A simple argument based on self‐similarity is used to derive a relationship between pointwise energy‐dissipation‐rate moments, 〈ε^q〉, and inertial‐range volume‐averaged moments, 〈ε^q_r〉, in homogeneous, isotropic and stationary turbulence. These results support the multifractal description of energy dissipation. The moment relationship implies that pointwise and inertial‐range volume‐averaged energy‐dissipation rates cannot both be lognormally distributed. Some pointwise moments may not even exist if the volume‐average counterpart is lognormal. The Schwartz inequalities for moments satisfying the self‐similar relationship are examined and support the realizability of such processes.

中文翻译：

---

湍流中的自相似性和多重分形

基于自相似性的简单参数用于导出<ε逐点能量耗散率的时刻之间的关系，^q >，和惯性范围体积平均的时刻，<ε ^q _{- [R} >，在均匀的，各向同性的和固定湍流。这些结果支持能量耗散的多重分形描述。弯矩关系表明，点向和惯性范围的体积平均能量耗散率不能同时呈对数正态分布。如果体积平均对应对象为对数正态，则甚至可能不存在一些逐点矩。施瓦兹不平等 对于满足自相似关系的时刻进行了检查，并支持了此类过程的实现。