Shear layer solutions of incompressible MHD and dynamo effect
Résumé
This paper is devoted to the equations of incompressible magnetohydrodynamics (MHD). Its general concern is the "dynamo effect", i.e. the growth of magnetic field through the movement of a conducting fluid. Motivated by the so-called "stretch-diffuse mechanism", we study the nonlinear stability of solutions (u, b = 0) where the velocity u is a regularized vortex sheet, and the magnetic component b is zero. We prove that dynamo effect is possible when both curvature of the sheet and magnetic diffusion are non-zero, and impossible otherwise. (c) 2006 Elsevier Masson SAS. All rights reserved.