Theoretical Elucidation on an Effect of Thermal Conduction on High-Speed and High-Frequency Nonlinear Pressure Waves in Bubbly Liquids

Abstract

High-speed and small-amplitude pressure wave propagating with almost sound speed in a pure water was observed by a shock tube experiment (Ohtani & Sugiyama, Shock Waves, 2005). The present study derives a nonlinear effective equation for weakly nonlinear propagation of such a pressure wave in bubbly liquids with a special attention to a thermal effect (i.e., thermal conduction, liquid viscosity, and so on). As a result, the nonlinear Schrödinger type equation with some correction terms was derived. The thermal effect contributed not only the dissipation effect but also the nonlinear effect. The thermal conduction strongly increased the wave dissipation. On the other hand, the dissipation due to liquid viscosity was considerably small.