An atmospheric pressure swirl-stabilized methane-air burner has been developed as a test platform for nanosecond repetitively pulsed (NRP) discharge plasma-assisted combustion research. Qualitative flame and plasma discharge characterizations were conducted with high-speed video and low-light ICCD imagery, along with a modal acoustic analysis of the entire assembly. A large eddy simulation (LES) of the burner was created using the commercial solver Ansys Fluent to investigate the plasma effects on swirl-stabilized turbulent combustion. A modified version of the solver's premixed combustion mechanism is presented along with a phenomenological plasma discharge model to simulate plasma-assisted combustion. Cold flow particle image velocimetry (PIV) data were collected to validate the non-reacting flow field and assess non-reacting NRP discharge effects. Optical emission spectroscopy (OES) measurements of the second positive system (SPS) of nitrogen mapped temperature characteristics of NRP discharge bursts for comparison to time-resolved simulation data. Finally, time-averaged CH* chemiluminescence data were collected to qualitatively assess the effects of plasma on the experimental burner and simulated flame structure. Overall, the phenomenologically-based combustion mechanism proposed in this work shows good agreement with several experimental observations and provides a promising framework for future plasma-assisted combustion modeling.