2006 73rd Annual Meeting of the Southeastern Section of the APS
Thursday–Saturday, November 9–11, 2006;
Williamsburg, Virginia
Session CC: Theory, General
10:45 AM–12:45 PM,
Thursday, November 9, 2006
Williamsburg Hospitality House
Room: Yorktown
Chair: Chris Carone, College of William & Mary
Abstract ID: BAPS.2006.SES.CC.4
Abstract: CC.00004 : Radial oscillation of a gas bubble in a fluid as a problem in canonical perturbation theory
11:21 AM–11:33 AM
Preview Abstract
Abstract
Author:
James Stephens
(University of Southern Mississippi)
The oscillation of a gas bubble is in a fluid is of interest in
many areas
of physics and technology. Lord Rayleigh treated the pressure
developed in
the collapse of cavitation bubbles and developed an expression
for the
collapse period. Minnaert developed a harmonic oscillator
approximation to
bubble oscillation in his study of the sound produced by running
water.
Besides recent interest in bubble oscillation in connection to
sonoluminescence, an understanding of oscillating bubbles is of
important to
oceanographers studying the sound spectrum produced by water waves,
geophysicists employing air guns as acoustic probes, mechanical
engineers
concerned with erosion of turbine blades, and military engineers
concerned
with the acoustic signatures developed by the propeller screws of
ships and
submarines. For the oceanographer, Minnaert's approximation is
useful, for
the latter two examples, Lord Rayleigh's analysis is appropriate.
For the
case of the airgun, a period of twice Rayleigh's period for the
``total
collapse'' of the cavitation bubble is often cited as a good
approximation
for the period of an air bubble ejected from an air gun port,
typically at
$\sim $2000 psi), however for the geophysical example, numerical
integration
is employed from the outset to determine the dynamics of the
bubble and the
emitted acoustic energy. On the one hand, a bubble can be treated
as a
harmonic oscillator in the small amplitude regime, whereas even
in the
relatively moderate pressure regime characteristic of air guns the
oscillation is strongly nonlinear and amplitude dependent. Is it
possible to
develop an analytic approximation that affords insight into the
behavior of
a bubble beyond the harmonic approximation of Minnaert? In this
spirit, the
free radial oscillation of a gas bubble in a fluid is treated as
a problem
in canonical perturbation theory. Several orders of the expansion
are
determined in order to explore the dependence of the oscillation
frequency
with bubble amplitude. The expansion to second order is inverted
to express
the time dependence of the oscillation.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2006.SES.CC.4