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# The effect of a depth-dependent bubble distribution on normal modes in the oceanic waveguide: quasistatic approximation.

preprint

posted on 2005-11-10, 11:13 authored by Roger Grimshaw, Karima KhusnutdinovaKarima KhusnutdinovaWe consider the effect of a depth-dependent distribution of bubbles on internal and
surface waves propagating horizontally in the oceanic waveguide. While our previous work
was restricted to the case of a locally monodisperse mixture, in this paper we show that
by using a quasistatic approximation (where attention is confined to those modes whose
typical frequencies are much less than the natural frequency for bubble oscillations), we
can extend that work to the case of more general discrete and continuous bubble distributions.
The equations of motion are formulated in terms of the usual fluid variables and
the void fraction of bubbles. Then, to leading order in the Boussinesq approximation,
we obtain the usual equation for internal wave modes, but the value of the buoyancy frequency
in the fluid is replaced by an effective buoyancy frequency which takes account of
the bubble distribution. Two physical factors are shown to affect the buoyancy frequency
in the mixture: the effective stratification due to the bubbles adds to the effect of stratification
in the liquid, while the compressibility of the mixture due to the bubbles reduces
the buoyancy frequency. Then, for a typical oceanic situation, the correction due to the
first effect is shown to be more significant than the second correction. In accordance with
existing observational evidence that the void fraction profile in the ocean decays exponentially
with depth, we obtain an explicit description of the normal modes, and show
that bubble distributions, when present, may considerably change the properties of the
oceanic waveguide.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

805950 bytes## Publication date

2005## Notes

This is a pre-print.## Language

- en