  We consider three-dimensional stochastically forced Navier-Stokes equations
subjected to white-in-time (colored-in-space) forcing in the absence of
boundaries. Upper and lower bounds of the mean value of the time-averaged
energy dissipation rate, $\mathbb{E} [\langle\varepsilon \rangle] $, are
derived directly from the equations. First, we show that for a weak
(martingale) solution to the stochastically forced Navier-Stokes equations, \[
\mathbb{E} [\langle\varepsilon \rangle] \leq G^2 + (2+
\frac{1}{Re})\frac{U^3}{L},\] where $G^2$ is the total energy rate supplied by
the random force, $U$ is the root-mean-square velocity, $L$ is the longest
length scale in the applied forcing function, and $Re$ is the Reynolds number.
Under an additional assumption of energy equality, we also derive a lower bound
if the energy rate given by the random force dominates the deterministic
behavior of the flow in the sense that $G^2 > 2 F U$, where $F$ is the
amplitude of the deterministic force. We obtain, \[\frac{1}{3} G^2 -
\frac{1}{3} (2+ \frac{1}{Re})\frac{U^3}{L} \leq \mathbb{E} [\langle\varepsilon
\rangle] \leq G^2 + (2+ \frac{1}{Re})\frac{U^3}{L}\,.\] In particular, under
such assumptions, we obtain the zeroth law of turbulence in the absence of the
deterministic force as, \[\mathbb{E} [\langle\varepsilon \rangle] = \frac{1}{2}
G^2.\] Besides, we also obtain variance estimates of the dissipation rate for
the model.
