Eddy diffusion coefficients and their upper limits based on application of the similarity theory
Eddy diffusion coefficients and their upper limits based on application of the similarity theory
复制标题
基于相似理论应用的涡流扩散系数及其上限
DOI：
10.5194/angeo-33-857-2015
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发表时间：
2015
影响因子：
1.9
通讯作者：
M. Kelley
中科院分区：
文献类型：
--
作者：
M. Vlasov;M. Kelley
抽象。中层和低热层（MLT）中的扩散速度方程包括分子扩散和涡动扩散项。这些术语非常相似。本文首次证明，利用相似理论，可以得到与Weinstock（1981）所导出的常用公式相同的涡动扩散系数公式。后者是以Taylor（1921）导出的扩散积分函数和三维Kolmogorov动能谱为基础得到的。这两个公式的精确一致性意味着方程中所用的涡动扩散系数和热输运系数，无论是扩散系数还是热传导系数，都必须满足一个标准，该标准将外部涡动尺度限制为远小于大气的尺度高度。这个要求与分子的自由程必须远小于大气的标度高度的要求是一样的。这一准则的进一步结果是，从能量耗散率的测量结果中推断出的涡动扩散系数Ked，对于在中间层和低热层（MLT）中测量到的2 W kg−1的能量耗散率的最大值，不能超过3.2 × 106 cm 2 s−1的最大值。这意味着大于最大值的涡流扩散系数对应于具有如此大的外尺度的涡流，以至于不可能在涡流扩散和涡流热输运方程中使用这些系数。将该准则应用于不同的实验数据表明，一些报道的涡流扩散系数不符合该准则。例如，在湍流氧混合实验（TOMEX）中估计的这些系数的大值（1 × 107 cm 2 s-1）不符合这一标准。Lubken（1997）在高纬度地区推断的Ked值在夏季和冬季的极地资料中均满足这一标准，但在低纬度地区夏季的Ked值大于该标准对应的Ked最大值。对流星群观测的实验数据的分析表明，大约0.2 W kg−1的小速率能量耗散有时可以引起湍流，其涡动尺度非常接近大气的尺度高度。我们的结果还解释了Vlasov和Kelley（2014）计算的大冷却速率与MSIS-E-90模型给出的温度之间的差异，因为在这些情况下，用于计算冷却速率的测量涡流扩散系数大于上述最大值。
Abstract. The equation for the diffusion velocity in the mesosphere and the lower thermosphere (MLT) includes the terms for molecular and eddy diffusion. These terms are very similar. For the first time, we show that, by using the similarity theory, the same formula can be obtained for the eddy diffusion coefficient as the commonly used formula derived by Weinstock (1981). The latter was obtained by taking, as a basis, the integral function for diffusion derived by Taylor (1921) and the three-dimensional Kolmogorov kinetic energy spectrum. The exact identity of both formulas means that the eddy diffusion and heat transport coefficients used in the equations, both for diffusion and thermal conductivity, must meet a criterion that restricts the outer eddy scale to being much less than the scale height of the atmosphere. This requirement is the same as the requirement that the free path of molecules must be much smaller than the scale height of the atmosphere. A further result of this criterion is that the eddy diffusion coefficients Ked, inferred from measurements of energy dissipation rates, cannot exceed the maximum value of 3.2 × 106 cm2 s−1 for the maximum value of the energy dissipation rate of 2 W kg−1 measured in the mesosphere and the lower thermosphere (MLT). This means that eddy diffusion coefficients larger than the maximum value correspond to eddies with outer scales so large that it is impossible to use these coefficients in eddy diffusion and eddy heat transport equations. The application of this criterion to the different experimental data shows that some reported eddy diffusion coefficients do not meet this criterion. For example, the large values of these coefficients (1 × 107 cm2 s−1) estimated in the Turbulent Oxygen Mixing Experiment (TOMEX) do not correspond to this criterion. The Ked values inferred at high latitudes by Lubken (1997) meet this criterion for summer and winter polar data, but the Ked values for summer at low latitudes are larger than the Ked maximum value corresponding to the criterion. Analysis of the experimental data on meteor train observations shows that energy dissipation with a small rate of about 0.2 W kg−1 sometimes can induce turbulence with eddy scales very close to the scale height of the atmosphere. Our results also explain the discrepancy between the large cooling rates calculated by Vlasov and Kelley (2014) and the temperatures given by the MSIS-E-90 model because, in these cases, the measured eddy diffusion coefficients used in calculating the cooling rates are larger than the maximum value presented above.