  In this paper we study a well-known three--dimensional turbulence model, the
filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES)
tensor-diffusivity model of turbulent flows with an additional spatial filter
of width alpha ($\alpha$). We show the global well-posedness of this model with
constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence
of a finite dimensional global attractor for this dissipative evolution system,
and we provide an anaytical estimate for its fractal and Hausdorff dimensions.
Our estimate is proportional to $(L/l_d)^3$, where $L$ is the integral spatial
scale and $l_d$ is the viscous dissipation length scale. This explicit bound is
consistent with the physical estimate for the number of degrees of freedom
based on heuristic arguments. Using semi-rigorous physical arguments we show
that the inertial range of the energy spectrum for the Clark-$\aa$ model has
the usual $k^{-5/3}$ Kolmogorov power law for wave numbers $k\aa \ll 1$ and
$k^{-3}$ decay power law for $k\aa \gg 1.$ This is evidence that the
Clark$-\alpha$ model parameterizes efficiently the large wave numbers within
the inertial range, $k\aa \gg 1$, so that they contain much less translational
kinetic energy than their counterparts in the Navier-Stokes equations.
