  Rotationally symmetric bodies with longitudinal cross sections of parabolic
shape are frequently used to model astrophysical objects, such as
magnetospheres and other blunt objects, immersed in interplanetary or
interstellar gas or plasma flows. We discuss a simple formula for the potential
flow of an incompressible fluid around an elliptic paraboloid whose axis of
symmetry coincides with the direction of incoming flow. Prescribing this flow,
we derive an exact analytical solution to the induction equation of ideal
magnetohydrodynamics for the case of an initially homogeneous magnetic field of
arbitrary orientation being passively advected in this flow. Our solution
procedure employs Euler potentials and Cauchy's integral formalism based on the
flow's stream function and isochrones. Furthermore, we use a particular
renormalization procedure that allows us to generate more general analytical
expressions modeling the deformations experienced by arbitrary scalar or
vector-valued fields embedded in the flow as they are advected first towards
and then past the parabolic obstacle. Finally, both the velocity field and the
magnetic field embedded therein are generalized from incompressible to mildly
compressible flow, where the associated density distribution is found from
Bernoulli's principle.
