中文摘要：

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等.研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量（压缩）耗散率所占比率也显著增长.标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高（p≥5）时,纵向速度结构函数的扩展自相似性则不再成立.对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的间歇性要强于横向湍流脉动.

英文摘要：

Statistical characteristics of turbulent flow and its compressibility effect within decaying isotropic turbulence have been studied using direct numerical simulation through fifth-order WENO scheme. The research reveals that turbulent kinetic energy mainly comes from solenoidal velocity field and small scale motions are sensitive to the compressibility. As the compressibility increases, turbulent kinetic energy transport between the large and the smM1 turbulent motions becomes more rapid. ~rthermore, the increasing initial turbulent Mach number leads to a fast rise of fraction of dissipation rate due to dilatation. Through scaling law analysis, it is shown that transverse velocity structure function （TVSF） still satisfies extended self-similarity （ESS）, so does longitudinal velocity structure function （LVSF） at low order; while if the order of LVSF is high （p≥ 5）, the ESS will not hold true. For weakly compressible turbulence, the transverse turbulent velocity fluctuations are more intermittent than the longitudinal fluctuations as same as that in the incompressible turbulence. In contrast, longitudinal fluctuations are more intermittent than transverse fluctuations for strongly compressible turbulence.