A damper seal for a turbomachine includes an annular body having an inner circumferential surface and an outer circumferential surface separated by a thickness. As such, the inner circumferential surface may define a plurality of cavities arranged into a plurality of circumferential rows and at least one partition positioned between at least two of the plurality of cavities. In addition, the inner circumferential surface may further define at least one plenum arranged between two of the plurality of circumferential rows.