Abstract

We study the energy cascade process, one of the most important aspects of fluid turbulence that also plays a crucial role in Large Eddy Simulations. Based on the scale-integrated Kolmogorov-Hill equation expressing the evolution of kinetic energy in spheres of sizes in the inertial range, we examine a new definition of entropy and entropy generation rate for turbulence. Its measurement from direct numerical simulations in isotropic turbulence leads to confirmation of the validity of the fluctuation relation (FR) from non-equilibrium statistical mechanics in the inertial range of turbulent flows. Specifically, the ratio of probability densities of forward and inverse cascade is shown to follow exponential behavior with the entropy generation rate, but only if the latter is defined by including an appropriately defined notion of “temperature of turbulence” proportional to the kinetic energy at the scale in question. The FR is directly linked with ideas connecting exponential phase-space contraction rates (finite-time Lyapunov exponents) to entropy generation rates. This insight leads us to examine a Lagrangian version of FR, i.e., following spherical fluid volumes in time. The results point to many, still entirely open, questions, such as connections to the number of possible micro (“subgrid”) states in turbulence, and appropriate definitions of coarse-grained momenta. These are necessary ingredients for translating the gained insights into useful prediction methods such as Large Eddy Simulations. This work was performed in collaboration with Hanxun Yao, Tamer Zaki and P.K. Yeung, was supported financially by the US National Science Foundation. The work of the JHTDB team is also gratefully acknowledged.

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brief bio:

Charles Meneveau is the Louis M. Sardella Professor in the Department of Mechanical Engineering and is Associate Director of the Institute for Data Intensive Engineering and Science (IDIES). His area of research is focused on understanding and modeling hydrodynamic turbulence, with application interests in Large Eddy Simulations (LES) of engineering and environmental flows, including wind farms. He also focuses on developing methods to democratize access to very large turbulence data sets from DNS and LES . He received his B.S. degree in Mechanical Engineering from the Universidad Técnica Federico Santa María in Valparaíso, Chile, in 1985 and advanced degrees from Yale University, followed by postdoctoral fellowship at the Center for Turbulence Research at Stanford. He has been on the Johns Hopkins University faculty since 1990. Prof. Meneveau is Deputy Editor of the Journal of Fluid Mechanics and has served as the Editor-in-Chief of the Journal of Turbulence. Professor Meneveau is a member of the US National Academy of Engineering, a foreign corresponding member of the Chilean Academy of Sciences, and a recipient of the APS Corrsin Award (2011), the AIAA Fluid Dynamics Award (2021), and the Batchelor Prize in 2024.