Estimating intermittency in three-dimensional Navier-Stokes turbulence

Abstract

The issue of why computational resolution in Navier-Stokes turbulence is so hard to achieve is addressed. It is shown that Navier-Stokes solutions can potentially behave differently in two distinct regions of space-time ${\mathbb{R}}^{\pm }$ where ${\mathbb{R}}^{-}$ is comprised of a union of disjoint space-time `anomalies'. Large values of $|\nabla\bom|$ dominate ${\mathbb{R}}^{-}$, which is consistent with the formation of vortex sheets or tightly-coiled filaments. The local number of degrees of freedom ${\mathcal{N}}^{\pm }$ needed to resolve the regions in ${\mathbb{R}}^{\pm }$ satisfies $$\mathcal{N}^{\pm}(\bx, t)\lessgtr c_{\pm}\mathcal{R}_{u}^{3}$$ where ${\mathcal{R}}_u=uL/\nu$ is a Reynolds number dependent on the local velocity field $u(\bx, t)$.

References in corpus (2)

• The multifractal nature of turbulent energy dissipation
• Asymptotic Exponents from Low-Reynolds-Number Flows

Cited by in corpus (2)

• The number of degrees of freedom of three-dimensional Navier--Stokes turbulence
• Extreme events in solutions of hydrostatic and non-hydrostatic climate models