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

• Published in: Transactions of the Indian National Academy of Engineering (Online) 2020-12, Vol.5 (4), p.649-662
• Main Authors: Verma, Mahendra K., Kumar, Abhishek, Gupta, Akanksha
• Format: Article
• Language: English
• Subjects: Engineering; Original Article
• ISSN: 2662-5423; 2662-5423
• DOI: 10.1007/s41403-020-00161-3

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 U 0 = 10 z ^ (10 times the rms speed) for which C ( k , τ ) exhibits damped oscillations with the frequency of | U 0 | k and decay time scale corresponding to the U 0 = 0 case. For U 0 = 10 z ^ , the phase of C ( k , τ ) shows the sweeping effect, but it is overshadowed by oscillations caused by U 0 . We also demonstrate that for U 0 = 0 and 10 z ^ , 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.