Application of the phase-integral method to the trapping of acoustic waves in a gravitating fluid. I - Planar polytrope and turning-point behavior

Details Application of the phase-integral method to the trapping of acoustic waves in a gravitating fluid. I - Planar polytrope and turning-point behavior Application of the phase-integral method to the trapping of acoustic waves in a gravitating fluid. I - Planar polytrope and turning-point behavior

Jun 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...391..845p&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 391, no. 2, June 1, 1992, p. 845-853.

Computer Science

Sound

3

Hydrodynamics, Polytropic Processes, Solar Oscillations, Sound Waves, Surface Waves, Approximation, Phase Shift, Wentzel-Kramer-Brillouin Method

Scientific paper

Attention is given to the use of asymptotically based phase-integral methods to describe the behavior at short surface wavelengths of acoustic (i.e., pressure-dominated) oscillations trapped within stratified gravitating fluids. The method is applied to a planar polytrope, for which exact results are well known, both to assess the overall picture of oscillation behavior that it provides and, more specifically, to determine the reflection phase shifts that occur at the trapping boundaries. The analysis yields significantly differing descriptions of the field behavior near the surface, depending on the level of approximation used. A local analysis, although usefully delineating the trapping region, recovers the exact modal dispersion relation without overly elaborate reflection coefficients (phase corrections) at the trapping limits only in the asymptotic limit. Refinement of the analysis to include gradient terms in the determination of the vertical wavenumber component recovers the exact dispersion relation without such restriction.

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