  This article is devoted to the study of an incompressible viscous flow of a
fluid partly enclosed in a cylindrical container with an open top surface and
driven by the constant rotation of the bottom wall. Such type of flows belongs
to a group of recirculating lid-driven cavity flows with geometrical
axisymmetry and of the prescribed boundary conditions of Dirichlet type --
no-slip on the cavity walls. The top surface of the cylindrical cavity is left
open with an imposed stress-free boundary condition, while a no-slip condition
with a prescribed rotational velocity is imposed on the bottom wall. The
Reynolds regime corresponds to transitional flows with some incursions in the
fully laminar regime. The approach taken here revealed new flow states that
were 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. Theses solutions are obtained through direct numerical
simulations based on a Legendre spectral element method.
