<p>The dynamical behaviors of swirling liquid jets in static air surroundings are examined through a combination of experiments and numerical simulations, with particular attention to how angular velocity, jet axial velocity, and liquid viscosity affect the perturbation development and the azimuthal mode transitions. As the angular velocity increases in experiments, the jet presents progressive transitions from axisymmetric mode to helical modes with higher azimuthal wavenumbers. In contrast, the increases of axial flow velocity or jet viscosity are found to promote the mode transitions to smaller azimuthal wavenumbers. Under high angular velocity and low axial velocity, the swirling jet expands radially without forming a stable region, eventually evolving into a radially expanded jet mode. Scaling analyses are developed to characterize the influence of jet angular velocity, axial velocity, and viscosity on characteristic flow features such as perturbation growth rate, perturbation wavelength, and length of stable jet. Three-dimensional numerical simulations are further carried out to explore the flow physics of swirling liquid jets quantitatively. The numerical results reveal that in the radial direction of the jet, the inertia induced by centrifugal force is balanced by pressure, and the centrifugal force increases with the enhancement of rotation. In the azimuthal and axial directions, the inertial forces are primarily balanced by the viscous forces. This work is supposed to offer valuable insights into the instability mechanisms of swirling liquid jets, providing guidance for a wide range of engineering applications.</p>