The final period of decay of non-homogeneous turbulence
The final period of decay of non-homogeneous turbulence
复制标题
非均匀湍流衰减的最后时期
DOI：
10.1017/s0305004100031066
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发表时间：
1956
影响因子：
0.8
通讯作者：
O. Phillips
中科院分区：
文献类型：
--
作者：
O. Phillips
本文研究了初始静止的无限大流体在一般局部扰动下的运动特性。两个不变量的运动被发现，这是确定的净线动量，或有效的偶极强度，和净角动量赋予流体，并推导出一个方程表示的有效四极强度的运动的变化率。解决方案得到的最后一段时间的衰减这样的运动，它表明，当净线动量的流体是非零的，运动对应于一种类型的粘性涡环。长度尺度随时间t以[v（t-t0）] 1/2增加，总能量以[v（t-t0）]-1衰减，其中v是运动粘度，t0是虚拟时间原点。如果净动量为零，总能量衰减为，并给出了这种情况下速度场的表达式。它表明，如果它是实现，任何湍流运动的最后一段时间可以找到从涡环型的解决方案，上述。均匀湍流的最后阶段显然是这种运动的一个特殊例子。轴对称紊流尾流的最后一个周期是这样处理的，它通常由两种运动的叠加组成：（i）平均流动运动，其尾流单位长度的能量按[v（t-t0）]-1衰减;（ii）叠加脉动运动，其尾流单位长度的能量按[v（t-t0）]-1衰减。给出了尾流均方涡量分布和能谱张量的表达式。
ABSTRACT In this paper, a study is made of the properties of the motion due to a general localized disturbance in an infinite fluid initially at rest. Two invariants of the motion are found, which are identified with the net linear momentum, or effective dipole strength, and the net angular momentum imparted to the fluid, and an equation is derived expressing the rate of change of the effective quadrupole strength of the motion. Solutions are obtained for the final period of decay of such a motion, and it is shown that, when the net linear momentum of the fluid is non-zero, the motion corresponds to a type of viscous vortex ring. The length scale increases with time t as [ν(t – t0)]½, and the total energy decays as [v(t–t0)]-1, where ν is the kinematic viscosity and t0 is a virtual time origin. If the net momentum is zero, the total energy decays as , and expressions are given for the velocity field in this case also. It is shown that, if it is attained, the final period of any turbulent motion can be found from the vortex ring type of solution described above. The final period of homogeneous turbulence is clearly one particular example of such a motion. The final period of an axially symmetrical turbulent wake is treated in this way and is shown to consist generally of the superposition of two types of motion: (i) a mean streaming motion whose energy per unit length of the wake decreases as [ν(t – t0)]-1, and (ii) a superimposed fluctuating motion whose energy per unit length decays as [v(t–t0)]-1. Expressions are given for the distribution of mean-square vorticity and the energy spectrum tensor in the wake.