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Professor Chen Shiyi’s team makes progress in compressible turbulence

Peking University, June 6, 2013: Recently, a research team in the College of Engineering has made an important progress in the study of compressible turbulence, which has been published in Physical Review Letters (Cascade of Kinetic Energy in Three-dimensional Compressible Turbulence, Phys. Rev. Lett. 110, 214505, 2013). The team is led by Professor Chen Shiyi from the State Key Laboratory for Turbulence and Complex Systems (SKLTCS) and Professor He Xiantu from the Center for Applied Physics and Technology (CAPT). Other contributors include Dr. Wang Jianchun, Dr. Yang Yantao, Professors Shi Yipeng and Xiao Zuoli.

 

High Mach number turbulence is of great importance to a large number of industrial applications and natural phenomena, including hypersonic aircrafts, inertial confinement fusion, high-temperature reactive flows, space exploration and astrophysics. Recently, the high Mach number turbulence and its mechanism become a hot area for turbulence research.

 

Based on their previous studies (Phys.Rev.Lett. 108, 214505, 2012; Phys. Rev. Lett. 110, 064503, 2013), Prof. Chen’s group continued to explore the compressible turbulence using high resolution numerical simulation. They investigated the physical mechanism of kinetic energy transfer in compressible turbulence, expanded the energy cascade theory of incompressible turbulence into compressible turbulence, and verified the Kolmogorov -5/3 energy spectrum in compressible turbulence. This study provides a solid theoretic basis for the -5/3 energy spectrum observed in the supersonic motions of interstellar medium, and is of guiding significance to the development of advanced turbulence models for high Mach number complex compressible turbulence.

 

It reveals that both solenoidal and compressive modes display conservative energy cascade process through an inertial range of scales, and the cascade rate of compressive mode is much larger compared to its solenoidal counterpart. As a result, the solenoidal component of kinetic energy dominates at small scales in the inertial range and exhibits the Kolmogorov -5/3 spectrum. They investigated the effect of shock waves on the kinetic energy spectrum and energy transfer process. Both numerical simulation and theoretic analysis showed that in the compressible turbulence driven by large-scale compressive forcing, large scale shock waves can be generated, leading to the -2 spectrum of compressive kinetic energy.

 

By using conditional average, they revealed that large-scale strain tensor and subgrid scale stress tensor are anti-parallel in shock regions, and the local subgrid scale flux of kinetic energy increase linearly with the square of local dilatation level. All these results could help develop more advanced model for compressible turbulence.

 

This study is supported by the National Natural Science Foundation of China, the National Science and Technology Ministry as a subproject of 973 program, China Postdoc Foundation, and CAPT of Peking University.

 

 

Left: Structures of solenoidal and compressive components of subgrid scale kinetic energy flux.
Right: Kinetic energy spectrum and its solenoidal and compressive components.

 

Source: College of Engineering

Edited by: Zhang Jiang