2022/11/05 by Jin-Han Xie, Xie, Jin-Han
Engineering · Environmental Science · Physics and Astronomy · #76F05 #Advanced Thermodynamics and Statistical Mechanics #Atmospheric aerosols and clouds #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Laser-induced spectroscopy and plasma
paper · pdf · doi:10.48550/arxiv.2211.02898
openalex publication_date 2022/11/05 · openalex created_date 2022/11/13 · openalex updated_date 2026/07/28
We explore the spatial-temporal structure functions of Burgers turbulence driven by a temporal Ornstein-Uhlenbeck (OU) process, where the characteristic time scale of the OU process is much larger than that of the energy flux across spatial scales. Based on the Kármán-Howarth-Monin equation, we obtain an expression for the third-order spatial-temporal structure function away from the dissipation scale. This expression combines Kolmogorov's exact result of spatial structure function and the exponential temporal decay of the external force. We numerically justify this expression and find that the high-order structure functions also decay exponentially, however, the dependence of decay rates on order is different for the odd- and even-order structure functions. Comparing the OU-driven Burgers turbulence with that driven by temporal white noise, their spatial structure functions are identical when the energy injection rates are the same, which justifies Kolmogorov's theory, but these two systems' temporal structure functions differ. Also, the velocity pdf in the OU-driven Burgers turbulence shows a bimodal distribution, contradicting the near-Gaussian distribution in white-noise-driven turbulence.