A profiled structure for an aircraft or turbomachine is elongated in a direction in which the structure has a length exposed to an airflow and includes serrations defined by successive teeth and depressions. The serrations may be transverse to a leading edge and/or a trailing edge of the profiled structure and in the direction of elongation. Along the profiled leading edge and/or profiled trailing edge, the successive teeth and depressions may extend only over a part of the length exposed to the flow. The amplitude and/or spacing of the teeth may vary monotonically except for the few teeth nearest each end of the part, with a remaining part of the length being smooth.