Internal waves in a three-layer bubbly waveguide

In many oceanic situations, clouds, or layers of bubbles are present which may influence the larger-scale dynamics. A two-dimensional model of a diluted locally monodisperse mixture of an incompressible fluid with gas bubbles is used to model and study such situations. The problem is simplified by ignoring the horizontal variability in the structure of the bubble layer and by focusing instead on the vertical variability. We consider waves propagating horizontally in the oceanic waveguide, assuming that bubbles are confined to a thin upper layer of the otherwise homogeneous upper ocean, and using a three layer model to represent this situation. The presence of the depth-dependent distribution of bubbles introduces an effective stratification and considerably changes the value of the buoyancy frequency Nl in the absence of bubbles, replacing it with an effective value N, where N2 = N2 l +g g0 [(ln n0)z + 3 g0(lnR0)z] /(1− g0) (here g0 is the void fraction, n0 is the number density, and R0 is the radius of bubbles in the basic state). This leads to the possibility of existence of the internal waves in the otherwise homogeneous upper mixed layer. Also the presence of the bubbly layer causes significant changes to the dispersion relation for the usual internal waves.