# Sweeping effect and Taylor's hypothesis via correlation function

## TL;DR

This paper investigates the sweeping effect in turbulence through numerical simulations, analyzing how velocity correlation functions decay and oscillate under different mean velocity conditions, and relates these findings to Taylor's hypothesis.

## Contribution

It demonstrates the sweeping effect in turbulence without mean velocity and clarifies the relation between correlation functions, oscillations, and spectral behaviors under different mean velocities.

## Key findings

- Velocity correlation function decays with eddy viscosity.
- Oscillations in correlation functions are caused by sweeping effect.
- Spectral behaviors differ for zero and non-zero mean velocities.

## Abstract

We demonstrate the sweeping effect in turbulence using numerical simulations of hydrodynamic turbulence without a mean velocity. The velocity correlation function, C(k, {\tau} ) decays with time due to the eddy viscosity. In addition, C(k, {\tau} ) shows oscillations due to the sweeping effect by "random mean velocity field" U_0. We also perform numerical simulation with a mean velocity U_0 = 10 for which C(k, {\tau} ) exhibits damped oscillations with the frequency of |U_0|k and decay time scale corresponding to the U_0 = 0 case. For U_0 = 10z, the phase of C(k, {\tau} ) show the sweeping effect, but it is overshadowed by oscillations caused by U_0 . We also demonstrate that for U0 = 0 and 10z, the frequency spectra of the velocity fields measured by real-space probes are respectively f^{-2} and f^{-5/3} these spectra are related to the Lagrangian and Eulerian space-time correlations respectively. respectively.