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.