Since most fluid motions are turbulent,it is important to co

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)
yieldsx05
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.Thenx05
V2U = B.curlv.x05(2.9)