Vibrational flows in the gap between two infinite cylinders

The flow in the gap between two cylinders with the inner one subject to high frequency vibrations is investigated. The equations for the mean and pulsating components of hydrodynamical fields are formulated taking into account the pulsating transport of the mean vorticity. It is shown that in the case of oscillations of circular polarization the main flow is axisymmetrical. Linear and nonlinear stability of the main flow is treated numerically. It is found that without taking into account the pulsating transport the problem is equivalent to the Couette-Taylor problem for two co-rotating cylinders. II is demonstrated that the pulsating transport effect leads to a marked lowering of the stability threshold and to a change of the secondary flow structure. The limiting case of a small gap is studied analytically.