Lagrangian chaos and the enstrophy cascade in Ekman-Navier-Stokes two-dimensional turbulence
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910042043711488 |
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| author | Ventrella, Francesco Michele Valadão, Victor de Jesus Boffetta, Guido Musacchio, Stefano De Lillo, Filippo |
| author_facet | Ventrella, Francesco Michele Valadão, Victor de Jesus Boffetta, Guido Musacchio, Stefano De Lillo, Filippo |
| contents | Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction, the enstrophy flux is suppressed in the cascade and, as a consequence, the small-scale vorticity field becomes passively transported by the large-scale, chaotic flow. We numerically address this problem by investigating how the statistics of the Lagrangian Finite Time Lyapunov Exponent in 2D Ekman-Navier-Stokes simulations are affected by the friction coefficient and by the other parameters of the flow. We derive a simple phenomenological model that interpolates the dependence of the Lyapunov exponent on the flow statistics from the large friction limit, where analytical predictions are available, to the small friction region. We find that the distribution of the FTLE around this mean value is always close to a Gaussian, and this allows to make a simple prediction for the correction of the spectral slope of the direct cascade which is in very good agreement with the numerical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lagrangian chaos and the enstrophy cascade in Ekman-Navier-Stokes two-dimensional turbulence Ventrella, Francesco Michele Valadão, Victor de Jesus Boffetta, Guido Musacchio, Stefano De Lillo, Filippo Fluid Dynamics Chaotic Dynamics Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction, the enstrophy flux is suppressed in the cascade and, as a consequence, the small-scale vorticity field becomes passively transported by the large-scale, chaotic flow. We numerically address this problem by investigating how the statistics of the Lagrangian Finite Time Lyapunov Exponent in 2D Ekman-Navier-Stokes simulations are affected by the friction coefficient and by the other parameters of the flow. We derive a simple phenomenological model that interpolates the dependence of the Lyapunov exponent on the flow statistics from the large friction limit, where analytical predictions are available, to the small friction region. We find that the distribution of the FTLE around this mean value is always close to a Gaussian, and this allows to make a simple prediction for the correction of the spectral slope of the direct cascade which is in very good agreement with the numerical results. |
| title | Lagrangian chaos and the enstrophy cascade in Ekman-Navier-Stokes two-dimensional turbulence |
| topic | Fluid Dynamics Chaotic Dynamics |
| url | https://arxiv.org/abs/2511.08220 |