Turbulent pair dispersion in the presence of gravity

Abstract

Turbulent pair dispersion of heavy particles is strongly altered when particles of two different Stokes numbers (bidisperse) are considered, and this is further compounded when a uniform gravitational acceleration is present. Lagrangian trajectories of fluid tracers, and bidisperse heavy particles with and without gravity were calculated from a direct numerical simulation of homogeneous, isotropic turbulence. Particle pair dispersion shows a short-time, ballistic (Batchelor) regime and a transition to super-ballistic dispersion that is suggestive of the emergence of Richardson scaling. A simple equation of motion for inertial, sedimenting particles captures the essential features of the pair dispersion at very short time and length scales. Kolmogorov scaling arguments are able to qualitatively describe the competition between gravity-induced and fluid-induced relative motion in modifying the amount of time the heavy particles spend in the ballistic regime. The transition from ballistic to super-ballistic dispersion for fluid tracers and monodisperse inertial particles exhibits a pronounced sub-ballistic behavior that can be attributed to the mixed velocity-acceleration structure function. The sub-ballistic behavior is strongly suppressed for bidisperse particles, both in the presence or absence of gravity, primarily because of a reduction in the correlation between velocity and acceleration increments. inherent aesthetic and intellectual merit. The parameter space corresponding to the inertial particle dispersion problem is enormous, so we use atmospheric clouds as a context for restricting the region of study within that space: particles small compared to the Kolmogorov length scale, heavy compared to the surrounding fluid, and obeying to good approximation a linear (Stokes) drag law. Significantly, from the point of view of this study, clouds consist of a population of condensing or evaporating water droplets advected by turbulent air flow in a thermodynamically varying environment, with the result that the size distribution of droplets can be quite broad [14]. There is considerable computational and experimental evidence already that different sizes and therefore different inertial response, can lead to significant changes in the behavior of inertial particles. For example, the tendency to cluster weakens in the case of inertial particles with a broad size distribution (e.g. [15,16]). Furthermore, the dynamics of this polydisperse population of particles can be significantly modified by the presence of a gravitational acceleration that results in particle decoupling from the fluid motions, and perhaps more importantly, a relative velocity of different-sized particles falling at terminal speed [17,18]. Simple Kolmogorov dissipative range scaling arguments (e.g. [19]) suggest that the mean turbulent acceleration in clouds is in the approximate range of 0.1-1 m s −2 , much less than gravitational acceleration. This has the consequence that gravity very likely has an immediate effect on the dispersion of polydispe...

Life and death of inertial particle clusters in turbulence

“…Because, here, we consider clusters with complex shapes and a broad range of sizes, a direct comparison with results obtained for particle-pair dispersion is not straightforward. We notice, however, that the slower separation in presence of gravity is qualitatively consistent with the results of Chang et al (2015). Fourth, and perhaps most striking, the radius of gyration shows only marginal variations during the cluster lifetime, indicating that the relative distance between the particles remains approximately unchanged during the lifetime.…”

“…only recently (Bec et al 2010;Chang, Malec & Shaw 2015;Bragg et al 2016): its impact on the particle dispersion rate compared to fluid tracers was found to be non-monotonic in time and strongly dependent on the initial separation. Because, here, we consider clusters with complex shapes and a broad range of sizes, a direct comparison with results obtained for particle-pair dispersion is not straightforward.…”

Enhanced and suppressed multiscale dispersion of bidisperse inertial particles due to gravity

“…We found that for particles with |∆St| ≥ 0.5, gravity enhances the mean-square separations of the particles both forward in time (FIT) and backward in time (BIT), whereas it suppresses the relative dispersion of weakly bidisperse particles with |∆St| = 0.1. We also observed that the duration over which the particles separate ballistically is much larger when they are subjected to gravity as compared to the case without gravity, as was also observed in [29] for weakly inertial particles. For Froude number F r = 0.052, the vertical relative dispersion is enhanced for the range of Stokes numbers considered, and the enhancement is primarily due to the differential sedimentation of the particles.…”

Long‐lifetime ice particles in mixed‐phase stratiform clouds: Quasi‐steady and recycled growth

“…This is in contrast to pair or multiparticle dispersion, for which subgrid‐scale velocity fluctuations are important when the initial particle separations are less than the grid scale [ Weil et al , ]. Second, strongly sedimenting particles tend to smooth over small‐scale, high‐frequency velocity fluctuations within the turbulent flow [ Chang et al , ]. The unresolved small scales in the LES are likely to be smoothed over based on the following observations.…”