The present work develops a model for the turbulent velocity spectra that considers the anomalous behaviour of the turbulent flow. The \(\beta \)-model assumes that the standard Kolmogorov phenomenology is valid only in active turbulence regions, and it proposes an expression for the turbulent velocity spectra in the inertial subrange that is a function of the Hausdorff fractal dimension. From this idea, expressions are obtained for the components of the turbulent velocity spectra that describe the turbulence that exists in geophysical turbulence above the ocean and in very stable situations in the planetary boundary layer where intermittent turbulence occurs. With these spectra, the main parameters used in dispersion models are obtained, that is, the eddy diffusivity and the Lagrangian time scale. The eddy diffusivity is used in an Eulerian dispersion model to estimate the concentration of contaminants in the stable boundary layer. The results obtained are compared with experimental data and other models in the literature.

目前的工作开发了一个湍流速度谱模型，该模型考虑了湍流的异常行为。\ ( \beta \)-模型假设标准 Kolmogorov 现象学仅在活跃湍流区域有效，并且它提出了惯性子范围内的湍流速度谱表达式，该表达式是 Hausdorff 分形维数的函数。根据这个想法，获得了湍流速度谱分量的表达式，描述了海洋上方地球物理湍流中存在的湍流，以及在发生间歇性湍流的行星边界层中非常稳定的情况下存在的湍流。有了这些光谱，就得到了弥散模型中使用的主要参数，即涡流扩散率和拉格朗日时间尺度。在欧拉扩散模型中使用涡流扩散率来估计稳定边界层中污染物的浓度。