Inverse energy cascade in nonlocal helical shellmodels of turbulence

TL;DR

This paper introduces a modified helical shell model with non-local interactions that demonstrates a stable inverse energy cascade, providing insights into turbulent energy transfer mechanisms.

Contribution

It presents a new class of helical shell models with non-local triadic interactions that exhibit inverse energy cascades, aligning with behaviors of the Navier-Stokes equations.

Findings

Existence of a class of models with inverse energy cascade.

Inverse cascade stability confirmed through analytical and numerical methods.

Supports the idea of entangled triads driving turbulent energy transfer.

Abstract

Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of helical shell models for turbulence with non-local triadic interactions. By using both an analytical argument and numerical simulation, we show that there exists a class of models, with a specific helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions. We further support the idea that turbulent energy transfer is the result of a strong entanglement among triads possessing different transfer properties.