Casimir preserving spectrum of two-dimensional turbulence
Other text in scientific journal, 2022

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.

Author

Paolo Cifani

Gran Sasso Science Institute (GSSI)

University of Twente

Milo Viviani

Scuola Normale Superiore di Pisa

Erwin Luesink

University of Twente

Klas Modin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Bernard J. Geurts

Eindhoven University of Technology

University of Twente

Physical Review Fluids

2469990X (eISSN)

Vol. 7 8 L082601

Subject Categories

Applied Mechanics

Computational Mathematics

Other Physics Topics

DOI

10.1103/PhysRevFluids.7.L082601

More information

Latest update

10/10/2022