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Dm This explains a number of important results in MHD where the magnetic Reynolds number is large: - the formation of thin sheets or filaments where a major part of the magnetic flux is concentrated, - the maintenance of magnetic turbulence by the turbulence of the velocity field, which in general stretches the magnetic filaments. 2 Fundamental theorems a. Alfven's theorem (1942) In a perfectly conducting fluid, the magnetic flux across a material surface S is constant. This result is the consequence of the global law (II-7) when a~ =.

E. that the other forces have been absorbed by a modified definition of the components of the stress tensor. (In practice the pressure is replaced by the sum of p + pgz, where g represents the gravity and z the upward vertical). The equation of motion is expressed as du; _ F· dCJJi ,+-. 1 Ex= 2 25 (1-92) dv. u dv with a + sign this time, which shows that this power, taken from the magnetic energy as shown in (1-81) is a contribution to the kinetic energy of the system. The other term of the second member can be written (1-94) ff ff and leads to a sum of two powers.

The circulation of the velocity r on a curve which encircles the object once is not only constant along the tube (since div w = 0) but also constant in time. 5 The Reynolds number Except in special conditions, the lengths L and L' are rather difficult to distinguish, the mechanisms characterised by them acting on the whole velocity field. Let us therefore restrict ourselves to the use of the kinematic scale L only. _ _£__ LIU v L 2. (1-76) It is the product of the Reynolds number (1-77) Re =IlL.

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