Combustion instability plagues the combustion community in a wide range of applications. This un-solved problem is especially prevalent and expensive in aerospace propulsion and ground power generation. The challenges associated with understanding and predicting combustion instability lie in the flame response to the acoustic field. One of the more complicated flame response mechanisms is the velocity coupled flame response, where the flame responds dynamically to the acoustic velocity as well as the vortically induced velocity field excited by the acoustics. This vortically induced, or hydrodynamic, velocity field holds critical importance to the flame response but is computationally expensive to predict, often requiring high fidelity CFD computations. Furthermore, its behavior can be a strong function of the numerous flow parameters that change over the operability map of a combustor. This research focuses on a nominally two dimensional bluff body combustor, which has rich hydrodynamic stability behavior with a manageable number of stability parameters. The work focuses first on experimentally characterizing the dynamical flow and flame behavior. Next, the research shifts focus toward hydrodynamic stability theory, using it to explain the physical phenomena observed in the experimental work. Additionally, the hydrodynamic stability work shows how the use of simple, model analysis can identify the important stability parameters and elucidate their governing physical roles. Finally, the research explores the forced response of the flow and flame while systematically varying the underlying hydrodynamic stability characteristics. In the case of longitudinal combustion instability of highly preheated bluff body combustors, it shows that conditions where an acoustic mode frequency equals the hydrodynamic global mode frequency are not especially dangerous from a combustion instability standpoint, and may actually have a reduced heat release response. This demonstrates the very non-intuitive role that the natural hydrodynamic flow stability plays in the forced heat release response of the flame. For the fluid mechanics community, this work contributes to the detailed understanding of both unforced and forced bluff body combustor dynamics, and shows how each is influenced by the underlying hydrodynamics. In particular, it emphasizes the role of the density-shear layer offset, and shows how its extreme sensitivity leads to complicated flow dynamics. For the flow-combustor community as a whole, the work reviews a pre-existing method to obtain the important flow stability parameters, and demonstrates a novel way to link those parameters to the governing flow physics. For the combustion instability community, this thesis emphasizes the importance of the hydrodynamic stability characteristics of the flow, and concludes by offering a paradigm for consideration of the hydrodynamics in a combustion instability problem.