2020 年 34 巻 1 号 p. 140-147
Weakly nonlinear propagation of plane pressure waves in a flowing water uniformlycontaining many spherical microbubbles is theoretically investigated. At the initial state, the gas and liquid phases have different flow velocity distributions as a small nonuniform effect in bubbly flows. The basic equations based on a two-fluid model are utilized to describe velocity distributions of gas and liquid phases. By using the method of multiple scales and the determination of size of three nondimensional ratios, we can systematically derive two types of nonlinear wave equations describing long-range propagation of waves. i.e., the Korteweg-de Vries-Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation with variable coefficients. As a result, initial velocity distributions affect an advection effect of waves induced by a relative velocity between gas and liquid phases and a moving bubble.
