Motion of a spherical solid particle in thermal counterflow turbulence

With numerical methods, we formulate and solve a mathematical model of solid-particle motion in thermal counterflow turbulence. We find a direct link between the intensity of vortex-particle collision induced Kelvin waves (vortex-gas ``temperature'') and the intensity of the particle-velocity fluctuations around its mean value. The latter mean value is determined by three factors: (a) the frequency of head-on particle-vortex collisions, (b) the formation of a vortex-tail behind the particle, and (c) the viscous drag. The frequency of head-on particle-vortex collisions depends on (a) the vortex line density, (b) the average tangle drift relative to the particle, and (c) the degree of tangle stratification normal to the counterflow direction. A higher stratification degree reduces the frequency of head-on collisions and allows the vortex-tail effect to dominate. At $T=1.3\text{K}$, vortex voids in the tangle act like barriers to particle motion; the particle-velocity fluctuations are comparable to its mean value and, thus, the particle's direction of motion is sporadically reversed.