Lagrangian acceleration in fully developed turbulence and its Eulerian decompositions

TL;DR

This study uses high-resolution simulations to analyze Eulerian and Lagrangian acceleration contributions in turbulence, revealing scaling behaviors that challenge traditional models and highlighting the dominance of pressure gradient effects.

Contribution

It provides new insights into the scaling of acceleration components in turbulence, contrasting with existing phenomenological and multifractal models.

Findings

Convective acceleration variance scales linearly with Reynolds number.

Lagrangian acceleration variance increases as Reynolds number to the 0.25 power.

Pressure gradient contributions dominate acceleration variance.

Abstract

We study the properties of various Eulerian contributions to fluid particle acceleration by using well-resolved direct numerical simulations of isotropic turbulence, with the grid resolution as high as $12288^3$ and the Taylor-scale Reynolds number $R_\lambda$ in the range between 140 and 1300. The variance of convective acceleration, when normalized by Kolmogorov scales, increases linearly with $R_\lambda$, consistent with simple theoretical arguments, but very strongly differing from phenomenological predictions of Kolmogorov's hypothesis as well as Eulerian multifractal models. The scaling of the local acceleration is also linear $R_\lambda$ to the leading order, but more complex in detail. The strong cancellation between the local and convective acceleration -- faithful to the random sweeping hypothesis -- results in the variance of the Lagrangian acceleration increasing only as $R_\lambda^{0.25}$, as recently shown by Buaria \& Sreenivasan [Phys. Rev. Lett. 128, 234502 (2022)]. The acceleration variance is dominated by irrotational pressure gradient contributions, whose variance also follows an $R_\lambda^{0.25}$ scaling; the solenoidal viscous contributions are relatively small and follow a $R_\lambda^{0.13}$, consistent with Eulerian multifractal predictions.