Intermittency corrections to the mean square particle acceleration in high Reynolds number turbulence

Abstract

The mean square particle acceleration in high Reynolds number turbulence is dominated by the mean square pressure gradient. Recent experiments by Voth et al [Phys. Fluids {\bf 10}, 2268 (1998)] indicate that this quantity, when normalized by the 1941 Kolmogorov value, $ε^{3/2}ν^{-1/2}$, is independent of Reynolds number at high Reynolds number. This is to be contrasted with direct numerical simulations of Vedula and Yeung [Phys. Fluids {\bf 11}, 1208, (1999)] which show a strong increase of the same quantity with increasing Reynolds number. In this paper we suggest that there is no inherent conflict between these two results. A large part of the increase seen in DNS is shown to be associated with finite Reynolds number corrections within the quasi-Gaussian approximation. The remaining intermittency corrections are relatively slowly increasing with Reynolds number, and are very sensitive to subtle cancellations among the longitudinal and transverse contributions to the mean square pressure gradient. Other possible theoretical subtleties are also briefly discussed.