Transport of an inertial particle advected by a two-dimensional steady laminar flow is numerically investigated in the presences of a constant force and a periodic potential. Within particular parameter regimes this system exhibits absolute negative mobility, which means that the particle can travel in a direction opposite to the constant force. It is found that the profile of the periodic potential plays an important role in the nonlinear response regime. Absolute negative mobility can be drastically enhanced by applying appropriate periodic potential, the parameter regime for this phenomenon becomes larger and the amplitude of negative mobility grows exceedingly large (giant negative mobility). In addition, giant positive mobility is also observed in the presence of appropriate periodic potential.
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