Effect of an Axial Magnetic Field on the Stability of an Axisymmetric Jet or Wake

Abstract

Theoretical calculations on the effect of a uniform axial magnetic field on the sinuous unstable mode of an axisymmetric jet or wake are presented. The fluid is incompressible. The viscous Reynolds number is assumed infinite, and the magnetic Reynolds number is low. The profile studied is trapezoidal with thin shear layers. The calculations are done for small axial wavenumber, α. In the nonmagnetic case, the approximate amplification rate as a function of α agrees with numerical calculations up to the α for maximum amplification rate, when properly scaled. In the magnetic case, a new effect occurs. Due to the helical nature of the instability, the electric field must be nonzero to make the electric current source-free. It is shown that the magnetic field always decreases the amplification rate. The effect is small, of order α2, because the electric field for small α cancels the current generated by fluid crossing field lines.