New instabilities affecting the meniscus of a viscous fluid are presen
ted. They occur in an experimental set-up introduced previously by Rab
aud et al. (1990) in which a small quantity of a viscous fluid is plac
ed in the narrow gap between two rotating cylinders. In this geometry
the downstream meniscus located in the region where the two solid surf
aces move away from each other is known to be unstable and to exhibit
directional viscous fingering. In the present article it is shown that
the upstream meniscus can also be unstable. Two types of instabilitie
s are observed. In the first supercritical transition the front become
s time-dependent with either standing or propagating waves. In a secon
d transition, which is subcritical, parallel fingers of finite amplitu
de are formed. The various types of spatio-temporal dynamical behaviou
r are discussed.