Anomalous dissipation and energy cascade in 3D inviscid flows

TL;DR

This paper demonstrates that anomalous dissipation in 3D inviscid flows can initiate an infinite energy cascade in decaying turbulence, confirming Onsager's predictions about energy transfer without viscosity.

Contribution

It extends the study of energy cascade and anomalous dissipation from viscous to inviscid flows, confirming Onsager's theory in a new setting.

Findings

Anomalous dissipation triggers energy cascade in 3D inviscid flows.

Cascade continues indefinitely in decaying turbulence.

Results support Onsager's predictions about turbulence behavior.

Abstract

Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flows, it is shown that the anomalous dissipation is -- in the case of decaying turbulence -- indeed capable of triggering the cascade which then continues ad infinitum, confirming Onsager's predictions.