Equidistribution of energy and other quantities in oscillating systems

Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve secon...

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Bibliographic Details
Published inThe Astrophysical journal Vol. 414; no. 2; pp. 892 - 897
Main Author Wolff, Charles L.
Format Journal Article
LanguageEnglish
Published Legacy CDMS University of Chicago Press 10.09.1993
Subjects
Astronomy
Earth, ocean, space
Exact sciences and technology
Fluid Mechanics And Heat Transfer
Oscillations and waves. Helioseismology
Pulsations, oscillations, and stellar seismology
Solar physics
Solar system
Stars
Stellar characteristics and properties
Solar granulation
Stars
Sturm-Liouville equation
Oscillations
Hydrodynamics
Stellar granulation
Sun
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Summary:Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation.
Bibliography:CDMS
Legacy CDMS
ISSN:0004-637X
1538-4357
DOI:10.1086/173132