Effects of compressibility on turbulent relative particle dispersion

Abstract

In this paper, phenomenological developments are used to explore several aspects of the relative particle dispersion (RPD) in different physical fully-developed turbulence (FDT) situations. The role played by the FDT cascade physics underlying this process is investigated. Many of these aspects are motivated by previous laboratory experiment and numerical simulation results. These are, * spatial intermittency effects exhibiting, (a) reduction of RPD in 3D FDT, corroborating the numerical simulation results (Boffetta and Sokolov [11]); (b) prevalence of power-law scaling of RPD in 2D FDT enstrophy cascade (no matter how weak spatial intermittency effects are), corroborating the difficulty in observing Lin [12] exponentical scaling law in laboratory experiments (Jullien [13]); * quasi-geostrophic FDT aspects exhibiting an enhanced RPD in the baroclinic regime of the energy cascade and a negative eddy-viscosity development to shed some insight into this aspect;* quasi-geostrophic FDT aspects exhibiting particle clumping in the baroclinic regime of the enstrophy cascade; * reduction of RPD, development of the ballistic regime and particle clustering due to compressibility effects in FDT, corroborating the laboratory experiment and numerical simulation results (Cressman et al. [14]).These results are developed from the established scaling relations for the various physical FDT cases and are further validated via alternative dimensional/scaling developments for the various physical FDT cases similar to the one given for 3D FDT by Batchelor and Townsend [15].