# Mean mass transport in an orbitally shaken cylindrical container

## TL;DR

This study experimentally investigates the structure and scaling of mean flows in a cylindrical container undergoing orbital shaking, revealing a robust global rotation and complex vortical patterns influenced by viscosity and forcing frequency.

## Contribution

It provides detailed experimental insights into the mean flow structures and their dependence on physical parameters in orbitally shaken cylindrical containers.

## Key findings

- Global rotation near the center matches Stokes drift predictions.
- Poloidal vortices vary with viscosity and forcing frequency.
- Mean flow structure is influenced by boundary layer dynamics.

## Abstract

A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean flow rotating in the same direction as the wave. Here we investigate experimentally the structure and the scaling of the wave flow and the Lagrangian mean flow in the weakly nonlinear regime, for small forcing amplitude and for forcing frequency far from the resonance, using conventional and stroboscopic particle image velocimetry. The Lagrangian mean flow is composed of a strong global rotation near the center and a non trivial pattern of poloidal recirculation vortices of weaker amplitude, mostly active near the contact line. The global rotation near the center is robust with respect to changes in viscosity and forcing frequency, and its amplitude compares well with the predicted Stokes drift for an inviscid rotating sloshing wave. On the other hand, the spatial structure of the poloidal vortices show strong variation with viscosity and forcing frequency, suggesting that it results from the streaming flow driven by the complex oscillatory boundary layers near the contact line.