Turbulent and intermittent phenomena in a universal total anomalous dissipator

Abstract

For all $\alpha \in (0,1)$, we construct an explicit divergence-free vector field $V\in L^{\infty }([0,1],C^{\alpha }({\mathbb{T}}^2))$ that exhibits universal anomalous (total) dissipation, accelerating dissipation enhancement, Richardson dispersion, anomalous regularization, and spatial intermittency. Additionally, we demonstrate the sharpness of the intermittent Obukhov-Corrsin regime for certain parameter ranges.

53 pages, 3 figures