Dynamics and nonlocal interactions of higher spherical-harmonic sectors

Investigate the dynamics of the higher odd spherical-harmonic sectors in the finite velocity-increment field, their coupling to the dipolar velocity-gradient sector, and whether they encode nonlocal interactions in scale or space related to the coarse-grained term I\widetilde A_{ij}\widetilde M_{ij}.

Background

The paper exactly decomposes the finite velocity increment on a spherical surface into a dipolar L=1 component determined by the coarse-grained velocity-gradient tensor and a residual consisting of higher odd angular modes. The dipolar component yields the identified strain self-amplification and vortex-stretching contributions to the real-space energy flux, while the residual contains angular information that cannot be represented by the local rank-two velocity-gradient tensor alone. The authors identify as unresolved the dynamics of these higher sectors, how they interact with the dipolar mode, and whether their effects correspond to nonlocal interactions in scale or physical space, potentially through the pressure, subgrid-stress, viscous, and forcing contributions collected in I\widetilde A_{ij}\widetilde M_{ij}.