  In this work we introduce a well-posed mathematical model for the processes
involved in the artificial circulation of water, in order to avoid
eutrophication phenomena, for instance, in a lake. This novel and general
formulation is based on the modified Navier-Stokes equations following the
Smagorinsky model of turbulence, and presenting a suitable nonhomogeneous
Dirichlet boundary condition. For the analytical study of the problem, we prove
several theoretical results related to existence, uniqueness and smoothness for
the solution of this recirculation model.
