  An asymptotic solution is derived for the motion of inertial particles
exposed to Stokes drag in an unsteady random flow. This solution provides the
finite-time Lyapunov exponents as a function of Stokes number and Lagrangian
strain- and rotation-rates autocovariances. The sum of these exponents, which
corresponds to a concentration-weighted divergence of particle velocity field,
is considered as a measure of clustering. For inertial particles dispersed in
an isotropic turbulent flow our analysis predicts maximum clustering at an
intermediate Stokes number and minimal clustering at small and large Stokes
numbers. Direct numerical simulations are performed for quantitative validation
of our analysis, showing a reasonable agreement between the two.
