Influence of atmospheric stratification on the integral scale and fractal dimension of turbulent flows

Abstract

In this work the relation between integral scale and fractal dimension and the type of stratification in fully developed turbulence is analyzed. The integral scale corresponds to that in which energy from larger scales is incoming into a turbulent regime. One of the aims of this study is the understanding of the relation between the integral scale and the bulk Richardson number, which is one of the most widely used indicators of stability close to the ground in atmospheric studies. This parameter will allow us to verify the influence of the degree of stratification over the integral scale of the turbulent flows in the atmospheric boundary layer (ABL). The influence of the diurnal and night cycles on the relationship between the fractal dimension and integral scale is also analyzed. The fractal dimension of wind components is a turbulent flow characteristic, as has been shown in previous works, where its relation to stability was highlighted. Fractal dimension and integral scale of the horizontal (u′) and vertical (w′) velocity fluctuations have been calculated using the mean wind direction as a framework. The scales are obtained using sonic anemometer data from three elevations 5.8, 13 and 32 m above the ground measured during the SABLES 98 field campaign (Cuxart et al., 2000). In order to estimate the integral scales, a method that combines the normalized autocorrelation function and the best Gaussian fit (R² ≥ 0.70) has been developed. Finally, by comparing, at the same height, the scales of u′ and w′ velocity components, it is found that the turbulent flows are almost always anisotropic.