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Multi-branch shell models of two-dimensional turbulence exhibit dual energy-enstrophy cascades
Phys. Rev. Fluids 11, 084604 – Published 11 August, 2026
DOI: https://doi.org/10.1103/5bxw-xd8z
Abstract
Classical shell models of turbulence do not display dual cascade—inverse for energy and direct for enstrophy—because they fail to reproduce the right thermal spectra. We propose here a multi-branch shell model, including a geometry hierarchically organized across scales, in order to overcome this limitation. For this model, we demonstrate numerically both the agreement of the thermal spectra with those of two-dimensional fluid equations and the emergence of a statistically stationary dual cascade. This construction also allows us to study local transfers and to investigate both self-similarity and non-Gaussianity.
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