Is Vorticity Amplification Essential for Anomalous Dissipation and Intermittency in Turbulence?

Abstract

The distinct dynamical roles of vorticity amplification (VA) and vortex tilting (VT) in three-dimensional homogeneous isotropic turbulence are investigated using direct numerical simulations of a modified Navier--Stokes system. By selectively suppressing VA while retaining VT, we demonstrate that gradient amplification by VA is strictly required to sustain the classical forward energy cascade. Progressively suppressing VA weakens small-scale velocity gradients, heavily depletes extreme fluctuations, and entirely eliminates the classical energy dissipative anomaly, causing the normalized energy dissipation to decay as $Re_λ^{-1}$. In the limit of complete VA suppression, enstrophy emerges as the relevant inviscid invariant. Scale-by-scale budget analyses confirm that the dynamics transition to a purely forward enstrophy cascade, characterized by an anomalous enstrophy dissipation and a robust $E(k) \sim k^{-3}$ intermediate energy spectrum. We verify that these asymptotic scaling limits---including a $Re_λ^{-1/2}$ finite-Reynolds-number correction for the enstrophy anomalous dissipation---are universal properties of the VA-suppressed dynamics, independent of whether the large-scale forcing is helical or non-helical. Remarkably, despite the smoothing of the velocity field and the elimination of the energy dissipative anomaly, anomalous structural scaling and a broad multifractal spectrum persist. These results reveal a fundamental mechanistic separation: while VA is responsible for amplifying intense localized fluctuations, geometric reorganization by VT alone is mechanically sufficient to sustain multifractal intermittency.