  The flow in a cylinder driven by time harmonic oscillations of the rotation
rate, called longitudinal librations, is investigated. Using a theoretical
approach and axisymmetric numerical simulations, we study two distinct
phenomena appearing in this librating flow. First, we investigate the
occurrence of a centrifugal instability near the oscillating boundary, leading
to the so-called Taylor-G\"ortler vortices. A viscous stability criterion is
derived and compared to numerical results obtained for various libration
frequencies and Ekman numbers. The strongly nonlinear regime well above the
instability threshold is also documented. We show that a new mechanism of
spontaneous generation of inertial waves in the bulk could exist when the
sidewall boundary layer becomes turbulent. Then, we analyse the librating flow
below the instability threshold and characterize the mean zonal flow correction
induced by the nonlinear interaction of the boundary layer flow with itself. In
the frequency regime where inertial modes are not excited, we show that the
mean flow correction in the bulk is a uniform rotation, independent of the
Ekman number and cylinder aspect ratio, in perfect agreement with the
analytical results of Wang [J. Fluid. Mech., 41, pp. 581 - 592, 1970]. When
inertial modes are resonantly excited, the mean flow correction is found to
have a more complex structure. Its amplitude still scales as the square of the
libration amplitude but now depends on the Ekman number.
