The coherent structure of the energy cascade in isotropic turbulence

Danah Park and Prof. Adrian Lozano-Duran from the Computational Turbulence Group apply pattern recognition methods to reveal the underlying structure in the chaotic motion of air, such as atmospheric flows.

Authors: Danah Park and Adrian Lozano-Duran
Citation: Sci Rep 15, 14 (2025)

Abstract:
The energy cascade, i.e. the transfer of kinetic energy from large-scale to small-scale flow motions, has been the cornerstone of turbulence theories and models since the 1940s. However, understanding the spatial organization of the energy transfer has remained elusive. In this work, we answer the question: What are the characteristic flow patterns surrounding regions of intense energy transfer? 

To that end, we utilize numerical data of isotropic turbulence to investigate the three-dimensional spatial structure of the energy cascade in the inertial range. Our findings indicate that forward energy-transfer events are predominantly confined in the high strain-rate region created between two distinct zones of elevated enstrophy. On average, these zones manifest in the form of two hairpin-like shapes with opposing orientations. The mean velocity field associated with the energy transfer exhibits a saddle point topology when observed in the frame of reference local to the event. The analysis also shows that the primary driving mechanism for the cascade involves strain-rate self-amplification, which is responsible for 85% of the energy transfer, whereas vortex stretching accounts for less than 15%.