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.
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机译：我们分析了飞机在22 Hz下获得的边界层速度和温度测量值。计算得出的纵向速度三阶结构函数与Kolmogorov的四分之五定律近似一致，尺度范围为〜10–100 m，下尺度能量通量为〜4×10⁻⁵m²s⁻³。对于大于约10 km的尺度，符号被反转，这意味着能量逆级联，其估计通量为约10 6 m 2 s s 3与二维分层湍流有关。纵向速度和平方温度增量的混合结构函数在相同的比例尺范围内遵循Yaglom的三分之四定律，得出的向下尺度温度变化通量约为5×10 6 K 2 s¹。对高阶结构函数的分析会产生速度和温度的异常缩放。定标还揭示了速度和温度数据的二阶多重分形相变。在过渡时刻之上，随着实现数量而变化的渐近线与对数泊松模型相抵触。对数征税模型能够更好地解释观察到的特征。
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