  We study the nonlinear response to an external force of an inertial tracer
advected by a two-dimensional incompressible laminar flow and subject to
thermal noise. In addition to the driving external field $F$, the main
parameters in the system are the noise amplitude $D_0$ and the characteristic
Stokes time $\tau$ of the tracer. The relation velocity vs force shows
interesting effects, such as negative differential mobility (NDM), namely a
non-monotonic behavior of the tracer velocity as a function of the applied
force, and absolute negative mobility (ANM), i.e. a net motion against the
bias. By extensive numerical simulations, we investigate the phase chart in the
parameter space of the model, $(\tau,D_0)$, identifying the regions where NDM,
ANM and more common monotonic behaviors of the force-velocity curve are
observed.
