Unsteady transitional swirling flow in the presence of a moving free surface

Unsteady incompressible viscous flows of a fluid partly enclosed in a cylindrical container with an open top surface are presented in this article. These moving free-surface flows are generated by the steady rotation of the solid bottom end wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry. The top surface of the cylindrical cavity is left open so that the free surface can freely deform. The Reynolds regime corresponds to unsteady transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new nonaxisymmetric flow states that are investigated based on a fully three-dimensional solution of the Navier-Stokes equations for the free-surface cylindrical swirling flow without resorting to any symmetry property unlike all other results available in the literature. The results are compared with those of Bouffanais and Lo Jacono ["Transitional cylindrical swirling flow in presence of a flat free surface," Comput. Fluids 38, 1651 (2009)] corresponding to the exact same parameters but with a flat-and-fixed top free surface. These solutions are obtained through direct numerical simulations based on a highly accurate Legendre spectral element method combined with a moving-grid technique.