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, {\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.