Turbulent and intermittent phenomena in a universal total anomalous dissipator

TL;DR

This paper constructs a divergence-free vector field demonstrating universal anomalous dissipation and intermittency phenomena, highlighting sharpness of certain turbulence regimes in fluid dynamics.

Contribution

It introduces an explicit vector field with properties like anomalous dissipation and intermittency, advancing understanding of turbulence models.

Findings

Demonstrates universal anomalous dissipation in constructed vector fields.

Shows acceleration of dissipation and Richardson dispersion effects.

Establishes sharpness of the Obukhov-Corrsin intermittency regime.

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.