摘要
自从著名的Kolmogorov关于不可压缩湍流的研究以来,惯性函数中的结构函数理论一直是现代湍流研究的关键.由于Burgers湍流的简单性,惯性区内的结构函数计算为任意阶,这为其他可压缩湍流系统提供了许多启示.本文推导了Burgers湍流高阶结构函数的精确解析表达式.与以往基于激波统计数据计算得到的惯性区内结构函数理论相比,我们的表达式连接了不同阶次的高阶结构函数(这些高阶结构函数不使用流动结构的信息),并且在惯性区外有效.因此它们很容易通过数值模拟进行检查.
Since the famous work by Kolmogorov on incompressible turbulence,the structure-function theory has been a key foundation of modern turbulence study.Due to the simplicity of Burgers turbulence,structure functions are calculated to arbitrary orders,which provides numerous implications for other compressible turbulent systems.We present the derivation of exact forcing-scale resolving expressions for high-order structure functions of the burgers turbulence.Compared with the previous theories,where the structure functions are calculated in the inertial range based on the statistics of shocks,our expressions link high-order structure functions in different orders without extra information on the flow structure and are valid beyond the inertial range,therefore they are easily checked by numerical simulations.
作者
谢金翰
Jin-Han Xie(Department of Mechanics and Engineering Science at College of Engineering and State Key Laboratory for Turbulence and Complex Systems,Peking University,Beijing 100871,China)
基金
supported by the National Natural Science Foundation of China(Grant No.92052102).
