The transport of vorticity and heat through fluids in turbulent motion
The transport of vorticity and heat through fluids in turbulent motion
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湍流运动中流体的涡度和热量传递
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发表时间：
1932
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通讯作者：
G. Taylor
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作者：
G. Taylor
在雷诺著名的紊流理论中，紊流对流体平均流量的影响被认为与应力系统的影响相同，应力系统与粘性应力系统一样，在任何平面单元上都有切向分量和法向分量。以层流平均流为例，即平均流是水平的，在任何给定高度上的方向和大小都是恒定的，在高度z处水平面上的应力分量为Fx和Fy，其中Fx = - ρ uw-，Fy = - ρ vw-，u，v，w是平行于两个水平轴x和y以及垂直轴z的湍流速度分量。条形表示在较大的水平区域上取得的平均值，ρ是流体的密度。因此，应力F x是由于u和w之间存在相关性。在雷诺理论的扩展中，由于普朗特的原因，这种相关性取决于平均速度的变化率。这个理论可以用最简单的形式表示如下.具有水平z的平均速度的流体的一部分可以被设想为向上移动到高度z +1的层，保持其起源的层的平均速度U。在这个高度，它被认为是与周围环境相混合的。如果l很小，这一层的平均速度是U +1 d U/ dz，U是高度z处的平均速度，因此u = -1 d U/ dz，因此Fx = ρ wl- d U/ dz。因此，量ρ wl-与粘度具有相同的量纲，在普朗特理论中，它实际上被当作一个粘度系数来处理，尽管不一定在场中的所有点上都具有相同的值。
In Reynolds’ well-known theory of turbulent flow the effect of turbulence on the mean flow of a fluid is conceived as the same as that of a system of stresses which, like those due to viscosity, may have tangential as well as normal components across any plane element. Taking the case of laminar mean flow, that is when the mean flow is, say, horizontal and constant in direction and magnitude at any given height, the components of stress over a horizontal plane at height z are F x and F y where F x = — ρ uw— , F y = — ρ vw— , and u , v , w are the components of turbulent velocity parallel to two horizontal axes x and y and the vertical axis z . The bar denotes that mean values have been taken over a large horizontal area and ρ is the density of the fluid. The stress F x , is therefore due to the existence of a correlation between u and w. In the extension of Reynolds’ theory due to Prandtl this correlation depends on the rate of change in mean velocity. In its most simplified form the theory may be expressed as follows. A portion of fluid possessing the mean velocity of a level z may be conceived to move upwards to a layer of height z + l preserving the mean velocity U of the layer from which it originated. At this height it is conceived to mix with its surroundings. If l is small the mean velocity of this layer is U + l d U/ dz , U being the mean velocity at height z , so that u = — l d U/ dz , and hence F x = ρ wl— d U/ dz . The quantity ρ wl— is therefore of the same dimensions as viscosity and in Prandtl’s theory it is treated as though it were in fact a coefficient of viscosity, though not necessarily as one which has the same value at all points in the field.