Since most fluid motions are turbulent,it is important to consider whether (2.6) still holds in any sense for turbulent flows.If we denotetime-mean quantities by a bar and turbulent fluctuations by a dash (so that U =U +Q,for instance),taking the tim

Since most fluid motions are turbulent,it is important to consider whether (2.6) still holds in any sense for turbulent flows.If we denotetime-mean quantities by a bar and turbulent fluctuations by a dash (so that U =U +Q,for instance),taking the tim
Since most fluid motions are turbulent,it is important to consider whether (2.6) still holds in any sense for turbulent flows.If we denote
time-mean quantities by a bar and turbulent fluctuations by a dash (so that U =U +Q,for instance),taking the time-mean of (2.6)
yields\x05
V2t=div(vxB + VxB/).\x05(2.7)
The second vector product term will be negligible for various reasons:there appears to be no reason to expect any strong correlation between the random velocity and field fluctuations;
the quantity B' is an induced field and,as will be seen in ch.3,is usually small in comparison with the imposed field even with liquid metals.With electrolytes it is quite negligible.Then,if we leave the last term out of (2.7),it simply becomes (2.6),interpreted so as to apply to the mean values of U,v and B.Thus the fact that a flow may be turbulent does not complicate the issue.An electromagnetic flowmeter can still measure the mean velocity.
Using a vector identity we may rewrite (2.6) as
\x05V2£7 = B.curlv-v.curlB,\x05(2.8)
in which the last term may be omitted if the magnetic field is not seriously affected by induced currents in the fluid (so that curl B = 0) and in any case if these currents flow perpendicularly to the fluid motion.Then\x05
V2U = B.curlv.\x05(2.9)

Since most fluid motions are turbulent,it is important to consider whether (2.6) still holds in any sense for turbulent flows.If we denotetime-mean quantities by a bar and turbulent fluctuations by a dash (so that U =U +Q,for instance),taking the tim
因为大多数流体运动是湍流的, 重要的是要考虑是否(2.6)仍然对湍流流动有意义.
如果我们用一杠表示均时量, 用一斜杠表示湍流波动 (例如, U = U + Q), 采用(2.6)的均时, 则
V2t = div(vxB + vxB /).(2.7)
第二个矢量的乘积项可忽略不计, 原因有多种：显然,没有理由预期在任何随机速度和磁场波动之间具有很强的相关性.
量B是一个感应磁场, 将出第三章中阐述. 通常与所施加的磁场甚至与液体金属相比都是很小的.由于电解质也可以忽略不计, 如果我们再把(2.7)的最后一项抛开, ,它就变成(2.6)了, 由此而解释了如何用于均值U, v和b .因此,流动可以是湍流,但并不意味着是问题.因此电磁流量计仍然可以测量均速. 使用矢量我们可以重写(2.6)
V2£7 = B.curlv-v.curlB(2.8)
如果在流体中的诱导电流不会严重地影响磁场 (所以 curl B = 0),其中最后一项可忽略不计.
在任何情况下,如果这些电流流动垂直于流体运动, 则
V2U = B.curlv.(2.9)