Physics
Scientific paper
Nov 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979rspsa.368..389d&link_type=abstract
Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences, vol. 368, no. 1734, Nov. 13, 1979, p. 389-41
Physics
39
Axisymmetric Bodies, Dynamic Stability, Perturbation Theory, Rotating Fluids, Stellar Models, Stellar Rotation, Adiabatic Conditions, Angular Momentum, Angular Velocity, Eigenvalues, Eigenvectors, Euler Equations Of Motion, Hilbert Space, Modes, Time Dependence
Scientific paper
It is noted that linear adiabatic perturbations of a differentially rotating, axisymmetric, perfect fluid stellar model have normal modes described by a quadratic problem. The paper studies the problem and the associated time evolution equation. It is shown that in the Hilbert space H-prime, whose norm is square-integration weighted by A, the operators (A to the -1st power)(B) and (A to the -1st power)(C) are anti-selfadjoint and selfadjoint, respectively, when restricted to vectors belonging to a particular but arbitrary axial harmonic. Bounds are found on the spectrum of normal modes and it is shown that any initial data in the domain of C leads to a solution whose growth rate is limited by the spectrum and which can be expressed in a certain weak sense as a linear superposition of the normal modes.
Dyson John
Schutz Bernard F.
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