Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976mnras.177..265n&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 177, Nov. 1976, p. 265-274.
Astronomy and Astrophysics
Astronomy
19
Astronomical Models, Interstellar Gas, Perturbation Theory, Velocity Distribution, Asymptotic Methods, Corrugating, Hermitian Polynomial, Hydrodynamic Equations, Linear Equations, Supernovae, Wave Interaction
Scientific paper
Linear perturbations of a differentially rotating gas layer that is uniform parallel to its own plane are analyzed. The linearized hydrodynamic equations governing perturbations of such a gas layer in equilibrium in the stellar potential are reduced to a pair of ordinary differential equations which determine the vertical and radial variations of the density perturbation, using a local approximation in which the waves are assumed to be confined to a small region of the layer. The vertical equation is solved under the boundary condition that the wave energy density approaches zero as vertical distance approaches infinity, and the radial equation is solved asymptotically in a weak-shear approximation to yield a dispersion relation for the wave frequency. The solutions of the dispersion relation are then classified by frequency into fast waves (corresponding to true vertical gravity waves) with a frequency related to the particle oscillation frequency in the vertical direction and into slow waves with a frequency related to the frequency of epicyclic-type oscillations in the radial gravitational field. It is shown that both the fast waves and the slow epicyclic waves exhibit corrugation structure because both types involve vertical motion and have the same vertical density structure.
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