Third-order structure function beyond the inertial range in homogeneous isotropic turbulence

• 主讲人：Jin-Han Xie (Peking University)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2022-12-09 16:00 - 2022-12-09 17:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/9525DF61A79763B92FA01C0BD83089FF
Valid Until: 2027-01-31 23:59

 

Abstract: In 1941, Kolmogorov proposed the 4/5 law for the inertial range in three-dimensional isotropic turbulence, which links measurable third-order structure functions with energy transfer. The inertial-range theories are applied to quantify the direction and magnitude of energy transfer in natural turbulence. However, the applicability of these theories is limited due to the effects of forcing scale and bidirectional energy transfer. Thus, expressions for structure functions beyond the inertial range are required. We derive a forcing-scale-resolving global expression that captures the bidirectional energy transfer. We apply this expression to analyse the drifter data in the Gulf of Mexico and provide evidence for bidirectional energy transfer in ocean turbulence. Also, this new expression implies a conjugate regime to Kolmogorov's theory for the scales larger than the forcing scale in three-dimensional homogeneous isotropic turbulence. This new regime points out the importance of the energy injection even in the large scales, which was believed to be described by absolute equilibrium because of zero averaged energy flux across scales, and potentially provides a foundation for superresolution.

 

Bio: Jin-Han Xie is an Assistant Professor in the Department of Mechanics and Engineering Science, College of Engineering at Peking University. He was a Courant Instructor at the Courant Institute of Mathematical Sciences, New York University. Before that, he was a postdoctoral researcher at the physics department of the University of California, Berkeley. He obtained his PhD degree in Applied and Computational Mathematics at the School of Mathematics of the University of Edinburgh in 2015. He got his Bachelor’s degree in Theoretical and Applied Mechanics at the College of Engineering, Peking University in 2011.