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Encyclopedia of Physical Science and Technology EN001-05 May 25, 2001 16:7
Acoustic Chaos
Werner Lauterborn
Universitat¨ Gottingen¨
I. The Problem of Acoustic Cavitation Noise
II. The Period-Doubling Noise Sequence
III. A Fractal Noise Attractor
IV. Lyapunov Analysis
V. Period-Doubling Bubble Oscillations
VI. Theory of Driven Bubbles
VII. Other Systems
VIII. Philosophical Implications
GLOSSARY a dynamic system. A point in phase space characterizes
a specific state of the system.
Bifurcation Qualitative change in the behavior of a sys- Strange attractor In dissipative systems, the motion
tem, when a parameter (temperature, pressure, etc.) is tends to certain limits forms (attractors). When the mo-
altered (., period-doubling bifurcation); related to es to rest, this attractor is called a fixed point.
phase change in thermodynamics. Chaotic motions run on a strange attractor, which has
Cavitation Rupture of liquids when subject to tension ei- involved properties (., a fractal dimension).
ther in flow fields (hydraulic cavitation) or by an acous-
tic wave (acoustic cavitation).
Chaos Behavior (motion) with all signs of statistics de- THE PAST FEW years have seen a remarkable develop-
spite an underlying deterministic law (often, determin- ment in physics, which may be described as the upsurge
istic chaos). of “chaos.” Chaos is a term scientists have adapted from
Fractal Object (set of points) that does not have a mon language to describe the motion or behavior of
structure with an integer dimension (., three dimen- a system (physical or biological) that, although governed
sional). Instead, a fractal (noninteger) dimension must by an underlying deterministic law, is irregular and, in the
be ascribed to them. long term, unpredictable.
Period doubling Special way of obtaining chaotic (irreg- Chaotic motion seems to appear in any sufficiently
ular) motion; the period of