  Using a 3D Lagrangian tracking technique, we determine experimentally the
trajectories of non-tumbling E. coli mutants swimming in a Poiseuille flow. We
identify a typology of trajectories in agreement with a kinematic "active
Bretherton-Jeffery" model, featuring an axi-symmetric self-propelled ellipsoid.
In particular, we recover the "swinging" and "shear tumbling" kinematics
predicted theoretically by Z\"ottl et al. Moreover using this model, we derive
analytically new features such as quasi-planar piece-wise trajectories,
associated with the high aspect ratio of the bacteria, as well as the existence
of a drift angle around which bacteria perform closed cyclic trajectories.
However, the agreement between the model predictions and the experimental
results remains local in time, due to the presence of Brownian rotational
noise.
