Electrically Induced Vortical Flows by V. Bojarevičs, J. A. Freibergs, E. I. Shilova, E. V.

By V. Bojarevičs, J. A. Freibergs, E. I. Shilova, E. V. Shcherbinin (auth.)

Every clinical topic most likely conceals unexplored or little investigated strata, that can appear on the right time while beneficial stipulations coincide (practical calls for, a circle of scientists ready to acknowledge the newness and able to giving impetus to the advance of a brand new concept, etc.). whatever like this happened in early seventies for magnetohydrodynamics, which on the time used to be thought of to be a comparatively entire department of hydro­ dynamics with out obvious extensive, unexplored parts. It was once unexpectedly discovered that, as well as the normal tools of affecting an electrically carrying out medium, there's yet one more means, one that accordingly bring about a brand new course in magnetohydrodynamics. within the Soviet medical literature this course has been termed 'electrically precipitated vortex flows', the essence of that are hydrodynamic results as a result of interplay of an electrical present passing during the fluid with its personal magnetic box. It can't be acknowledged that this path was once created ex nihilo: person stories on the topic of the flows pushed in a current-carrying medium within the absence of exterior magnetic fields seemed within the sixties; within the thirties the flows them­ selves have been identified to happen inside electric arcs; and but the 1st observa­ tions at the behaviour of liquid current-carrying conductors have been made in the beginning of this century.

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VI ~. ~ ;:, ~ ;::: ~ ~ S ~ ;:, ~ o· a s· o .... ~ ~ ;::;. Q, ~ ~. ~ '1j '1:l ~ ;::;. 1. (continued) ,. u _1 ... u 2 )[(1 Flow around a nonconducting disc in uniform current - - 4 3 ....... ::l ~ ;: ~ '"0~ ~ ~ ""s' ;: 6' 2$ o ;:;' ~ ~ '< Table 1,1, (continued) ~ ~ Ei' ...... ~ '"~' ~ Cl '1:::l ;:;' 54 Chapter 1 Maxwell's equation j = 1/lio curl 8 expressed for the axisymmetric case in the form 1 j= H)i) H2i2 H3 i3 d dq, d dq2 H)B) H2B2 ° 1 H,H 2H 3 lio H3 B CP it follows that f, = 1 liD 1 H2 H 3 d q2 - - - -d- H3Brp , lId - - - - - H3 Brp, liD H,H3 dq, f2 = - - f3 = frp = _1_ H 1H liD '2 (-l-q, H2B2 - d: 2 H,B,).

1. 1. (continued) r -In R(I Semi-infinite line source and sink separated by distance 2a from each other I 1-11 -In - 2 1 + 11 A; 1 A-I -In - 2 A+1 11; + cos 0) R(I - cos 0); 4 Coordinates o/prolate spheroid Semi-infinite line source (sink) 3 - I,C) ~ ~. 0·o~ r;. :;; ~ ~ ~ ~ '< ~ ~ ;:;. ~. ;:;. ~ "I:J (3 "I:J ~ r;. 1. (continued) r I" Flow around a nonconducting prolate spheroid placed in uniform current Line source and sink of finite length a 3 , A-I n+- 1- - 2 ) ( A lA + fl2) A-I + 2eA ] Ail - 1 A() + -,--; A+l /-I.

Solutions of the equations E2'I/JI = 0 and V2 = 0 determine the functions 'l/JI and apart from constant terms. 1) of this system, the former ones describe the surfaces of electrical insulators and the latter are the surfaces of ideally conducting electrodes. 13) in spherical coordinates: a2lP, aR 2 e sin a + ~ ae 1 sin e alP, ~ = O. 3) n(n - I)M = O. 4) The solutions of these equations are well known [41. 3) is + B fl R'-I1. 6) the particular solutions of which are Gegenbauer functions of the two kinds of order -1/2 and degree n.

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