This thesis addresses some of the central issues in the combustion dynamics of annular systems, essentially focusing on understanding, interpreting, and predicting combustion instabilities coupled with azimuthal modes. These modes are the most dangerous among those encountered in gas turbines and aero-engines as they correspond to the lowest eigenfrequencies where combustion is most sensitive to incoming disturbances. The work specifically considers the case where the flames established in the combustor are formed by a spray of liquid fuel and on injection systems generating a swirling flow, idealizing those found in practical applications. Systematic experiments are carried out on a multiple-injector annular combustor (MICCA-Spray), allowi...