Point-source inertial particle dispersion

Details Point-source inertial particle dispersion Point-source inertial particle dispersion

2009-05-29

arxiv.org/abs/0905.4955v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, submitted to JFM

Scientific paper

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.

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