for averaged turbulence on the sphere
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918121734930432 |
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| author | Ephrati, Sagy Jansson, Erik Modin, Klas |
| author_facet | Ephrati, Sagy Jansson, Erik Modin, Klas |
| contents | Spectral analysis for a class of Lagrangian-averaged Navier--Stokes (LANS) equations on the sphere is carried out. The equations arise from the Navier--Stokes equations by applying a Helmholtz filter of width $α$ to the advecting velocity $β$ times. Power laws for the energy spectrum are derived and indicate a $β$-dependent scaling at wave numbers $l$ with $αl\gg 1$. The energy and enstrophy transfer rates distinctly depend on the averaging, allowing control over the energy flux and the enstrophy flux separately through the choice of averaging operator. A necessary condition on the averaging operator is derived for the existence of the inverse cascade in two-dimensional turbulence. Numerical experiments with a structure-preserving integrator confirm the expected energy spectrum scalings and the robustness of the double cascade under choices of the averaging operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_05368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On spectral scaling laws for averaged turbulence on the sphere Ephrati, Sagy Jansson, Erik Modin, Klas Fluid Dynamics 76F02, 35Q30, 76F05 Spectral analysis for a class of Lagrangian-averaged Navier--Stokes (LANS) equations on the sphere is carried out. The equations arise from the Navier--Stokes equations by applying a Helmholtz filter of width $α$ to the advecting velocity $β$ times. Power laws for the energy spectrum are derived and indicate a $β$-dependent scaling at wave numbers $l$ with $αl\gg 1$. The energy and enstrophy transfer rates distinctly depend on the averaging, allowing control over the energy flux and the enstrophy flux separately through the choice of averaging operator. A necessary condition on the averaging operator is derived for the existence of the inverse cascade in two-dimensional turbulence. Numerical experiments with a structure-preserving integrator confirm the expected energy spectrum scalings and the robustness of the double cascade under choices of the averaging operator. |
| title | On spectral scaling laws for averaged turbulence on the sphere |
| topic | Fluid Dynamics 76F02, 35Q30, 76F05 |
| url | https://arxiv.org/abs/2503.05368 |