Dynamics of inertial particles in a random flow with strong permanent shear

Abstract: We consider advection of small inertial particles by a random fluid flow with a strong steady shear component. It is known that inertial particles suspended in a random flow can exhibit clusterization even if the flow is incompressible. We study this phenomenon through statistical characteristics of a separation vector between two particles. As usual in a random flow, moments of distance between particles grow exponentially. We calculate the rates of this growth using the saddle-point approximation in the path-integral formalism. We also calculate correction to the Lyapunov exponent due to small inertia by a perturbation theory expansion.