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Abstract: The issue of why computational resolution in Navier-Stokes turbulence is sohard to achieve is addressed. It is shown that Navier-Stokes solutions canpotentially behave differently in two distinct regions of space-time$\mathbb{R}^{\pm}$ where $\mathbb{R}^{-}$ is comprised of a union of disjointspace-time `anomalies-. Large values of $| abla\bom|$ dominate$\mathbb{R}^{-}$, which is consistent with the formation of vortex sheets ortightly-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 $\mathcal{R} {u} = uL- u$ is a Reynolds number dependent on the localvelocity field $u\bx, t$.



Author: J. D. Gibbon

Source: https://arxiv.org/







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