We investigate analytically and numerically the statistical properties of the dynamics of rigid spherical particles with neutral buoyancy. The particles are placed in a turbulent flow with a strong shear component. As a simple model, we consider the shear flow of an axisymmetric vortex with turbulent fluctuations and calculate the particle distribution from the distance to the vortex center. We present quantitative results obtained within the framework of a point particle model with fluctuations that are correlated in time.

In 3D turbulent flows of a rotating system, where the Coriolis force prevails over the inertia in dynamics, formation of the columnar vortices takes place that is observed both experimentally [1] and numerically [2]. They are large-scale coherent flows that are homogeneous along the axis of rotation. Our work is about to build analytical model describing how axisymmetric vortex flow supports itself by absorbing inertial waves. We consider the following pumping mode: inertial waves reach the vortex from the periphery of system, where turbulence is excited. In the limits of short wavelengths and low viscosity we show that quasi-monochromatic wave that enters in the vortex transmits its energy and momentum only in the narrow vicinity of its critical layer [3] formed by an average shear flow. In our model we determine the Reynolds shear stress component averaged over inertial wave ensemble that sets the velocity profile of vortex [4].

[1] D.D. Tumachev, A.A. Levchenko, S.S. Vergeles, S.V. Filatov, Observation of a large stable anticyclone in rotating turbulence, PoF, 36(12), 126620 (2024).
[2] Seshasayanan, K. & Alexakis, A. Condensates in rotating turbulent flows. JFM, 841, 434–462 (2018).
[3] Haynes, P., 2015. Critical Layers. In: G. R. North et al., Encyclopedia of Atmospheric Sciences, 2nd edition, Vol 2.
[4] I.V. Kolokolov, L.L. Ogorodnikov, and S.S. Vergeles, Structure of coherent columnar vortices in three-dimensional rotating turbulent flow, Phys. Rev. Fluids 5, 034604 (2020).