Sweeping effect and Taylor's hypothesis via correlation function

TL;DR

This study uses high-resolution simulations to analyze the sweeping effect and Taylor's hypothesis in turbulence, revealing how mean velocity influences velocity correlation decay, oscillations, and frequency spectra.

Contribution

It demonstrates the impact of mean velocity on turbulence correlation functions and provides insights into the sweeping effect and Taylor's hypothesis through numerical simulations.

Findings

Velocity correlation decays due to eddy viscosity and shows fluctuations from sweeping.

For U0=10, correlation exhibits damped oscillations at frequency U0k.

Frequency spectra are f^{-2} for U0=0 and f^{-5/3} for U0=10, linking to space-time correlations.

Abstract

We performed high-resolution numerical simulations of hydrodynamic turbulence with and without mean velocity ($U_0=0,10$), and demonstrate the sweeping effect. For $U_0=0$, the velocity correlation function, $C({\bf k},\tau)$ decays with time due to eddy viscosity, but it also shows fluctuations due to the sweeping effect. For $U_0=10$, $C({\bf k},\tau)$ exhibits damped oscillations with the frequency of $U_0 k$ and decay time scale corresponding to the $U_0=0$ case. A closer examination of $\Im[C({\bf k},\tau)]$ also demonstrates sweeping effect for $U_0=10$. We also demonstrate that the frequency spectra of the velocity fields measured by real-space probes are respectively $f^{-2}$ and $f^{-5/3}$ for $U_0=0$ and 10; these spectra are related to the Lagrangian and Eulerian space-time correlations.