  We study the mobility and the diffusion coefficient of an inertial tracer
advected by a two-dimensional incompressible laminar flow, in the presence of
thermal noise and under the action of an external force. We show, with
extensive numerical simulations, that the force-velocity relation for the
tracer, in the nonlinear regime, displays complex and rich behaviors, including
negative differential and absolute mobility. These effects rely upon a subtle
coupling between inertia and applied force which induce the tracer to persist
in particular regions of phase space with a velocity opposite to the force. The
relevance of this coupling is revisited in the framework of non-equilibrium
response theory, applying a generalized Einstein relation to our system. The
possibility of experimental observation of these results is also discussed.
