Multi-branch Shell Models of Two-Dimensional Turbulence exhibit Dual Energy-Enstrophy Cascades

TL;DR

This paper introduces a multi-branch shell model for 2D turbulence that successfully reproduces dual energy-enstrophy cascades and realistic thermal spectra, overcoming limitations of classical models.

Contribution

The authors develop a novel multi-branch shell model with hierarchical geometry that captures dual cascades and realistic spectra in 2D turbulence.

Findings

Model reproduces thermal spectra of 2D fluid equations

Demonstrates statistically stationary dual cascade

Allows study of local transfers and non-Gaussianity

Abstract

Classical shell models of turbulence do not display dual cascade - inverse of energy and direct of 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.