We study a system of Skorokhod stochastic differential equations modeling the pairwise dispersion (in spatial dimension \(d=2\) ) of inertial particles transported by a rough turbulent flow with Hölder exponent \(h\in (0,1)\) . Under the assumption that \(h>0\) is sufficiently small, we use Lyapunov methods and control theory to show that the Markovian system is nonexplosive and has a unique, exponentially attractive invariant probability measure. Furthermore, our Lyapunov construction is radially sharp and gives partial confirmation on a predicted asymptotic behavior with respect to the Hölder exponent h of the invariant probability measure. A physical interpretation of the asymptotics is that intermittent clustering is weakened when the carrier flow is sufficiently rough.
