  We consider a Large Eddy Simulation model for a homogeneous incompressible
Newtonian fluid in a box space domain with periodic boundary conditions on the
lateral boundaries and homogeneous Dirichlet conditions on the top and bottom
boundaries, thus simulating a horizontal channel. The model is obtained through
the application of an anisotropic horizontal filter, which is known to be less
memory consuming from a numerical point of view, but provides less regularity
with respect to the standard isotropic one defined as the inverse of the
Helmholtz operator.
  It is known that there exists a unique regular weak solution to this model
that depends weakly continuously on the initial datum. We show the existence of
the global attractor for the semiflow given by the time-shift in the space of
paths. We prove the continuity of the horizontal components of the flow under
periodicity in all directions and discuss the possibility to introduce a
solution semiflow.
