  Complex network approaches have been successfully applied for studying
transport processes in complex systems ranging from road, railway or airline
infrastructure over industrial manufacturing to fluid dynamics. Here, we
utilize a generic framework for describing the dynamics of geophysical flows
such as ocean currents or atmospheric wind fields in terms of Lagrangian flow
networks. In this approach, information on the passive advection of particles
is transformed into a Markov chain based on transition probabilities of
particles between the volume elements of a given partition of space for a fixed
time step. We employ perturbation-theoretic methods to investigate the effects
of modifications of transport processes in the underlying flow for three
different problem classes: efficient absorption (corresponding to particle
trapping or leaking), constant input of particles (with additional source terms
modeling, e.g., localized contamination), and shifts of the steady state under
probability mass conservation (as arising if the background flow is perturbed
itself). Our results demonstrate that in all three cases, changes to the steady
state solution can be analytically expressed in terms of the eigensystem of the
unperturbed flow and the perturbation itself. These results are potentially
relevant for developing more efficient strategies for coping with
contaminations of fluid or gaseous media such as ocean and atmosphere by oil
spills, radioactive substances, non-reactive chemicals or volcanic aerosols.
