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We study a system of Skorokhod stochastic differential equations (SDEs)modeling the pairwise dispersion (in spatial dimension $d=2$) of heavyparticles transported by a rough self-similar, turbulent flow with H\"{o}lderexponent $h\in (0,1)$. Under the assumption that $h>0$ is sufficiently small,we use Lyapunov methods and control theory to show that the Markovian system isnonexplosive and has a unique, exponentially attractive invariant probabilitymeasure. Furthermore, our Lyapunov construction is radially sharp and givespartial confirmation on a predicted asymptotic behavior with respect to theH\"{o}lder exponent $h$ of the invariant probability measure. A physicalinterpretation of the asymptotics is that intermittent clustering is weakenedwhen the carrier flow is sufficiently rough.

Stability and invariant measure asymptotics in a model for heavy particles in rough turbulent flows