2009/05/29 by Marco Martins Afonso, Afonso, Marco Martins, Andrea Mazzino +1
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Aeolian processes and effects #Chaotic Dynamics (nlin.CD) #Classical Physics (physics.class-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Other Condensed Matter (cond-mat.other) #Particle Dynamics in Fluid Flows #Wind and Air Flow Studies #cond-mat.other #nlin.CD #nlin.SI #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0905.4955
10 pages, submitted to JFM
arxiv created 2009/05/29 · openalex publication_date 2009/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.