Lagrangian chaos and the enstrophy cascade in Ekman-Navier-Stokes two-dimensional turbulence

Fuente: arXiv
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Main Authors: Ventrella, Francesco Michele, Valadão, Victor de Jesus, Boffetta, Guido, Musacchio, Stefano, De Lillo, Filippo
Format: Preprint
Published: 2025
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_version_ 1866910042043711488
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
id 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