Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers

Abstract

In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers Ku, for arbitrary Stokes numbers St. Our results are consistent with those obtained earlier in the limit of small Ku and and large St, such that Ku^2 St remains constant. We show how finite-time correlations and non-ergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.

arXiv comment12 pages, 3 figures

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• Abrupt growth of large aggregates by correlated coalescences in turbulent flow
• Caustics and clustering in the vicinity of a vortex
• Flow structures govern particle collisions in turbulence
• Relative velocities in bidisperse turbulent suspensions
• Relative velocities in bi-disperse turbulent aerosols: simulations and theory
• Statistical model for collisions and recollisions of inertial particles in mixing flows
• Paths to caustic formation in turbulent aerosols
• Lyapunov exponents for particles advected in compressible random velocity fields at small and large Kubo numbers
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• Caustic formation in a non-Gaussian model for turbulent aerosols
• Heavy particles in a persistent random flow with traps
• Fluid dynamics in clouds: The sum of its parts
• Fractal dimensions and trajectory crossings in correlated random walks