STEADY STREAMING IN OSCILLATORY VISCOUS-FLOW UNDER A TRANSVERSE MAGNETIC-FIELD

In this paper we deal with the oscillatory laminar boundary layer flow of an electrically conducting fluid near an insulating solid body und er a transverse, uniform magnetic field. It is assumed that the two-di mensional flow is produced by an external stream velocity which varies periodically and that the magnetic field induced in the fluid can be neglected. The solution of the boundary layer equations is found by an expansion on the small parameter epsilon (the inverse of the Strouhal number). Both the primary oscillatory flow and the secondary flow whi ch is composed of an oscillatory motion and a steady contribution, i.e . the steady streaming, are analytically determined. The magnetohydrod ynamic (MHD) flow correctly reduces to the hydrodynamic limit when the magnetic field vanishes. However, differently from the hydrodynamic c ase, the MHD second order steady solution satisfies the vanishing of t he steady streaming motion as the distance from the body tends to infi nity. This result is a consequence of the suppression of the only vort icity component, which is perpendicular to the magnetic field. Further , when the magnetic interaction parameter is sufficiently high, the st reaming motion can be completely suppressed. (C) 1997 American Institu te of Physics.