Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus

Abstract

Laboratory experiments with a rotating cylindrical annulus are reported that reveal a prograde jet, which is adjacent to a (longitudinally) librating inner straight cylindrical wall. Here, wall libration is realised as a time-harmonic modulation of the inner cylinder's rotation rate. The outer cylindrical wall and bottom and top lids rotate with constant angular velocity. The main purpose of our study is to contribute to a qualitative and quantitative understanding of non-linearities that are present in oscillating, but centrifugally stable, vertical boundary layers frequently encountered in rotating wall-bounded flows. We consider a problem that is in a sense complementary to that of previous works that focused on oscillating Ekman layers but neglected the vertical Stokes−Stewartson layers. A simple analytical model is proposed that is able to predict the magnitude and spatial structure of the emerging prograde near-wall jet in terms of nonlinearity inherent in the inner cylinder's boundary layer dynamics.