Universität zu Köln, Institut fur Geophysik und Meteorologie, Pohligstrasse 3, 50969 Köln, Germany.
Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0424, USA.
Phys Rev E. 2017 Nov;96(5-1):053116. doi: 10.1103/PhysRevE.96.053116. Epub 2017 Nov 30.
Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.
在大雷诺数的渐近极限下分析了自引力等温超声湍流。基于总能量的无粘性不变性，推导出了一个适用于均匀（不一定各向同性）湍流的精确关系。使用修改后的两点能量相关函数定义来满足声学极限下详细能量均衡的要求。与之前的关系（S. Galtier 和 S. Banerjee，Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501；S. Banerjee 和 S. Galtier，Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019）相比，当前的精确关系表明压力膨胀项在能量级联中几乎没有作用。通量项和源项都用两点差来表示。源项以混合二阶结构函数的形式进入关系。与动能和热力学势能不同，引力贡献不存在于通量项中。估计表明，对于各向同性情况，密度和重力加速度之间的相关性可能在修改自引力湍流中的能量传递中起重要作用。精确关系也以两点相关函数的另一种形式表示，然后用于描述谱空间中的标度间能量预算。
