Spatial development of single void pulse in a horizontal turbulent bubbly channel flow investigated by a time-resolved two-laser measurement

The presence of void waves, alternative dense and sparse distribution of bubbles, can promote frictional drag reduction in horizontal turbulent boundary layers compared with the uniform passage of bubbles. This paper aims to determine how long a void pulse (i.e. simplest waveform in void waves) can persist downstream. First, we explored the internal structure of the void pulse and its spatial development by establishing a time-resolved two-laser measurement system. Then, advection and distortion of the pulse were analyzed and modeled by a one-dimensional Korteweg de Vries–Burgers (KdV–B) equation for water including and excluding surfactant, leading to the following conclusions; (i) the KdV–B equation well approximates the measured void pulse behavior and can be used as a mathematical predictor for the downstream propagation, (ii) advection velocity and diffusion of the pulses are explained by the velocity variation of bubbles and the depth of the bubbly layer, (iii) the pulse contains significant nonlinear advection velocity associated to local void fraction, and it causes the pulse to lean backward to retain a sharp streamwise gradient in each rear part of the pulse, and (iv) the pulse finally disappears in the channel flow because it does not include the solitary wave appearing in the KdV equation, judged by a combination of the nonlinear advection velocity and the dispersion coefficient.