The Effect of Bubbles on Internal Waves
Journal of Physical Oceanography
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 depthdependence 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
... mechanisms. It is shown that bubbles, when present in the upper part of the ocean, change the value of the buoyancy frequency N l in the absence of bubbles, replacing it with an effective value N , where N 2 ≈ N 2 l + gα g0 (ln n 0 ) z (α g0 is the void fraction and n 0 is the number density of the bubbles). First we consider plane linear waves in a uniformly stratified Boussinesq fluid, 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 , while 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 we obtain the dispersion relation 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 confined to a thin nearly homogeneous upper layer.