@MISC{Montgomery_magneticdynamo, author = {David C. Montgomery and P. D. Mininni}, title = {Magnetic dynamo calculations inside a sphere}, year = {} }

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Abstract

This presentation describes some recent computational efforts to demonstrate magnetic dynamo action inside a sphere that is filled with an incompressible electrically conducting fluid, avoiding rectangular periodic boundary conditions. The motivation is ultimately directed toward planetary and laboratory dynamos, but our first concern is to identify and understand the physical processes involved at the simplest level consistent with the magnetohydrodynamic (MHD) equations. The idea is to compute the simplest dynamo situations first, and put in the imaginable complications (thermal convection, irregularities on the inner surface of the Earthâ€™s mantle, variable fluid mass density, a differentially rotating inner core, for examples) one at a time. We are not putting a high priority on realistic numbers at this point. The system studied is a sphere with a weightless, rigid, perfectly conducting shell at a radius r = R. The shell is assumed to be coated on the inside with a very thin layer of insulating dielectric, so that the normal components of the magnetic field and current density vanish there. The normal components of the velocity field and vorticity are also assumed to vanish at r = R. These conditions are implied by, but do not imply, no-slip boundary conditions on the velocity field. In addition to being difficult to implement, there are conceptual difficulties associated with no-slip boundary conditions that remain unresolved (e.g., [1] and [2]) and controversial, and are better engaged with in simpler situations than this one.