This work addresses the issue of transverse combustion instabilities in annular gas turbine combustor geometries. While modern low-emissions combustion strategies have made great strides in reducing the production of toxic emissions in aircraft engines and power generation gas turbines, combustion instability remains one of the foremost technical challenges in the development of next generation combustor technology. To that end, this work investigates the response of a swirling flow and swirl-stabilized flame to a transverse acoustic field is using a variety of high-speed laser techniques, especially high-speed particle image velocimetry (PIV) for detailed velocity measurements of this highly unsteady flow phenomenon. A description of the velocity-coupled transverse instability mechanism is explained with companion measurements describing each of the velocity disturbance pathways. Dependence on acoustic frequency, amplitude, and field symmetry is discussed. Significant emphasis is placed on the response of a swirling flow field to a transverse acoustic field. Details of the dynamics of the vortex breakdown bubble and the shear layers are explained using a wide variety of measurements for both non-reacting and reacting flow cases. This thesis concludes with an overview of the impact of this work and suggestions for future research in this area.