By P. H Roberts

ISBN-10: 0582447283

ISBN-13: 9780582447288

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**Extra info for An introduction to magnetohydrodynamics**

**Sample text**

Gradopo = -divo(Po~). 32 (133) (134) (135) (136) - PROBLEMS I I. grad w = -grad ro+IXV 2 W- pV 2 v, divv = divw = 0, where p ro = -', P IX = ·H'1 + v), 2. ' ° 3. ) These solutions are known as 'aligned flows,' since Band U are parallel. _ - . The EquatioiiSof Magnetohyllroaynamrcs'-----' '-----' ---~--"----------'. (Problems] 4. In the text we have evaluated integrals of the type ataJgdV = Jag -at dV, where V is a volume fixed in space. e. a volume whose surface S is always composed of the same elements of fluid, show that J ~tJ gdV = [~~ + diV(9U)] dV.

If Rm ~ 1, the effective electric field IE+u x BI is very small compared with either lEI or lu x BI separately and, except in boundary layers (see below), (6) and (5) reduce, in a first approximation, to aB = curl (u x B), at (Rm ~ 1), (12) E=-uxB, (Rm~I), (13) which are the equations governing induction in a perfect conductor (u = (0). Two consequences of (13) should be noted: first, E is always perpendicular to both u and B; second, although (E+u x B) -+ 0 and u -+ 00, their product j is finite and non-zero (cf.

The approximation v --+ 0 is a familiar one in hydrodynamics. By analogy with the discussion in (b) above we might say that, in the limit v --+ 0, a boundary layer develops on S which contains a net surface vorticity, n, (m/s) and (100) is replaced by

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