Self-similarity and the direct (enstrophy) cascade in two-dimensional fluid turbulence
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909317037293568 |
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| author | Reynoso, Mateo Zhigunov, Dmitriy Grigoriev, Roman O. |
| author_facet | Reynoso, Mateo Zhigunov, Dmitriy Grigoriev, Roman O. |
| contents | A widely used statistical theory of 2D turbulence developed by Kraichnan, Leith, and Batchelor (KLB) predicts a power-law scaling for the energy, $E(k)\propto k^α$ with an integral exponent $α={-3}$, in the inertial range associated with the direct cascade. In the presence of large-scale coherent structures, a power-law scaling is observed, but the exponent often differs substantially from the value predicted by the KLB theory. Here we present a dynamical theory which describes the key physical mechanism behind the direct cascade and sheds new light on the relationship between the structure of the large-scale flow and the scaling of the small-scale structures in the inertial range. This theory also goes a step beyond KLB, to predict the upper and lower bounds of the inertial range as well as the energy scaling in the dissipation range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03007 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-similarity and the direct (enstrophy) cascade in two-dimensional fluid turbulence Reynoso, Mateo Zhigunov, Dmitriy Grigoriev, Roman O. Fluid Dynamics A widely used statistical theory of 2D turbulence developed by Kraichnan, Leith, and Batchelor (KLB) predicts a power-law scaling for the energy, $E(k)\propto k^α$ with an integral exponent $α={-3}$, in the inertial range associated with the direct cascade. In the presence of large-scale coherent structures, a power-law scaling is observed, but the exponent often differs substantially from the value predicted by the KLB theory. Here we present a dynamical theory which describes the key physical mechanism behind the direct cascade and sheds new light on the relationship between the structure of the large-scale flow and the scaling of the small-scale structures in the inertial range. This theory also goes a step beyond KLB, to predict the upper and lower bounds of the inertial range as well as the energy scaling in the dissipation range. |
| title | Self-similarity and the direct (enstrophy) cascade in two-dimensional fluid turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2308.03007 |