A Helmholtz decomposition of structure functions and spectra calculated from aircraft data
A Helmholtz decomposition of structure functions and spectra calculated from aircraft data
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DOI：
10.1017/jfm.2014.685
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发表时间：
2015-01-01
影响因子：
3.7
通讯作者：
Lindborg, Erik
中科院分区：
文献类型：
--
作者：
Lindborg, Erik
纵向和横向结构函数 D-ll = 和 D-tt = delta u(t)delta u(t) 可根据飞机数据计算。这里，d表示相隔距离r的两点之间的增量，u(l)和u(t)分别是平行于和垂直于飞机航迹的速度分量以及平均值。假设统计轴对称并对水平速度进行亥姆霍兹分解，u = u(r) + u(d)，其中 u(r) 是速度的旋转分量，u(d) 是速度的发散分量，我们推导出与结构函数 D-rr = delta u(r) 相关的表达式。 δ u(r) 和 D-dd = δ u(d)。 delta u(d) 至 D-ll 和 D-tt。在谱空间中也推导了相应的表达式。该分解应用于根据飞机数据计算的结构函数。在平流层低层，D-rr 和 D-dd 都对 r epsilon [2, 20] km 表现出良好的 r(2/3) 依赖性。在此范围内，旋转能量和发散能量之间的比率略大于1，不包括重力波作为观测背后的主要因素。在对流层上层，D-rr 和 D-dd 没有表现出明显的 r(2/3) 依赖性，尽管对于 r epsilon [2, 400] km，D-dd 的总体斜率接近 2/3。对于 r < 100 km，旋转能量和发散能量之间的比率约为 3，在这种情况下也不包括重力波。我们认为，在 10 公里量级的分解中可能出现的误差是微乎其微的。
Longitudinal and transverse structure functions, D-ll = and D-tt = delta u(t)delta u(t), can be calculated from aircraft data. Here, d denotes the increment between two points separated by a distance r, u(l) and u(t) the velocity components parallel and perpendicular to the aircraft track respectively and < > an average. Assuming statistical axisymmetry and making a Helmholtz decomposition of the horizontal velocity, u = u(r) + u(d), where u(r) is the rotational and u(d) the divergent component of the velocity, we derive expressions relating the structure functions D-rr = delta u(r). delta u(r) and D-dd = delta u(d). delta u(d) to D-ll and D-tt. Corresponding expressions are also derived in spectral space. The decomposition is applied to structure functions calculated from aircraft data. In the lower stratosphere, D-rr and D-dd both show a nice r(2/3)-dependence for r epsilon [2, 20] km. In this range, the ratio between rotational and divergent energy is a little larger than unity, excluding gravity waves as the principal agent behind the observations. In the upper troposphere, D-rr and D-dd show no clean r(2/3)-dependence, although the overall slope of D-dd is close to 2/3 for r epsilon [2, 400] km. The ratio between rotational and divergent energy is approximately three for r < 100 km, excluding gravity waves also in this case. We argue that the possible errors in the decomposition at scales of the order of 10 km are marginal.