  We consider a dilute gas of inertial particles transported by the turbulent
flow. Due to inertia the particles concentrate preferentially outside vortices.
The pair-correlation function of the particles' concentration is known to obey
at small separations a power-law with a negative exponent, if the hydrodynamic
interactions between the particles are neglected. The divergence at zero
separation is the signature of the random attractor asymptoted by the
particles' trajectories at large times. However the hydrodynamic interactions
produce a repulsion between the particles that is non-negligible at small
separations. We introduce equations governing the repulsion and show it
smoothens the singular attractor near the particles where the pair correlation
function saturates. The effect is most essential at the Stokes number of order
one, where the correlations decrease by a factor of a few.
