Casimir preserving spectrum of two-dimensional turbulence
Fluid Dynamics
2024-11-28 v2
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
Cite
@article{arxiv.2204.11794,
title = {Casimir preserving spectrum of two-dimensional turbulence},
author = {Paolo Cifani and Milo Viviani and Erwin Luesink and Klas Modin and Bernard J. Geurts},
journal= {arXiv preprint arXiv:2204.11794},
year = {2024}
}