Hydrodynamic Turbulence: Sweeping Effect and Taylor’s Hypothesis via Correlation Function

Abstract

We demonstrate the sweeping effect in turbulence using numerical simulations of hydrodynamic turbulence without a mean velocity. The velocity correlation function, C(k,τ), decays with time due to the eddy viscosity. In addition, C(k,τ) shows oscillations due to the sweeping effect by “random mean velocity field” U~0. We also perform numerical simulation with mean velocity U0=10z^ (10 times the rms speed) for which C(k,τ) exhibits damped oscillations with the frequency of |U0|k and decay time scale corresponding to the U0=0 case. For U0=10z^, the phase of C(k,τ) shows the sweeping effect, but it is overshadowed by oscillations caused by U0. 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.