We calculate the Lyapunov exponents for particles suspended in a randomthree-dimensional flow, concentrating on the limit where the viscous dampingrate is small compared to the inverse correlation time. In this limit Lyapunovexponents are obtained as a power series in epsilon, a dimensionless measure ofthe particle inertia. Although the perturbation generates an asymptotic series,we obtain accurate results from a Pade-Borel summation. Our results prove thatparticles suspended in an incompressible random mixing flow can show pronouncedclustering when the Stokes number is large and we characterise two distinctclustering effects which occur in that limit.
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