Oscillations were imposed on the coaxial air flow of a Swirl-stabilised burner with natural gas fuel injected axially and radially in the centre of the flow and with and without a diffuser at the burner exit. The frequency of the imposed oscillations was varied between 200 and 920 Hz, including a resonance at 350 Hz, over a range of amplitudes and for a range of Swirl numbers from 0 to 0.9 and overall equivalence ratio between 0.2 and 4. Imposed oscillations improved lean-flammability limits without the diffuser and radial fuel injection and Swirl numbers below 0.6 by up to 15% with little dependence on the frequency of the imposed oscillations. Imposed oscillations could either lift-off the flames or reattach already lifted flames due to the influence of the generated vortex rings at the burner exit on flow and mixing. Measurements of flow velocity, flame chemiluminescence for heat release rate and flame shape and mixing of air and fuel in the vortex rings were obtained which allowed to develop a phenomenological model linking mixing between air and fuel with amplitude and frequency of imposed oscillations. The flow measurements quantified the amplitude of imposed oscillations, in terms of rotational velocity of the generated vortex rings, which was directly proportional to the volume flowrate fluctuations at the burner exit. The model identified the oscillation frequency, the bulk flow velocity, the rotational velocity of the generated vortex rings and the penetration depth of the fuel into the vortex rings, as key parameters characterising mixing induced by the vortex rings and the amount of fuel present in the vortices and described them in terms of a dimensionless vortex rotation number and a dimensionless fuel jet penetration length. The ability of the model to describe flame behaviour at different frequencies was verified by showing that flames with constant dimensionless vortex rotation and dimensionless fuel jet penetration length had similar characteristics.