Effect of a transverse magnetic field on the stability of Hartman flow: three-dimensional instabilities

A numerical study is conducted in order to determine the influence of a transverse magnetic field on the three-dimensional instabilities of the Hartmann flow. We prove that the Squire transformation currently used to characterize such instabilities give satisfactory results only in the case where Ha is weak and 3D modes are slightly deviated from the 2D modes. Such a study is justified by the fact that the two-dimensional instabilities could not always explain successfully the experimental observations relating to the transition phenomenon.