The first part of this paper surveys the distinctive features of trains of disturbance waves in high-speed annular two-phase flow. This data is then used to construct a mathematical model that predicts relations between the speed, height, and spacing of the waves, and the net liquid flow rate. These relations highlight the importance of the vorticity in the waves, a quantity that has received little experimental attention. (C) 2014 Elsevier Ltd. All rights reserved.