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Atmospheric turbulence, recognized as a quintessential space–time chaotic system, can be characterized by its fractal properties. The characteristics of the time series of multiple orders of fractal dimensions, together with their relationships with stability parameters, are examined using the data from an observational station in Horqin Sandy Land to explore how the diurnal variation, synoptic process, and stratification conditions can affect the fractal characteristics. The findings reveal that different stratification conditions can disrupt the quasi-three-dimensional state of atmospheric turbulence in different manners within different scales of motion. Two aspects of practical applications of fractal dimensions are explored. Firstly, fractal properties can be employed to refine similarity relationships, thereby offering prospects for revealing more information and expanding the scope of application of similarity theories. Secondly, utilizing different orders of fractal dimensions, a systematic algorithm is developed. This algorithm distinguishes and eliminates non-turbulent motions from observational data, which are shown to exhibit slow-changing features and result in a universal overestimation of turbulent fluxes. This overestimation correlates positively with the boundary frequency between turbulent and non-turbulent motions. The evaluation of these two aspects of applications confirms that fractal properties hold promise for practical studies on atmospheric turbulence.
Liu et al. (Mon,) studied this question.
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