The Decay of Isotropic Temperature Fluctuations in an Isotropic Turbulence
The Decay of Isotropic Temperature Fluctuations in an Isotropic Turbulence
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各向同性湍流中各向同性温度脉动的衰减
DOI：
10.2514/8.1982
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发表时间：
1951
期刊：
影响因子：
--
通讯作者：
S. Corrsin
中科院分区：
文献类型：
--
作者：
S. Corrsin
冯·卡门和豪沃思（对各向同性湍流）的方法已被应用于衰减的各向同性湍流中各向同性温度波动的衰减，条件是温度差太小而对速度场没有任何影响。从关联方程中可以看出，如果假定相关的二次和三次关联的标量函数下降到零的速度比r~ 2快，则二次温度关联系数的二阶矩与均方温度涨落的乘积在衰减过程中是一个常数。这类似于Loitsiansky关于湍流能量与湍流衰减中速度相关系数的四阶矩的乘积的恒定性的“定理”。对于极小的Peclet数，关联方程简化为具有球对称性的三维热传导方程。相应的速度场线性粘性衰减方程是一个准五维方程。的衰减和规模增长的温度波动t的估计都非常小和非常大的Peclet数的湍流的相应结果进行了比较。也许最实际的结果是，温度“斑点”似乎总是以比速度“斑点”更慢的速度消失。"
The approach of von Karman and Howarth (to isotropic turbulence) has been applied to the decay of isotropic temperature fluctuations in a decaying isotropic turbulence, under the restriction that the temperature differences are too small to have any effect on the velocity field. From the correlation equation it is found that, if the scalar functions characteristic of the pertinent double and triple correlations are assumed to descend to zero faster than r~, the product of the second moment of the double temperature correlation coefficient and the mean square temperature fluctuation is a constant during decay. This is analogous to Loitsiansky's "theorem" for the constancy of the product of turbulent energy and fourth moment of the velocity correlation coefficient in the turbulence decay. For extremely small Peclet Number the correlation equation reduces to the three-dimensional heat conduction equation with spherical symmetry. The corresponding equation for the linear viscous decrement of the velocity field is a quasi-five-dimensional equation. Estimates of decay and scale growth of the temperature fluctuations a t both extremely small and extremely large Peclet Numbers are compared with the corresponding results for the turbulence. Perhaps the most practical result is that the temperature "spottiness" always seems to die off at a slower rate than the velocity "spottiness."