  We consider a system of two cubic-quintic non-linear Schr\"odinger equations
in two dimensions, coupled by repulsive cubic terms. We analyse situations in
which a probe lump of one of the modes is surrounded by a fluid of the other
one and analyse their interaction. We find a realization of D'Alembert's
paradox for small velocities and non-trivial drag forces for larger ones. We
present numerical analysis including the search of static and traveling
form-preserving solutions along with simulations of the dynamical evolution in
some representative examples.
