Lagrangian versus Eulerian view on the mean drift and streaming flows in orbital sloshing

Orbital sloshing, a common technique in fluid mixing for processes like cell cultivation and fermentation, generates complex wave dynamics at the interface and a hidden Lagrangian mean flow in the fluid bulk. Distinguishing between the Eulerian viscous streaming and Stokes drift contributions to the overall Lagrangian motion has remained challenging, particularly in highly viscous fluids. This study presents a weakly nonlinear analysis, revealing that Stokes drift and Eulerian viscous corrections can be equally important in the mean flow generation, offering new insights into orbital sloshing wave dynamics beyond traditional inviscid models.