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
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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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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.
Original language | English |
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Article number | L082601 |
Journal | Physical review fluids |
Volume | 7 |
Issue number | 8 |
DOIs | |
Publication status | Published - 24 Aug 2022 |
Keywords
- Turbulence simulation
- Geometric integration
- Lie-Poisson system
- Energy spectrum