  To date, axisymmetric internal wave fields, which have relevance to
atmospheric internal wave fields generated by storm cells and oceanic
near-inertial wave fields generated by surface storms, have been experimentally
realized using an oscillating sphere or torus as the source. Here, we use a
novel wave generator configuration capable of exciting axisymmetric internal
wave fields of arbitrary radial form to generate axisymmetric internal wave
modes. After establishing the theoretical background for axisymmetric mode
propagation, taking into account lateral and vertical confinement, and also
accounting for the effects of weak viscosity, we experimentally generate and
study modes of different order. We characterize the efficiency of the wave
generator through careful measurement of the wave amplitude based upon group
velocity arguments. This established, we investigate the ability of vertical
confinement to induce resonance, identifying a series of experimental resonant
peaks that agree well with theoretical predictions. In the vicinity of
resonance, the wave fields undergo a transition to non-linear behaviour that is
initiated on the central axis of the domain and proceeds to erode the wave
field throughout the domain.
