@article{8a4dab88db8e434bb7b4e940ac6d141e,
title = "Casimir preserving spectrum of two-dimensional turbulence",
abstract = "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.",
keywords = "Turbulence simulation, Geometric integration, Lie-Poisson system, Energy spectrum",
author = "Paolo Cifani and Milo Viviani and Erwin Luesink and Klas Modin and Geurts, \{Bernard J.\}",
note = "Funding Information: This publication is part of the project SPRESTO which is financed by the Dutch Research Council (NWO). This work was also supported by the Swedish Research Council Grant No. 2017-05040, and the Knut and Alice Wallenberg Foundation Grant No. WAF2019.0201. Simulations were carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. We wish to thank Prof. Guido Boffetta for his valuable suggestions in the setup of the simulations. Publisher Copyright: {\textcopyright} 2022 American Physical Society.",
year = "2022",
month = aug,
day = "24",
doi = "10.1103/PhysRevFluids.7.L082601",
language = "English",
volume = "7",
journal = "Physical review fluids",
issn = "2469-990X",
publisher = "American Physical Society",
number = "8",
}