  In the frame of a three-layer quasi-geostrophic analytical model of a
$f$-plane geophysical flow, Lagrangian advection being induced by the
interaction of a monopole vortex with an isolated topographic feature is
addressed. Two different cases when the monopole locates either within the
upper or the middle layer are of our interest. In the bottom layer, there is a
delta function topographic feature, which generates a closed recirculation
region in its vicinity due to the background flow. This recirculation region
extends to the middle and upper layers, and it plays the role of a topographic
vortex. The interaction between the monopole and the topographic vortex causes
complex, including chaotic, advection of fluid particles. We show that the
model's parameters, namely, the monopole and topographic vortices' strengths
and initial positions, the layers' depths and densities are responsible for the
diverse advection patterns. While the patterns are rather complicated, however,
one can single out two major processes, which mostly govern fluid particle
advection. The first one is the variation in time of the system's phase space
structure, so that within the closed region of the topographic vortex, there
appear periodically unclosed particle pathways by which the particles leave the
topographic vortex. The second one is chaotic advection that arises from the
nonstationarity of the monopole-topography interaction.
