Caustic Frequency in 2D Stochastic Flows Modeling Turbulence

Stochastic flows mimicking 2D turbulence in compressible media are considered. Particles driven by such can collide and we study the collision (caustic) frequency. Caustics occur when Jacobian of a flow vanishes. First, system nonlinear stochastic differential equations involving is derived reduced to smaller number unknowns. Then, for special cases forcing, upper lower bounds found mean caustics as function Stokes number. The yield an exact asymptotic small numbers. efficiency verified numerically. As auxiliary results give rigorous proofs well known expressions caustic frequency Lyapunov exponent one-dimensional model. Our findings may also be used estimating time Riemann type partial equation with forcing loses uniqueness solutions.