The Effect of Bubbles on Internal Waves

The influence of gas bubbles on the properties of internal waves in a continuously stratified fluid is studied in the framework of a two-dimensional model of a diluted monodisperse mixture of an incompressible fluid with gas bubbles. The model takes into account surface tension on the walls of the bubbles and an effective viscosity. The dispersion relation is obtained for linear waves in the Boussinesq approximation for a uniformly stratified fluid, and it is shown that in the presence of a uniform distribution of bubbles, there are two classes of plane waves. One class, the “bubble” wave may propagate with frequencies higher than the buoyancy frequency, while the other class is a modified internal wave, whose frequency is less than the buoyancy frequency, with a finite gap existing at all wavenumbers. The effective viscosity introduces a damping of both modes, and has a greater effect on the “bubble” mode. The dispersion relation is also obtained for waves propagating horizontally in the oceanic waveguide, both for the case when the fluid is uniformly stratified and contains bubbles, and when the bubbles are in a thin nearly homogeneous upper layer. PACS numbers: 47.55.Hd, 47.55.Kf