Spatial and velocity statistics of inertial particles in turbulent flows

Abstract

Abstract. Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re λ ∼ 200 and Re λ ∼ 400, corresponding to resolutions of 512 3 and 2048 3 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular -multifractal-measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events -where particle velocity is approximately the same of the fluid velocity-, and caustic contributions -when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv:1012.1789v1 [physics.fludyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.

Turbulence and cloud droplets in cumulus clouds

“…The efficiency in the Hall table is quite small, and below 0.5 for droplets with a radius of about 30 μm, which are computed for the laminar flows. However, since other studies have reported that the turbulence enhances droplet collisions, it is expected that the collision efficiency of droplets in turbulent flows would be between those for the Hall table and unity [5,6,8,9,11,14,18,19,[57][58][59].…”

“…The central issue in such research has been the growth of the droplet spectrum (size distribution), especially the broadening of the distribution over time. Turbulence fluctuations affect the spatial distribution of cloud condensation nuclei (CCN) and cloud droplets, thereby enhancing droplet clustering via intermittency [5,6,8,11,15,18,19,57,58,76], and supersaturation fluctuations broaden the size distribution of cloud droplets depending on the number density of the aerosols [10,55].…”

“…The condensation process governs droplet growth up to about 30 μm in radius, and collision and coalescence are considered to be the primary mechanisms responsible for subsequent raindrop formation. Over the last two decades, numerous studies have been made in attempts to understand these collisions and various other effects, such as droplet inertia [37,51,53,70,71,73], sedimentation [3,4,20], hydrodynamic interactions [3,46,78], turbulent fluctuations [5,6,8,9,11,14,18,19,[57][58][59], and so on.…”

New insights from comparing statistical theories for inertial particles in turbulence: II. Relative velocities

“…However, recent investigations (e.g. [9][10][11]) have shown that for finite St, S p 2 may deviate significantly from the smooth scaling behavior of S f 2 in the dissipation range (i.e. η ≪ r ), and this has been explained in terms of the formation of 'caustics' (also referred to as the 'sling effect' [12,13] and 'random uncorrelated motion' [14,15], although it should be noted that random uncorrelated motion is really a statistical manifestation of caustics, which are instantaneous events).…”

Continuous growth of cloud droplets in cumulus cloud

“…The collision process of particles in turbulent flow, and its statistical properties, have been studied extensively since Saffman and Turner [18]. Many studies have analytically and numerically examined particle density [19,20], collision frequency [21][22][23][24], and various influences on collision efficiency such as sedimentation [25][26][27], the clustering and spatial distribution of the inertial particles [28][29][30][31][32][33][34][35][36], and the hydrodynamic interaction [37][38][39]. It was found that the collision of cloud droplets with a similar size depends on the Stokes number t t = St p K , where t p and t K are the characteristic time of the droplet and the Kolmogorov time of turbulent flow, respectively, and becomes frequent for ( ) = St O 1 , at which the droplet radius is about 30 μm.…”