2002/10/31 by Victor S. L’vov, Victor S. L'vov, Gijs Ooms +2
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Aeolian processes and effects #Granular flow and fluidized beds #Particle Dynamics in Fluid Flows #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.67.046314
published as Phys. Rev. E, 67 046314 (2003). · 21 pages, 5 figues,included, PRE, submitted
arxiv created 2003/02/04 · openalex publication_date 2003/04/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose a one-fluid analytical model for a turbulently flowing dilute suspension, based on a modified Navier-Stokes equation with a k-dependent effective density of suspension rho(eff)(k) and an additional damping term proportional, variant gamma(p)(k), representing the fluid-particle friction (described by Stokes law). The statistical description of turbulence within the model is simplified by a modification of the usual closure procedure based on the Richardson-Kolmogorov picture of turbulence with a differential approximation for the energy transfer term. The resulting ordinary differential equation for the energy budget is solved analytically for various important limiting cases and numerically in the general case. In the inertial interval of scales, we describe analytically two competing effects: the energy suppression due to the fluid-particle friction and the energy enhancement during the cascade process due to decrease of the effective density of the small-scale motions. An additional suppression or enhancement of the energy density may occur in the viscous subrange, caused by the variation of the extent of the inertial interval due to the combined effect of the fluid-particle friction and the decrease of the kinematic viscosity of the suspensions. The analytical description of the complicated interplay of these effects supported by numerical calculations is presented. Our findings allow one to rationalize the qualitative picture of the isotropic homogeneous turbulence of dilute suspensions as observed in direct numerical simulations.