Evaluation of the Integral Scale and Fractal Dimension in Stratified Turbulent Flows

The structure of the turbulent flows in the atmosphere boundary layer (ABL) is irregular, with fluid mechanical quantities fluctuate in a disordered manner, with layers of wind that moves at different speeds. The analysis of this structure can be observed in series of wind velocities, the irregular behaviour of these flows is due to the superimposed of waves and turbulence onto a mean wind. These fluctuations are also due to a broad range of scales from the smallest to the largest scales corresponding to the integral scale, where the kinetic energy is maximum. The fractal dimension of wind components determines those flow irregularities and is a turbulent flow characteristic. It is of interest in this work to analyse the correlation between the fractal dimension and integral scale. The mean values of these two magnitudes are related to atmospheric stability and instability. The stratification of the turbulent flow is evaluated with the Bulk Richardson number. We investigate during the diurnal and night cycles how the integral scale and fractal dimension of the components (u') horizontal and (w') vertical velocity influences in stratified turbulent flows. The scales are obtained using sonic anemometer data from three elevations 5.8 m, 13 m and 32 m above the ground measured during the SABLES- 98 field campaign. These components have been calculated using the mean wind direction as framework. The integral scale has been estimated using a method that combines the normalized autocorrelation function and the best Gaussian fit (R2 0.70). The effects of unstable thermal stratification in diurnal hours increase the average values of the integral scale and fractal dimension of both components. During the nights, the existence of the stable stratification decreases the integral scale with increase in fractal dimension. These variations of the average values for u' horizontal component can be adjusted to the straight regression line and for w' vertical component the average values have fit a quadratic function with R2 0.80, in most of the fits. The integral scale for the u' component varies between around 100 m on their smaller scales and above 1500 m for their larger scales. The integral scales for w' component are slightly lower than for the u' component between a few tens of meter and 1000 m. Finally, we study the anisotropy of the turbulent flows by comparing the scales of u` and w` velocity components at the same height.