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Reynolds stress: Difference between revisions
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<ref>[http://dx.doi.org/10.1088/0741-3335/43/10/308 S.B. Korsholm et al, ''Reynolds stress and shear flow generation'', Plasma Phys. Control. Fusion '''43''' (2001) 1377]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/43/10/308 S.B. Korsholm et al, ''Reynolds stress and shear flow generation'', Plasma Phys. Control. Fusion '''43''' (2001) 1377]</ref> | ||
Starting from the incompressible momentum balance equation, neglecting the dissipative pressure tensor: | Starting from the incompressible momentum balance equation, neglecting the dissipative pressure tensor, in slab coordinates: | ||
<ref>R. Balescu, ''Aspects of Anomalous Transport in Plasmas'', Institute of Physics Pub., Bristol and Philadelphia, 2005, ISBN 9780750310307</ref> | <ref>R. Balescu, ''Aspects of Anomalous Transport in Plasmas'', Institute of Physics Pub., Bristol and Philadelphia, 2005, ISBN 9780750310307</ref> | ||
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:<math>\frac{\partial u_y}{\partial t} + \nabla_x \left ( u_x u_y \right ) = 0</math> | :<math>\frac{\partial u_y}{\partial t} + \nabla_x \left ( u_x u_y \right ) = 0</math> | ||
It may seem as if one has lost all information concerning the background field. | |||
However, this is not true, as the choice of the ''x,y,z'' coordinate system depends, precisely, on the background magnetic field (and, in particular, on the cited flux surfaces). | |||
The corresponding anisotropy is in fact essential to the effectiveness of the Reynolds Stress mechanism. | |||
Now, writing the flow as the sum of a mean and a fluctuating part | Now, writing the flow as the sum of a mean and a fluctuating part | ||