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Instabilities of the Ekman‐Hartmann Boundary Layer

 

作者: Peter A. Gilman,  

 

期刊: Physics of Fluids(00319171)  (AIP Available online 1971)
卷期: Volume 14, issue 1  

页码: 7-12

 

ISSN:0031-9171

 

年代: 1971

 

DOI:10.1063/1.1693290

 

出版商: AIP

 

数据来源: AIP

 

摘要:

Gilman and Benton have demonstrated the existence of composite Ekman‐Hartmann layer flow in rotating, electrically conducting fluids permeated by a magnetic field normal to the boundary. This flow was shown to evolve smoothly from a pure Ekman layer to a pure Hartmann layer as the parameter&agr; ≡ (2&mgr;&rgr;&lgr;&OHgr;0)−1/2 B0increases (&mgr; is magnetic permeability,&rgr;is density,&lgr;is magnetic diffusivity,&OHgr;0is the rotation rate, andB0is the imposed magnetic field). Here, it is shown that in the Cartesian, low magnetic Prandtl number limit, this flow exhibits the two instabilities to two‐dimensional rolls characteristic of the pure Ekman layer, but at Reynolds numbers that increase rapidly as&agr;increases. Both rolls decrease in horizontal scale, orient more nearly parallel to the flow far from the boundary, and acquire smaller phase velocities. Coriolis forces are seen to give a parallel roll instability of the Hartmann layer, at much lower Reynolds numbers than given by Roberts for Hartmann layer instability in the absence of rotation.

 

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