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Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani1,2,*, Milo Viviani3, Erwin Luesink1, Klas Modin4, and Bernard J. Geurts1,5

  • 1Multiscale Modeling and Simulation, Faculty EEMCS, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 2Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L'Aquila, Italy
  • 3Scuola Normale Superiore di Pisa, 56126 Pisa, Italy
  • 4Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Gothenburg, Sweden
  • 5Multiscale Energy Physics, CCER, Faculty Applied Physics, Eindhoven University of Technology, P.O. Box 213, 5600 MB Eindhoven, The Netherlands

  • *p.cifani@utwente.nl
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Phys. Rev. Fluids 7, L082601 – Published 24 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.L082601

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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Phys. Rev. Fluids 7, L082601– Published 24 August, 2022
  • Received 25 April 2022
  • Accepted 2 August 2022
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