  In this paper we consider the (simplified) 3-dimensional primitive equations
with \emph{physical boundary conditions}. We show that the equations with
constant forcing have a bounded absorbing ball in the $H^1$-norm and that a
solution to the unforced equations has its $H^1$-norm decay to 0. From this, we
argue that there exists an invariant measure (on $H^1$) for the equations under
random kick-forcing.
