An introduction to magnetohydrodynamics by P. H Roberts
By P. H Roberts
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Extra resources for An introduction to magnetohydrodynamics
The value of Rm is 1000 lJI = - - (1 - 4y 2)4 cos nx. The fluid has to be driven against this force in order to achieve the interaction shown. Once diffusion has severed and reconnected the tubes into one, the two sides of the neck again repel and, since their 51 I : I ~ , J , , , ' • . 4] Electromagnetic Induction repulsion is now unopposed, they separate to produce the almost circular tube shown in the last diagram of the sequence and, in this way, remove the high field gradients. Energetically, the energy supplied to effect the collision is initially passed to the magnetic field.
In the limit t/7:~ -+ 0, (31) reduces simply to Bxit) -+ Bxn(O) = constant, (1]t -+ 0). (36) Alternatively, we may say that, for fixed t, B -+ constant, in the limit 1]. --+ O. This agrees with the observation we made above that, the larger the conductivity, the longer the field and currents in the conductor persist. e. B = B(x, y, z). e. qualitatively speaking, 'the system behaves like a perfect conductor for t ~ 7:~ '. In the limit z/d~ --+ 00, (2I) and (24) reduce to ° lwt --+ - O b e- , I IJ y (37) Alternatively, we may say that, for fixed z (> 0), (37) holds in the limit 11 -+ O.
The result of this diffusion is to separate the fluid from the field lines, allowing them to cross S, in defiance of (45), and pass into V [see Fig. 6(b)]. 4(d) below] is equal and opposite to the speed at which the fluid motion carries them upward. $ and 0/1. It is important to emphasize, however, that the process of creating flux in V is one of detaching flux tubes from the material within them by electromagnetic diffusion. fE/0/I. And this behaviour is not peculiar to this example. fE 2 ; and when Rm ~ I this is evidently much slower.