Casimir preserving spectrum of two-dimensional turbulence
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913587801358336 |
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| author | Cifani, Paolo Viviani, Milo Luesink, Erwin Modin, Klas Geurts, Bernard J. |
| author_facet | Cifani, Paolo Viviani, Milo Luesink, Erwin Modin, Klas Geurts, Bernard J. |
| contents | We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the -3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11794 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Casimir preserving spectrum of two-dimensional turbulence Cifani, Paolo Viviani, Milo Luesink, Erwin Modin, Klas Geurts, Bernard J. Fluid Dynamics We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the -3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods. |
| title | Casimir preserving spectrum of two-dimensional turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2204.11794 |