The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{ E} [\varepsilon ]$ and enstrophy dissipation rates $\mathbb{ E} [\chi] $ for 2D flows sustained by a variety of stochastic driving forces. We show that $$\mathbb{ E} [ \varepsilon ] \rightarrow 0 \hspace{ 0.5cm}\mbox{ and} \hspace{ 0.5cm} \mathbb{ E} [ \chi ] \lesssim \mathcal{ O}(1)$$ in the inviscid limit, consistent with the dual-cascade in 2D turbulence.
Categories: physics.flu-dyn math.AP