Stokes Flow of an Electrically Conducting Fluid in a Uniform Magnetic Field

概要

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The flow of an incompressible, viscous, electrically conducting fluid past an obstacle in a uniform magnetic field is investigated using Stokes approximation. No particular configuration of the flow and the magnetic field is assumed, so that the result applies to the general three-dimensional problems. §§2 and 3 deal with the general theory. It is found that the neutrality of the electric charge density does not hold exactly, when the undisturbed magnetic field is not perpendicular to the vorticity vector. It is also found that the vorticity and the electric current density are confined in a paraboloidal region, thus making a 'wake' which extends in the direction of the undisturbed magnetic field. Distribution of the electric charge density also shows the same structure. In §4, the flow past a sphere is investigated as an example. The drag is obtained in a power series of the Hartmann number M. The component of the drag perpendicular to the undisturbed magnetic line of force is found to be larger than its parallel component. It is pointed out as an interesting feature of the three-dimensional cases that the velocity field includes components which express the two-dimensional irrotational flow.
社団法人日本物理学会の論文
1960-04-05