Aircraft observations of boundary layer turbulence: Intermittency and the cascade of energy and passive scalar variance

Abstract

We analyze boundary layer velocity and temperature measurements acquired by aircraft at 22 Hz. The calculated longitudinal velocity third‐order structure function yields approximate agreement with Kolmogorov's four‐fifths law for the scale range ∼10–100 m with a downscale energy flux of ∼4×10−5 m2 s−3. For scales greater than ∼10 km the sign is reversed, implying an inverse energy cascade with an estimated flux of ∼10−5 m−2 s−3 associated with two‐dimensional stratified turbulence. The mixed structure function of longitudinal velocity and squared temperature increment follows Yaglom's four‐thirds law in the same scale range, yielding an estimated downscale temperature variance flux of ∼5×10−7 K2 s−1. Analysis of higher‐order structure functions yields anomalous scaling for both velocity and temperature. The scaling also reveals second‐order multifractal phase transitions for both velocity and temperature data. Above the transition moments, asymptotes varying with the number of realizations argue against the log‐Poisson model. The log‐Levy model is better able to explain the observed characteristics.