This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that it can be considered a complex system whose structural units support dynamics on continuous but non-differentiable multifractal curves. Implementing the theoretical framework of multifractality through non-differentiable functions in the form of scale relativity theory with arbitrary and constant fractal dimension, the minimal vortex of an instance of turbulent flow is considered. The results of this assumption lead to an equation that describes the minimal vortex itself, and the velocity fields that compose it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow. These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.

本文旨在提出一种湍流大气的多重分形方法，方法是将其视为一个复杂的系统，其结构单元支持连续但不可微的多重分形曲线上的动力学。通过具有任意和恒定分形维数的尺度相对论，通过不可微函数实现多重分形的理论框架，考虑了湍流实例的最小涡旋。该假设的结果导致了一个方程，该方程描述了最小涡旋本身以及组成该最小涡旋的速度场，并绘制并研究了由涡旋产生的涡旋和湍流能量耗散。通过对其数学结构的描述，在采用经典动力学湍流模型以及湍流能量耗散与最小涡旋之间的关系的同时，再推导关系，以允许使用湍流的内部和外部长度尺度求解多个湍流参数。然后将这些方程式解为高度轮廓，并具有从处理激光雷达数据获得的必要长度比例尺。最后，定期获取概要文件并将其组合成时间序列，以举例说明该方法并将结果与​​已知文献进行比较。然后将这些方程式解为高度轮廓，并具有从处理激光雷达数据获得的必要长度比例尺。最后，定期获取概要文件并将其组合成时间序列，以举例说明该方法并将结果与​​已知文献进行比较。然后将这些方程式解为高度轮廓，并具有从处理激光雷达数据获得的必要长度比例尺。最后，定期获取概要文件并将其组合成时间序列，以举例说明该方法并将结果与​​已知文献进行比较。