Hydromagnetic Instability of a Two-Dimensional Jet at Small Magnetic Reynolds Numbers

The effect of a uniform and parallel magnetic field upon the instability of a Bickley jet is investigated at small magnetic Reynolds numbers. The equation of disturbance is solved numerically and it is shown that the flow is stabilized with the magnetic field. The change of the lowest critical Reynolds number R c is shown graphically. When magnetic field is measured by the parameter S (\({=}\sqrt{MR}\)), where M is the Hartmann number and R is the Reynolds number, R c is caused by the two-dimensional disturbance provided 0≦ S <5.5. For S >5.5, R c is expressed as R c =3.3 S and the responsible disturbance is the three-dimensional one which propagates at angle cos -1 (5.5/ S ) to the direction of the basic flow.