Casimir preserving spectrum of two-dimensional turbulence

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

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2 Citations (Scopus)
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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

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.
Original languageEnglish
Article numberL082601
JournalPhysical review fluids
Issue number8
Publication statusPublished - 24 Aug 2022


  • Turbulence simulation
  • Geometric integration
  • Lie-Poisson system
  • Energy spectrum


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