The Effect of Bubbles on Internal Waves

Abstract

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 locally monodisperse mixture of an incompressible fluid with gas bubbles. The model takes into account the depth dependence of the void fraction of the bubbles, surface tension on the walls of the bubbles, and an effective viscosity, which accounts for the fluid viscosity, thermal damping, and other dissipative mechanisms. It is shown that bubbles, when present in the upper part of the ocean, change the value of the buoyancy frequency Nl in the absence of bubbles, replacing it with an effective value N, where N2 ≈ N2l + gαg0(lnn0)z (αg0 is the void fraction and n0 is the number density of the bubbles). First, plane linear waves in a uniformly stratified Boussinesq fluid are considered, and it is shown that there are two classes of plane waves. One class, the ?bubble? wave, may propagate with frequencies higher than the effective buoyancy frequency N, and the other class is a modified internal wave, whose frequency is less than the effective buoyancy frequency, with a finite gap in the spectrum existing for all wavenumbers. The effective viscosity introduces a damping of both modes and has a greater effect on the bubble mode. Then the dispersion relation for waves propagating horizontally in the oceanic waveguide is obtained, for both the case in which the fluid is uniformly stratified and contains bubbles and the case in which the bubbles are confined to a thin nearly homogeneous upper layer.