Effect of particle inertia on the turbulence in a suspension

We propose a one-fluid analytical model for a turbulently flowing dilute suspension, based on modified Navier-Stokes equation with a $k$-dependent effective density of suspension, $\rho_ {eff}(k)$, and an additional damping term $\propto \gamma_ p(k)$, 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.Comment: 21 pages, 5 figues,included, PRE, submitte

The influence of temperature dynamics and dynamic finite ion Larmor radius effects on seeded high amplitude plasma blobs

Thermal effects on the perpendicular convection of seeded pressure blobs in the scrape-off layer of magnetised fusion plasmas are investigated. Our numerical study is based on a four field full-F gyrofluid model, which entails the consistent description of high fluctuation amplitudes and dynamic finite Larmor radius effects. We find that the maximal radial blob velocity increases with the square root of the initial pressure perturbation and that a finite Larmor radius contributes to highly compact blob structures that propagate in the poloidal direction. An extensive parameter study reveals that a smooth transition to this compact blob regime occurs when the finite Larmor radius effect strength, defined by the ratio of the magnetic field aligned component of the ion diamagnetic to the $\vec{E}\times\vec{B}$ vorticity, exceeds unity. The maximal radial blob velocities agree excellently with the inertial velocity scaling law over more than an order of magnitude. We show that the finite Larmor radius effect strength affects the poloidal and total particle transport and present an empirical scaling law for the poloidal and total blob velocities. Distinctions to the blob behaviour in the isothermal limit with constant finite Larmor radius effects are highlighted

Nonlinear damping of slab modes and cosmic ray transport

By applying recent results for the slab correlation time scale onto cosmic ray scattering theory, we compute cosmic ray parallel mean free paths within the quasilinear limit. By employing these results onto charged particle transport in the solar system, we demonstrate that much larger parallel mean free paths can be obtained in comparison to previous results. A comparison with solar wind observations is also presented to show that the new theoretical results are much closer to the observations than the previous results

Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxen forces

The dynamics of particles in turbulence when the particle-size is larger than the dissipative scale of the carrier flow is studied. Recent experiments have highlighted signatures of particles finiteness on their statistical properties, namely a decrease of their acceleration variance, an increase of correlation times -at increasing the particles size- and an independence of the probability density function of the acceleration once normalized to their variance. These effects are not captured by point particle models. By means of a detailed comparison between numerical simulations and experimental data, we show that a more accurate model is obtained once Faxen corrections are included.Comment: 10 pages, 4 figure