2020/08/06 by Nadeem A. Malik, Fazle Hussain, Malik, Nadeem A. +1
Earth and Planetary Sciences · Engineering · Environmental Science · #Aeolian processes and effects #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Particle Dynamics in Fluid Flows #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.2008.02911
openalex publication_date 2020/08/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Turbulence consists of interacting flow structures covering a wide range of\nlength and time scales. A long-standing question looms over pair diffusion of\nparticles in close proximity i.e. particle pair diffusion at small separations:\nwhat range of turbulence length scales governs pair diffusion? Here, we attempt\nto answer this question by addressing pair diffusion by both fine scales and\nlarger scale coherent structures in which the fine scales are embedded - we\nunavoidably encounter a combination of both local and non-local interactions\nassociated with the small and large length scales. The local structures possess\nlength scales of the same order of magnitude as the pair separation l, and\nthey induce strong relative motion between the particle pair. However, the\nnon-local structures, possessing length scales much larger than l, also\ninduce (via Biot-Savart) significant relative motion, an effect ignored in\nprior studies (based on Richardson-Obukhov R-O theory). This fundamentally\nchanges the interpretation of the pair diffusion process, giving the pair\ndiffusivity K scaling as K\∼ l1.556 -- agreeing within 1 % of data.\nThe `R-O constant' gl is shown to be not a constant, although widely assumed\nto be a constant. However, new constants (representing pair diffusivity GK\nand pair separation Gl) are identified, which we show to asymptote to\nGK\≈ 0.73 and Gl\∼ 0.01 at high Reynolds numbers. As an\napplication, we show that the radius of a cloud of droplets in a spray is\nsmaller by an order of magnitude as compared to R-O theory.\n