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arXiv · 2204.11794

Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani·Milo Viviani·Erwin Luesink·Klas Modin·Bernard J. Geurts
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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.

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Paolo Cifani, Milo Viviani, Erwin Luesink, Klas Modin, Bernard J. Geurts. 2022-04-25. Casimir preserving spectrum of two-dimensional turbulence. https://doi.org/10.1103/physrevfluids.7.l082601

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