The linear stability of a Stokes layer with an imposed axial magnetic field

The effects of a uniform axial magnetic field directed towards an oscillating wall in a semi-infinite viscous fluid (or Stokes layer) is investigated. The linear stability and disturbance characteristics are determined using both Floquet theory and via direct numerical simulations. Neutral stability curves and critical parameters for instability are presented for a range of magnetic field strengths. Results indicate that a magnetic field directed towards the boundary wall is stabilizing, which is consistent with that found in many steady flows.